From b3f3a8ecd454359a2e992161844f2fb599f8238a Mon Sep 17 00:00:00 2001 From: prashantsinalkar Date: Fri, 4 Oct 2019 12:24:07 +0530 Subject: Initial commit/added all books --- .../CH11/EX11.18/Ex11_18.R | 18 +++++++++ .../CH11/EX11.19/Ex11_19.R | 18 +++++++++ .../CH11/EX11.22/Ex11_22.R | 11 ++++++ .../CH11/EX11.24/Ex11_24.R | 11 ++++++ .../CH11/EX11.28/Ex11_28.R | 10 +++++ .../CH13/EX13.17/Ex13_17.R | 22 +++++++++++ .../CH13/EX13.18/Ex13_18.R | 18 +++++++++ .../CH13/EX13.4/Ex13_4.R | 9 +++++ .../CH14/EX14.18/Ex14_18.R | 31 +++++++++++++++ .../CH14/EX14.19/Ex14_19.R | 31 +++++++++++++++ .../CH14/EX14.22/Ex14_22.R | 34 ++++++++++++++++ .../CH14/EX14.26/Ex14_26.R | 27 +++++++++++++ .../CH14/EX14.5/Ex14_5.R | 31 +++++++++++++++ .../CH14/EX14.7/Ex14_7.R | 31 +++++++++++++++ .../CH15/EX15.1/Ex15_1.R | 6 +++ .../CH15/EX15.2/Ex15_2.R | 7 ++++ .../CH15/EX15.3/Ex15_3.R | 6 +++ .../CH15/EX15.4/Ex15_4.R | 6 +++ .../CH15/EX15.6/Ex15_6.R | 6 +++ .../CH16/EX16.1/Ex16_1.R | 6 +++ .../CH16/EX16.15/Ex16_15.R | 19 +++++++++ .../CH16/EX16.18/Ex16_18.R | 34 ++++++++++++++++ .../CH16/EX16.19/Ex16_19.R | 25 ++++++++++++ .../CH16/EX16.2/Ex16_2.R | 20 ++++++++++ .../CH16/EX16.3/Ex16_3.R | 18 +++++++++ .../CH16/EX16.4/Ex16_4.R | 12 ++++++ .../CH16/EX16.5/Ex16_5.R | 12 ++++++ .../CH22/EX22.1/Ex22_1.R | 14 +++++++ .../CH22/EX22.10/Ex22_10.R | 5 +++ .../CH22/EX22.11/Ex22_11.R | 7 ++++ .../CH22/EX22.2/Ex22_2.R | 16 ++++++++ .../CH22/EX22.3/Ex22_3.R | 25 ++++++++++++ .../CH22/EX22.4/Ex22_4.R | 22 +++++++++++ .../CH22/EX22.5/Ex22_5.R | 39 ++++++++++++++++++ .../CH22/EX22.6/Ex22_6.R | 45 +++++++++++++++++++++ .../CH22/EX22.8/Ex22_8.R | 11 ++++++ .../CH22/EX22.9/Ex22_9.R | 15 +++++++ .../CH26/EX26.10/Ex26_10.R | 27 +++++++++++++ .../CH26/EX26.11/Ex26_11.R | 12 ++++++ .../CH26/EX26.12/Ex26_12.R | 13 ++++++ .../CH26/EX26.13/Ex26_13.R | 18 +++++++++ .../CH26/EX26.14/Ex26_14.R | 18 +++++++++ .../CH26/EX26.15/Ex26_15.R | 19 +++++++++ .../CH26/EX26.16/Ex26_16.R | 16 ++++++++ .../CH26/EX26.17/Ex26_17.R | 15 +++++++ .../CH26/EX26.18/Ex26_18.R | 17 ++++++++ .../CH26/EX26.2/Ex26_2.R | 17 ++++++++ .../CH26/EX26.3/Ex26_3.R | 23 +++++++++++ .../CH26/EX26.4/Ex26_4.R | 21 ++++++++++ .../CH26/EX26.5/Ex26_5.R | 17 ++++++++ .../CH26/EX26.6/Ex26_6.R | 15 +++++++ .../CH26/EX26.7/Ex26_7.R | 22 +++++++++++ .../CH26/EX26.8/Ex26_8.R | 16 ++++++++ .../CH27/EX27.1/Ex27_1.R | 12 ++++++ .../CH27/EX27.10/Ex27_10.R | 22 +++++++++++ .../CH27/EX27.11/Ex27_11.R | 10 +++++ .../CH27/EX27.12/Ex27_12.R | 21 ++++++++++ .../CH27/EX27.13/Ex27_13.R | 27 +++++++++++++ .../CH27/EX27.15/Ex27_15.R | 20 ++++++++++ .../CH27/EX27.16/Ex27_16.R | 13 ++++++ .../CH27/EX27.2/Ex27_2.R | 13 ++++++ .../CH27/EX27.3/Ex27_3.R | 14 +++++++ .../CH27/EX27.4/Ex27_4.R | 17 ++++++++ .../CH27/EX27.5/Ex27_5.R | 22 +++++++++++ .../CH27/EX27.6/Ex27_6.R | 15 +++++++ .../CH27/EX27.8/Ex27_8.R | 13 ++++++ .../CH27/EX27.9/Ex27_9.R | 14 +++++++ .../CH28/EX28.1/Ex28_1.R | 14 +++++++ .../CH28/EX28.11/Ex28_11.R | 15 +++++++ .../CH28/EX28.12/Ex28_12.R | 8 ++++ .../CH28/EX28.13/Ex28_13.R | 20 ++++++++++ .../CH28/EX28.15/Ex28_15.R | 12 ++++++ .../CH28/EX28.18/Ex28_18.R | 11 ++++++ .../CH28/EX28.23/Ex28_23.R | 42 ++++++++++++++++++++ .../CH28/EX28.24/Ex28_24.R | 10 +++++ .../CH28/EX28.29/Ex28_29.R | 21 ++++++++++ .../CH28/EX28.4/Ex28_4.R | 11 ++++++ .../CH28/EX28.5/Ex28_5.R | 10 +++++ .../CH28/EX28.9/Ex28_9.R | 7 ++++ .../CH33/EX33.1/Ex33_1.R | 11 ++++++ .../CH33/EX33.2/Ex33_2.R | 11 ++++++ .../CH33/EX33.3/Ex33_3.R | 18 +++++++++ .../CH33/EX33.4/Ex33_4.R | 38 ++++++++++++++++++ .../CH33/EX33.5/Ex33_5.R | 6 +++ .../CH33/EX33.6/Ex33_6.R | 18 +++++++++ .../CH34/EX34.1/Ex34_1.R | 16 ++++++++ .../CH34/EX34.2/Ex34_2.R | 15 +++++++ .../CH34/EX34.3/Ex34_3.R | 17 ++++++++ .../CH34/EX34.4/Ex34_4.R | 18 +++++++++ .../CH34/EX34.5/Ex34_5.R | 22 +++++++++++ .../CH34/EX34.6/Ex34_6.R | 22 +++++++++++ .../CH34/EX34.7/Ex34_7.R | 26 ++++++++++++ .../CH34/EX34.8/Ex34_8.R | 9 +++++ .../CH34/EX34.9/Ex34_9.R | 18 +++++++++ .../CH35/EX35.11/Ex35_11.R | 12 ++++++ .../CH35/EX35.12/Ex35_12.R | 9 +++++ .../CH35/EX35.16/Ex35_16.R | 9 +++++ .../CH35/EX35.25/Ex35_25.R | 11 ++++++ .../CH35/EX35.6/Ex35_6.R | 9 +++++ .../CH35/EX35.9/Ex35_9.R | 9 +++++ .../CH36/EX36.18/Ex36_18.R | 8 ++++ .../CH36/EX36.20/Ex36_20.R | 8 ++++ .../CH36/EX36.22/Ex36_22.R | 8 ++++ .../CH36/EX36.24/Ex36_24.R | 8 ++++ .../CH37/EX37.10/Ex37_10.R | 21 ++++++++++ .../CH37/EX37.12/Ex37_12.R | 15 +++++++ .../CH37/EX37.14/Ex37_14.R | 15 +++++++ .../CH37/EX37.16/Ex37_16.R | 46 ++++++++++++++++++++++ .../CH37/EX37.20/Ex37_20.R | 18 +++++++++ .../CH37/EX37.22/Ex37_22.R | 15 +++++++ .../CH37/EX37.23/Ex37_23.R | 14 +++++++ .../CH37/EX37.4/Ex37_4.R | 19 +++++++++ .../CH5/EX5.1/Ex5_1.R | 7 ++++ .../CH5/EX5.10/Ex5_10.R | 19 +++++++++ .../CH5/EX5.12/Ex5_12.R | 20 ++++++++++ .../CH5/EX5.14/Ex5_14.R | 15 +++++++ .../CH5/EX5.15/Ex5_15.R | 12 ++++++ .../CH5/EX5.18/Ex5_18.R | 14 +++++++ .../CH5/EX5.21/Ex5_21.R | 15 +++++++ .../CH5/EX5.23/Ex5_23.R | 8 ++++ .../CH5/EX5.4/Ex5_4.R | 10 +++++ .../CH5/EX5.7/Ex5_7.R | 10 +++++ 122 files changed, 2027 insertions(+) create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.18/Ex11_18.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.19/Ex11_19.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.22/Ex11_22.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.24/Ex11_24.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.28/Ex11_28.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.17/Ex13_17.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.18/Ex13_18.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.4/Ex13_4.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.18/Ex14_18.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.19/Ex14_19.R create mode 100644 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create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.15/Ex5_15.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.18/Ex5_18.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.21/Ex5_21.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.23/Ex5_23.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.4/Ex5_4.R create mode 100644 Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.7/Ex5_7.R (limited to 'Basic_Engineering_Mathematics_by_John_Bird') diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.18/Ex11_18.R b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.18/Ex11_18.R new file mode 100644 index 00000000..4e355398 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.18/Ex11_18.R @@ -0,0 +1,18 @@ +#page no .95 +#problem 17 +#load package ---->measurements +library(measurements) +#functions: +area_wire = function(p,l,r) +{ + return(p*l/r) +} +#formula used: R = p*l/a +#given: +r = 5 #resistance of wire +l = 1.5 #lenght in kilmeter +l1 = conv_unit(l,'km','m') +p = 17.2 * 10^-6 # resistivity of wire in mm +p1 = conv_unit(p,'mm','m') +a = area_wire(p1,l1,r) #area of cross-section of wire +print(a) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.19/Ex11_19.R b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.19/Ex11_19.R new file mode 100644 index 00000000..e5d76171 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.19/Ex11_19.R @@ -0,0 +1,18 @@ +#page no .95 +#problem 19 +#load package ---->measurements +library(measurements) +#functions: +R = function(p,v,n,t) +{ + return((p*v)/(n*t)) +} +#formula used: pv=nrt +# r = pv/nt +#given: +p = 3 * 10^6 #pressure of gas in pascal +v = 0.90 #volume of gas +m = 2.81 #mass of gas in kg +t = 231 # temperature in kelvin +r = R(p,v,m,t) #constant +print(r) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.22/Ex11_22.R b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.22/Ex11_22.R new file mode 100644 index 00000000..84a47792 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.22/Ex11_22.R @@ -0,0 +1,11 @@ +#page no. 96 +#problem 22 +#formula used : s=ut+(1/2)at^2 +# a = ((s-ut)*2)/t^2 + +#given: +s = 168 #distance travelled in meter +u = 10 #initial velocity in m/s +t = 6 #time in seconds +a = ((s-u*t)*2)/t^2 # acceleration in m/s^2 +print(a) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.24/Ex11_24.R b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.24/Ex11_24.R new file mode 100644 index 00000000..26ba2554 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.24/Ex11_24.R @@ -0,0 +1,11 @@ +#page no.97 +#problem 24 +#formula used: e=fl/ax +# x = fl/ae + +f = 20*10^6 #force when carrying load +e = 70 * 10^9 # modulus of elasticity +a = 0.1 #cross-sectional area +l = 1.4 # lenght of bar +x = (f*l)/(a*e) #extension of bar in m +print(x*1000) #extension in mm diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.28/Ex11_28.R b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.28/Ex11_28.R new file mode 100644 index 00000000..d230f6c1 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH11/EX11.28/Ex11_28.R @@ -0,0 +1,10 @@ +#page no. 97 +#problem 28 +#formula used: D/d = sqrt((f+p)/(f-p)) +# (D/d)^2= (f+p)/(f-p) +#given: +D= 21.5 +d = 10.75 +p = 1800 +f = (p*(1+(D/d)^2))/(((D/d)^2)-1) #stress of thick cylinder +print(f) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.17/Ex13_17.R b/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.17/Ex13_17.R new file mode 100644 index 00000000..0944c8a7 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.17/Ex13_17.R @@ -0,0 +1,22 @@ +#page no . 120 +#problem 17 +# formula used : matrix multiplication +# x = A(inverse) * B +#given: c = a+bt + + + #case 1 + c1 = 52 + t1 = 100 + #eq1 = (52 = a + 100b) + #case 2 + c2 = 172 + t2 = 400 + #eq2 = (172 = a+400b) + +# for solving a and b, form matrix + A = array(data = c(1,1,100,400),dim = c(2,2)) + B = c(52,172) + + solve(A,B) #value of a and b respectivily + \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.18/Ex13_18.R b/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.18/Ex13_18.R new file mode 100644 index 00000000..36e4ec23 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.18/Ex13_18.R @@ -0,0 +1,18 @@ +#page no. 121 +#problem 18 +#given: +# x+y+z = 4 +# 2x-2y+4z = 33 +#3x-2y-2z = 2 + +# formula used : matrix multiplication +# x = A(inverse) * B + +A = array(data=c(1,2,3,1,-2,-2,1,4,-2),dim =c(3,3)) +B = c(4,33,2) +X = solve(A,B) +cat("x=",X[1]) #value of x + +cat("y=",X[2]) #value of y + +cat("z=",X[3]) #value of z \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.4/Ex13_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.4/Ex13_4.R new file mode 100644 index 00000000..bd393170 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH13/EX13.4/Ex13_4.R @@ -0,0 +1,9 @@ +#page no. 113 +#problem 4 +# formula used : matrix multiplication +# x = A(inverse) * B + +A = array(data = c(7,6,-2,5), dim = c(2,2)) +B = c(26,29) + +solve(A,B) #value of a and b respectivily \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.18/Ex14_18.R b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.18/Ex14_18.R new file mode 100644 index 00000000..cd8d6aed --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.18/Ex14_18.R @@ -0,0 +1,31 @@ +#page no. 129 +#problem 18 + +#function: + +# Constructing Quadratic Formula +roots <- function(a,b,c){ + if(delta(a,b,c) > 0){ # first case D>0 + x_1 = (-b+sqrt(delta(a,b,c)))/(2*a) + x_2 = (-b-sqrt(delta(a,b,c)))/(2*a) + result = c(x_1,x_2) + } + else if(delta(a,b,c) == 0){ # second case D=0 + x = -b/(2*a) + } + else {"There are no real roots."} # third case D<0 +} + +# Constructing delta +delta<-function(a,b,c){ + b^2-4*a*c +} + +#given: quadratic eq. +# x^2+2x-8 = 0 + +a = 1 +b = 2 +c = -8 +x12 = roots(a,b,c) #roots of quadratic equation +print(x12) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.19/Ex14_19.R b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.19/Ex14_19.R new file mode 100644 index 00000000..f67ccafc --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.19/Ex14_19.R @@ -0,0 +1,31 @@ +#page no. 129 +#problem 18 + +#function: + +# Constructing Quadratic Formula +roots <- function(a,b,c){ + if(delta(a,b,c) > 0){ # first case D>0 + x_1 = (-b+sqrt(delta(a,b,c)))/(2*a) + x_2 = (-b-sqrt(delta(a,b,c)))/(2*a) + result = c(x_1,x_2) + } + else if(delta(a,b,c) == 0){ # second case D=0 + x = -b/(2*a) + } + else {"There are no real roots."} # third case D<0 +} + +# Constructing delta +delta<-function(a,b,c){ + b^2-4*a*c +} + +#given: quadratic eq. +# 3x^2+-11x-4 = 0 + +a = 3 +b = -11 +c = -4 +x12 = roots(a,b,c) #roots of quadratic equation +print(x12) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.22/Ex14_22.R b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.22/Ex14_22.R new file mode 100644 index 00000000..cb5509bd --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.22/Ex14_22.R @@ -0,0 +1,34 @@ +#page no. 129 +#problem 18 + +#function: + + +roots <- function(a, b, c){ + + pos_root <- ((-b) + sqrt((b^2) - 4*a*c)) / (2*a) + + neg_root <- ((-b) - sqrt((b^2) - 4*a*c)) / (2*a) + + return(pos_root) #length can not be negative, so take +ve root + + print(neg_root) + +} + +#given: +area = 23.6 #area of rectangle +#l = x #let lenght of rectangle be x +#b = x -3.10 # breadth is 3.10 shorter than length +#eq. formed --->area = l*b +# 23.6 = x*(x-3.10) +# 23.6 = x^2-3.1x +# x^2-3.1x-23.6=0 +a = 1 +b = -3.1 +c = -23.6 +x12 = roots(a,b,c) #roots of quadratic equation +l = x12 +b = x12 - 3.10 +print(l) #length of rectangle +print(b) #breadth of rectangle diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.26/Ex14_26.R b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.26/Ex14_26.R new file mode 100644 index 00000000..98629397 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.26/Ex14_26.R @@ -0,0 +1,27 @@ +#page no. 131 +#problem 26 +# funtion: +roots <- function(a, b, c){ + + pos_root <- ((-b) + sqrt((b^2) - 4*a*c)) / (2*a) + + neg_root <- ((-b) - sqrt((b^2) - 4*a*c)) / (2*a) + + return(pos_root) #radius can not be negative, so take +ve root + + print(neg_root) + +} +# given: area of cone = (pi*r*l) + pi*r^2 + +area = 486.2 #area of cone +l = 15.3 # slant height of cone +# after placing values we get eq. +# r^2+15.3r-482.2/pi + +a = 1 +b = 15.3 +c = -482.2/pi +r = roots(a,b,c) +dia = 2*r #diameter of cone base +print(dia) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.5/Ex14_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.5/Ex14_5.R new file mode 100644 index 00000000..0ab10241 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.5/Ex14_5.R @@ -0,0 +1,31 @@ +#page no. 125 +#problem 5 + +#function: + +# Constructing Quadratic Formula +roots <- function(a,b,c){ + if(delta(a,b,c) > 0){ # first case D>0 + x_1 = (-b+sqrt(delta(a,b,c)))/(2*a) + x_2 = (-b-sqrt(delta(a,b,c)))/(2*a) + result = c(x_1,x_2) + } + else if(delta(a,b,c) == 0){ # second case D=0 + x = -b/(2*a) + } + else {"There are no real roots."} # third case D<0 +} + +# Constructing delta +delta<-function(a,b,c){ + b^2-4*a*c +} + +#given: quadratic eq. +# x^2+3x-4 = 0 + +a = 1 +b = 3 +c = -4 +x12 = roots(a,b,c) #roots of quadratic equation +print(x12) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.7/Ex14_7.R b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.7/Ex14_7.R new file mode 100644 index 00000000..bc58e795 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH14/EX14.7/Ex14_7.R @@ -0,0 +1,31 @@ +#page no. 126 +#problem 7 + +#function: + +# Constructing Quadratic Formula +roots <- function(a,b,c){ + if(delta(a,b,c) > 0){ # first case D>0 + x_1 = (-b+sqrt(delta(a,b,c)))/(2*a) + x_2 = (-b-sqrt(delta(a,b,c)))/(2*a) + result = c(x_1,x_2) + } + else if(delta(a,b,c) == 0){ # second case D=0 + x = -b/(2*a) + } + else {"There are no real roots."} # third case D<0 +} + +# Constructing delta +delta<-function(a,b,c){ + b^2-4*a*c +} + +#given: quadratic eq. +# x^2-5x+6 = 0 + +a = 1 +b = -5 +c = 6 +x12 = roots(a,b,c) #roots of quadratic equation + print(x12) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.1/Ex15_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.1/Ex15_1.R new file mode 100644 index 00000000..cdbe39bf --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.1/Ex15_1.R @@ -0,0 +1,6 @@ +#page no. 135 +#problem 1 +#function used: log(x,base) +n = 9 # number to evaluate +base = 3 #log base +print(log(n,base)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.2/Ex15_2.R b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.2/Ex15_2.R new file mode 100644 index 00000000..81fde93f --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.2/Ex15_2.R @@ -0,0 +1,7 @@ +#page no. 135 +#problem 2 +#function used: log10(x) +#given: +n = 10 # number to evaluate +val = log10(n) #log base 10 function +print(val) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.3/Ex15_3.R b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.3/Ex15_3.R new file mode 100644 index 00000000..3427a7e7 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.3/Ex15_3.R @@ -0,0 +1,6 @@ +#page no. 135 +#problem 3 +#function used: log(x,base) +n = 8 # number to evaluate +base = 16 #log base 16 +print(log(n,base)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.4/Ex15_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.4/Ex15_4.R new file mode 100644 index 00000000..39b1bc98 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.4/Ex15_4.R @@ -0,0 +1,6 @@ +#page no. 135 +#problem 4 +#function used: log10(x) +n = 0.001 # number to evaluate +val = log10(n) +print(val) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.6/Ex15_6.R b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.6/Ex15_6.R new file mode 100644 index 00000000..4e7dd937 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH15/EX15.6/Ex15_6.R @@ -0,0 +1,6 @@ +#page no. 136 +#problem 6 +#function used: log(x,base) +n = 1/81 # number to evaluate +base = 3 #log base +print(log(n,base)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.1/Ex16_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.1/Ex16_1.R new file mode 100644 index 00000000..f1d43b89 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.1/Ex16_1.R @@ -0,0 +1,6 @@ +#page no.141 +#problem 1 +#Function used: exp(x) +#given: +print(0.0256*(exp(5.21)-exp(2.49))) #evaluate the following + diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.15/Ex16_15.R b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.15/Ex16_15.R new file mode 100644 index 00000000..c81ff162 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.15/Ex16_15.R @@ -0,0 +1,19 @@ +#page no. 147 +#problem 15 +#function: +log(exp(1)) + +find_x = function(l,r) +{ + #apply log on both sides L.H.S and R.H.S + l = log(l) #r = log(exp(3*x)) + #r = 3*x*log(exp(1)) ------>log(exp(1))=1 + # to find x + return(x=l/r) +} + +#given: +l = 7/4 # values on L.H.S +r = 3 # exp power and multiple factor of x +result = find_x(l,r) +print(result) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.18/Ex16_18.R b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.18/Ex16_18.R new file mode 100644 index 00000000..0b76afb0 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.18/Ex16_18.R @@ -0,0 +1,34 @@ +#page no. 147 +#problem 18 +#load package --->measurements +library(measurements) +#formula used: alpha = (1/theta)log(R/R0) +# +#function: + +find_alpha = function(theta,R,R0) +{ + return((1/theta)*log(R/R0)) +} + + +find_theta = function(alpha,R,R0) +{ + return((1/alpha)*log(R/R0)) +} + +#given: +r0 = 5 #kilo_ohms +R0 = conv_unit(r0,'km','m') # resistance in ohms + +r = 6 #kilo_ohms +R = conv_unit(r,'km','m') # resistance in ohms + +theta = 1500 #temperature in C +alpha = find_alpha(theta,R,R0) + +r_new = 5.4 #kilo_ohm +R_new = conv_unit(r_new,'km','m') +theta_new = find_theta(alpha,R_new,R0) + +print(theta_new) # temperature to nearest degree diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.19/Ex16_19.R b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.19/Ex16_19.R new file mode 100644 index 00000000..4183ad95 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.19/Ex16_19.R @@ -0,0 +1,25 @@ +#page no. 147 +#problem 19 + +#load package --->measurements +library(measurements) +#formula used: Q = Q0*exp((-k*t) +# k = (1/t)log(Q0/Q)------> after applying log on both sides +#NEWTON's COOLING LAW +#function: + +find_k = function(t,Q0,Q) +{ + return((1/t)*log(Q0/Q)) +} + + +#given: +Q0 = 56.6 #tenperature in C + +Q = 16.5 #tenperature in C + +t = 76 #time in seconds +k_constant = find_k(t,Q0,Q) + +print(k_constant) # constant value diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.2/Ex16_2.R b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.2/Ex16_2.R new file mode 100644 index 00000000..84d58732 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.2/Ex16_2.R @@ -0,0 +1,20 @@ +#page no. 142 +#problem 2 +#function used: exp() + +exp_add = function(x,y) +{ + return(exp(x)+exp(y)) +} + + +exp_sub = function(x,y) +{ + return(exp(x)-exp(y)) +} + +#given: +a = 0.25 #powers of exp +b = -0.25 +cal = 5*(exp_sub(a,b)/exp_add(a,b)) # evaluate +print(cal) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.3/Ex16_3.R b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.3/Ex16_3.R new file mode 100644 index 00000000..f368a1dd --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.3/Ex16_3.R @@ -0,0 +1,18 @@ +#page no. 142 +#problem 3 +#function used: exp() +#formula used: v = V*exp(-t/CR) +#load package ------>measurements +library(measurements) +#given: + +V = 300 # volts +t = 50 # time in milliseconds +t1 = conv_unit(t,'msec','sec') #time in seconds +c = 10 #in microFarad +c1 = conv_unit(c,'um','m') +R = 47 # kilo_ohms +R1 = conv_unit(R,'km','m') + +v =V*exp(-t1/(c1*R1)) +print(v) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.4/Ex16_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.4/Ex16_4.R new file mode 100644 index 00000000..df12e931 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.4/Ex16_4.R @@ -0,0 +1,12 @@ +#page no. 143 +#problem 4 +#function used: factorial() +exp_expansion = function(x) +{ + return(1+(x/1)+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))) +} + +#given: +n = 0.5 #power of exp +val = 5*exp_expansion(n) +print(val) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.5/Ex16_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.5/Ex16_5.R new file mode 100644 index 00000000..2605421f --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH16/EX16.5/Ex16_5.R @@ -0,0 +1,12 @@ +#page no. 143 +#problem 5 +#function used: factorial() +exp_expansion = function(x) +{ + return(1+(x/1)+(x^2/factorial(2))+(x^3/factorial(3))+(x^4/factorial(4))) +} + +#given: +n = -1 #power of exp +val = 3*exp_expansion(n) +print(val) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.1/Ex22_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.1/Ex22_1.R new file mode 100644 index 00000000..dcb7c0df --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.1/Ex22_1.R @@ -0,0 +1,14 @@ +#page no. 221 +#problem 1 +#formula used: pythagoras theorem + +hypo = function(base,perp) +{ + return(sqrt(base^2+perp^2)) +} + +#given: +p = 4 #perpendicular height of triangle +b = 3 #base of triangle +h = hypo(b,p) #hypotenuse of triangle +print(h) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.10/Ex22_10.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.10/Ex22_10.R new file mode 100644 index 00000000..b7412ee9 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.10/Ex22_10.R @@ -0,0 +1,5 @@ +#page no .225 +#problem 10 +#given: +angle = 1.481 +sinQ = sin(angle) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.11/Ex22_11.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.11/Ex22_11.R new file mode 100644 index 00000000..9fb8db93 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.11/Ex22_11.R @@ -0,0 +1,7 @@ +#pageno.225 +#problem 11 +#function used: cos() +#given: + angle=3*pi/5 + cosQ = cos(angle) + print(cosQ) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.2/Ex22_2.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.2/Ex22_2.R new file mode 100644 index 00000000..09e6f62c --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.2/Ex22_2.R @@ -0,0 +1,16 @@ +#page no. 221 +#problem 2 +#formula used: pythagoras theorem + + +prep = function(hypo , base) +{ + return(sqrt(hypo^2 - base^2)) +} + + +#given: +b = 5 #perpendicular height of triangle +h = 13 #hypotenuse of triangle +p = prep(h,b) #base of triangle +print(p) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.3/Ex22_3.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.3/Ex22_3.R new file mode 100644 index 00000000..3040faa2 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.3/Ex22_3.R @@ -0,0 +1,25 @@ +#page no. 221 +#problem 3 +#formula used: pythagoras theorem + + +hypotenuse = function(base,perp) +{ + return(sqrt(base^2+perp^2)) +} + +distance = function(speed,time) +{return(speed*time)} + +#given: +s1 = 300 #speed of one air craft in km/hr +s2 = 220 #speed of second air craft in km/hr +time = 4 #In hr +d1=distance(s1,time) #travels in north +d2=distance(s2,time) #travels in west + +# both airplane make right angle triangle +d3 = hypotenuse(d1,d2) #distance b/w two airplanes +print(d3) + + diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.4/Ex22_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.4/Ex22_4.R new file mode 100644 index 00000000..f0823af9 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.4/Ex22_4.R @@ -0,0 +1,22 @@ +#page no. 223 +#problem 4 +#formula used: sin=p/h cos=b/h tan=p/b + +sinQ = function(x,y) +{return(x/y)} + +cosQ = function(x,y) +{return(x/y)} + +tanQ = function(x,y) +{return(x/y)} + +#given: right angle triangle +b = 12 +p =5 +h = 13 +cat("sinQ=",sinQ(p,h)) + +cat("cosQ=",cosQ(b,h)) + +cat("tanQ=",tanQ(p,b)) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.5/Ex22_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.5/Ex22_5.R new file mode 100644 index 00000000..03909554 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.5/Ex22_5.R @@ -0,0 +1,39 @@ +#page no. 223 +#problem 5 +#formula used: sin=p/h cos=b/h tan=p/b + + +hypotenuse = function(base,perp) +{ + return(sqrt(base^2+perp^2)) +} + +sinQ = function(x,y) +{return(x/y)} + +cosQ = function(x,y) +{return(x/y)} + +tanQ = function(x,y) +{return(x/y)} + +#given: right angle triangle +base = 4.62 +perp = 3.47 +height = hypotenuse(base,perp) +print(height) +cat("sinC=",sinQ(perp,height)) + +cat("cosC=",cosQ(base,height)) + +cat("tanC=",tanQ(perp,base)) + +# rotate the sides +b = perp +p = base +h = height +cat("sinA=",sinQ(p,h)) + +cat("cosA=",cosQ(b,h)) + +cat("tanA=",tanQ(p,b)) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.6/Ex22_6.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.6/Ex22_6.R new file mode 100644 index 00000000..108ddeeb --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.6/Ex22_6.R @@ -0,0 +1,45 @@ +#page no. 223 +#problem 6 +#formula used: sin=p/h cos=b/h tan=p/b + + +hypotenuse = function(base,perp) +{ + return(sqrt(base^2+perp^2)) +} + +sinQ = function(x,y) +{return(x/y)} + +cosQ = function(x,y) +{return(x/y)} + +tanQ = function(x,y) +{return(x/y)} + + + +#given: right angle triangle + tanB = 8/15 #tan = p/b + #according to angle B + p = 8 #perpendicular lenght opposite angle B + b = 15 #base lenght opposite angle B + h = hypotenuse(b,p) + + cat("sinB=",sinQ(p,h)) + + cat("cosB=",cosQ(b,h)) + + #cat("tanB=",tanQ(p,b)) + + #according to angle A + base = p#base lenght opposite angle A + perp = b#perpendicular lenght opposite angle A + height = h + + cat("sinA=",sinQ(perp,height)) + + #cat("cosA=",cosQ(base,height)) + + cat("tanA=",tanQ(perp,base)) + \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.8/Ex22_8.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.8/Ex22_8.R new file mode 100644 index 00000000..62276316 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.8/Ex22_8.R @@ -0,0 +1,11 @@ +#page no. 225 +#problem 8 +#formula used: sin=p/h cos=b/h tan=p/b + +#given: +angle_degree = 43 # angle in degree +angle_min = 39 # angle in min + +#angel is 43 degree 39 min +angle = ((angle_degree*60)+angle_min)/60 #conversion of angle into degree +sinQ = sin(angle) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.9/Ex22_9.R b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.9/Ex22_9.R new file mode 100644 index 00000000..e1a1ca02 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH22/EX22.9/Ex22_9.R @@ -0,0 +1,15 @@ +#page no .225 +#problem 9 +# conversion minutes to degree +angle = function(x,y) +{ + return(((x*60)+y)/60) +} +#given: +angle_degree = 62 # angle in degree +angle_min = 12 # angle in min + +deg = angle(angle_degree,angle_min) + +cosQ = cos(deg) +cat("6cosQ:",6*cosQ) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.10/Ex26_10.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.10/Ex26_10.R new file mode 100644 index 00000000..5971b266 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.10/Ex26_10.R @@ -0,0 +1,27 @@ +#page no. 272 +#problem 10 +# formula used : #formula used : area of rectangle = l*b +#given: +l = 6 # length of building +b = 8#breadth of building + +###triangle on top +base = 8 +base_right = base/2 #base of right angle triangle +hypo = 5 +height = sqrt(hypo^2 - (base_right^2)) + +area_rect <- function(x,y) #area of rectangle +{ + a = x*y + return(a) +} + +area_triangle <- function(x,y) #area of right angle triangle +{ + a = (x*y)/2 + return(a) +} + +area_building = area_rect(l,b) + area_triangle(base,height) +print(area_building) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.11/Ex26_11.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.11/Ex26_11.R new file mode 100644 index 00000000..e943322e --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.11/Ex26_11.R @@ -0,0 +1,12 @@ +#page no.273 +#problem 11 +#formula used: area of circle = pi*r^2 + +area_circle = function(r) +{ + return(pi*r^2) +} + +#given: +r = 5 #radius of circle +print(area_circle(r)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.12/Ex26_12.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.12/Ex26_12.R new file mode 100644 index 00000000..454812b2 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.12/Ex26_12.R @@ -0,0 +1,13 @@ +#page no.273 +#problem 12 +#formula used: area of circle = pi*r^2 + +area_circle = function(r) +{ + return(pi*r^2) +} + +#given: +dia = 15 #diameter of circle +r = dia/2 #radius of circle +print(area_circle(r)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.13/Ex26_13.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.13/Ex26_13.R new file mode 100644 index 00000000..76480b64 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.13/Ex26_13.R @@ -0,0 +1,18 @@ +#page no.273 +#problem 13 +#formula used: area of circle = pi*r^2 + +area_circle = function(r) +{ + return(pi*r^2) +} + +radius_cir <- function(cir) +{ + r = cir/(2*pi) + return(r) +} +#given: +circ = 70 #circumference of circle +r = radius_cir(circ) #radius of circle +print(area_circle(r)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.14/Ex26_14.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.14/Ex26_14.R new file mode 100644 index 00000000..2412e61b --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.14/Ex26_14.R @@ -0,0 +1,18 @@ +#page no. 274 +#problem 14 +# formula used : area of sector=(theta/360)*area of circle + +area_circle = function(r) +{ + return(pi*r^2) +} + +area_sector<- function(theta,r) +{ + a = (theta/360)*area_circle(r) +} + +#given: +r = 6 #radius of circle +theta = 50 # angle subtended at center +print(area_sector(theta,r)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.15/Ex26_15.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.15/Ex26_15.R new file mode 100644 index 00000000..47924d96 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.15/Ex26_15.R @@ -0,0 +1,19 @@ +#page no. 274 +#problem 15 +# formula used : area of sector=(theta/360)*area of circle + +area_circle = function(r) +{ + return(pi*r^2) +} + +area_sector<- function(theta,r) +{ + a = (theta/360)*area_circle(r) +} + +#given: +dia = 80 #diameter of circle +r = dia/2 #radius of circle +theta = 107 # angle subtended at center(107 degree 42 minutes) +print(area_sector(theta,r)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.16/Ex26_16.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.16/Ex26_16.R new file mode 100644 index 00000000..dac38a76 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.16/Ex26_16.R @@ -0,0 +1,16 @@ +#page no. 274 +#problem 16 +#formula used: area of circle = pi*r^2 + +area_circle = function(r) +{ + return(pi*r^2) +} + +#give: +D = 5.45 #diameter of outer circle +d = 2.25 #diameter of inner circle +R = D/2 #radius of outer circle +r = d/2 #radius of inner circle +area_shaft = area_circle(R) - area_circle(r) +print(area_shaft) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.17/Ex26_17.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.17/Ex26_17.R new file mode 100644 index 00000000..abaab8fc --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.17/Ex26_17.R @@ -0,0 +1,15 @@ +#page no. 275 +#problem 17 +# formula used : area of regular octagon =8*((1/2)*base*height) +# 8 times area of triangle + +area_triangle = function(b,h) +{ + return((b*h)/2) +} +#given: +base = 5 +H = 12 # total height across the flat +h = H/2 +area_octagon=8*area_triangle(base,h) +print(area_octagon) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.18/Ex26_18.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.18/Ex26_18.R new file mode 100644 index 00000000..475b65a1 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.18/Ex26_18.R @@ -0,0 +1,17 @@ +#page no. 275 +#problem 18 +# formula used : area of regular hexagon =6*((1/2)*base*height) +# 6 times area of triangle + +area_triangle = function(b,h) +{ + return((b*h)/2) +} +#given: +base = 8 +b = base/2 #base of right angle triangle +hypo = base #hypotenuse of right angle triangle +h = sqrt(hypo^2 - b^2) + +area_hexagon=6*area_triangle(base,h) +print(area_hexagon) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.2/Ex26_2.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.2/Ex26_2.R new file mode 100644 index 00000000..a70d8925 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.2/Ex26_2.R @@ -0,0 +1,17 @@ +#page n0.269 +#problem 2 +area_square <- function(x) +{ + a = x^2 + return(a) +} + +peri_square <- function(x) +{ + return(p = 4*x) + +} + +n = 4#side of square +print(area_square(n)) +print(peri_square(n)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.3/Ex26_3.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.3/Ex26_3.R new file mode 100644 index 00000000..38ed9024 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.3/Ex26_3.R @@ -0,0 +1,23 @@ +#page no.269 +#problem 3 +#formula used : area of rectangle = l*b +# perimeter of rectangle = 2*(l+b) +#given: + +l = 7 #length of rectangle +b = 4.5 #breadth of rectangle +area_rect <- function(x,y) #area of rectangle +{ + a = x*y + return(a) +} + +peri_rect <- function(x,y) #perimeter of rectangle +{ + return(p = 2*(l+b)) + +} + +print(area_rect(l,b)) + +print(peri_rect(l,b)) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.4/Ex26_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.4/Ex26_4.R new file mode 100644 index 00000000..ec157a47 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.4/Ex26_4.R @@ -0,0 +1,21 @@ +#page no. 269 +#problem 4 + +#formula used : area of parallelogram = base * perpendicular height +#given: + +l = 16 #one side of parallelogram +b = 9 #second side of parallelogram +L = 21 # distance from one point to another point (horizontally) +base = L-l #base of right angle triangle +hypo = b # hypotenuse of right angle triangle +h = sqrt(hypo^2 - base^2) + + +area_para <- function(x,y) #area of parallelogram +{ + a = x*y + return(a) +} + +print(area_para(l,h)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.5/Ex26_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.5/Ex26_5.R new file mode 100644 index 00000000..4438c936 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.5/Ex26_5.R @@ -0,0 +1,17 @@ +#page no.271 +#problem 5 +#formula used : area of right angle triangle = base*height/2 + +#given: +base = 1.92 +hypo = 5.68 +height = sqrt(hypo^2 - base^2) + + +area_triangle <- function(x,y) #area of right angle triangle +{ + a = (x*y)/2 + return(a) +} + +print(area_triangle(base,height)) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.6/Ex26_6.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.6/Ex26_6.R new file mode 100644 index 00000000..0e979a01 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.6/Ex26_6.R @@ -0,0 +1,15 @@ +#page no. 271 +#problem 6 +#formula used: area of trapezium = ((sum of parallel sides)*perpendicular distance)/2 + +#given: +l1 = 27.4 #length of one parallel side +l2 = 8.6 # length of 2nd parallel side +h = 5.5 # perpendicular distance b/w two parallel sides +area_trapezium <- function(x,y,z) #area of trapezium +{ + a = ((x+y)*z)/2 + return(a) +} + +print(area_trapezium(l1,l2,h)) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.7/Ex26_7.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.7/Ex26_7.R new file mode 100644 index 00000000..0c57907a --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.7/Ex26_7.R @@ -0,0 +1,22 @@ +#page no. 271 +#problem 7 +# formula used : #formula used : area of rectangle = l*b +#load package ----->measurments +library(measurements) +#given: +l = 820 #length of rectangle in mm +b = 400 #breadth of rectangle in mm +area_rect <- function(x,y) #area of rectangle +{ + a = x*y + return(a) +} +area = area_rect(l,b) +#part(a) +cat("area in mm^2:",area) + +#part(b) +cat("area in cm^2:",conv_unit(area,'mm2','cm2')) + +#part(c) +cat("area in m^2:",conv_unit(area,'mm2','m2')) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.8/Ex26_8.R b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.8/Ex26_8.R new file mode 100644 index 00000000..6755c459 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH26/EX26.8/Ex26_8.R @@ -0,0 +1,16 @@ +#page no. 271 +#problem 8 +# formula used : #formula used : area of rectangle = l*b +#given: +L = 100 #outer length of frame +B = 50 #outer breadth of frame +w = 4 # width of frame +l = L-2*w # inner length of frame +b = B -2*w #inner breadth of frame +area_rect <- function(x,y) #area of rectangle +{ + a = x*y + return(a) +} +area_frame = area_rect(L,B) - area_rect(l,b) +print(area_frame) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.1/Ex27_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.1/Ex27_1.R new file mode 100644 index 00000000..8875da74 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.1/Ex27_1.R @@ -0,0 +1,12 @@ +#page no. 279 +#problem 1 +#formula used: circumference of circle = 2*pi*r + +peri_circle = function(r) +{ + return(pi*r*2) +} + +#given: +r = 12 #radius of circle +print(peri_circle(r)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.10/Ex27_10.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.10/Ex27_10.R new file mode 100644 index 00000000..941ac028 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.10/Ex27_10.R @@ -0,0 +1,22 @@ +#page no. 282 +#problem 10 +#formula used: area of circle = pi*r^2 +# cicumference of circle = 2*pi*r + +area_circle = function(r) +{ + return(pi*r^2) +} + +radius_cir <- function(cir) +{ + r = cir/(2*pi) + return(r) +} + + +#given: +circ = 60 # circumference of circle +r = radius_cir(circ) +area = area_circle(r) #area of circle +print(area) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.11/Ex27_11.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.11/Ex27_11.R new file mode 100644 index 00000000..f6e125a7 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.11/Ex27_11.R @@ -0,0 +1,10 @@ +#page no. 282 +#problem 11 +#formula used: length of arc = r*theta +arc_length = function(r,theta) +{return(r*theta)} +#given: +r = 5.5 #radius of circle +theta = 1.20 # angel subtended at center in radians +s = arc_length(r,theta) # length of arc +print(s) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.12/Ex27_12.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.12/Ex27_12.R new file mode 100644 index 00000000..d46f903d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.12/Ex27_12.R @@ -0,0 +1,21 @@ +#page no. 282 +#problem 12 +#formula used: length of arc = r*theta + +arc_radius = function(s,theta) +{return(s/theta)} + +peri_circle = function(r) +{ + return(pi*r*2) +} + +#given: + +s = 4.75 #arc of length +theta = 0.91 # angle in radian +r = arc_radius(s,theta) +dia = 2*r +print(dia) # diameter of circle + +print(peri_circle(r)) # circumference of circle \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.13/Ex27_13.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.13/Ex27_13.R new file mode 100644 index 00000000..b68164b3 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.13/Ex27_13.R @@ -0,0 +1,27 @@ +#page no. 282 +#problem 13 +# formula used: minor arc = r*theta +# circumference of circle = 2*pi*r +# major arc = circumference - minor arc + +deg2rad <- function(deg) {return((deg * pi) / (180))} #degree to radian + +peri_circle = function(r) +{ + return(pi*r*2) +} + +arc_length = function(r,theta) +{return(r*theta)} + +#given: +r = 8.4# radius of circle +theta = 125 # angle in degree +rad = deg2rad(theta) #angle in radian +#part(a) +minor_arc = arc_length(r,rad) +print(minor_arc) +#part(b) +major_arc = peri_circle(r) - minor_arc +print(major_arc) + diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.15/Ex27_15.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.15/Ex27_15.R new file mode 100644 index 00000000..829e4280 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.15/Ex27_15.R @@ -0,0 +1,20 @@ +#page no. 282 +#problem 15 +#formula used: area of sector = (1/2)*r^2*theta + +deg2rad <- function(deg)#degree to radian + { + return((deg * pi) / (180)) + } + + +area_sector<- function(theta,r) +{ + a = (1/2)*r^2*theta +} +#given: +r = 55 #radius of stadium +theta = 45 #angle in degree +rad = deg2rad(theta) #angle in radian +area = area_sector(rad,r) # maximum area +print(area) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.16/Ex27_16.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.16/Ex27_16.R new file mode 100644 index 00000000..d4758088 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.16/Ex27_16.R @@ -0,0 +1,13 @@ +#page no. 282 +#problem 15 +#formula used: area of sector = (1/2)*r^2*theta +angle = function(r,area) +{theta = (area*2)/r^2} +rad2deg <- function(rad) {return((rad * 180) / (pi))} #radian to degree +#given: +r = 1.8 #radius of garden sprayer distance +area = 2.5 # area of sector sprayed +theta = angle(r,area) # angle in radian +print(theta) +degree = rad2deg(theta) #angle in degree +print(degree) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.2/Ex27_2.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.2/Ex27_2.R new file mode 100644 index 00000000..02731d8d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.2/Ex27_2.R @@ -0,0 +1,13 @@ +#page no. 279 +#problem 2 +#formula used: circumference of circle = 2*pi*r + +peri_circle = function(r) +{ + return(pi*r*2) +} + +#given: +dia = 75 #diameter of circle +r = dia/2 #radius of circle +print(peri_circle(r)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.3/Ex27_3.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.3/Ex27_3.R new file mode 100644 index 00000000..6cc2d87e --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.3/Ex27_3.R @@ -0,0 +1,14 @@ +#page no. 279 +#problem 3 +#formula used: circumference of circle = 2*pi*r + +radius_cir <- function(cir) +{ + r = cir/(2*pi) + return(r) +} + +#given: +circ = 112 +radius = radius_cir(circ) +print(radius) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.4/Ex27_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.4/Ex27_4.R new file mode 100644 index 00000000..5504b4c6 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.4/Ex27_4.R @@ -0,0 +1,17 @@ +#page no. 279 +#problem 4 +#formula used: pythagoras theorem + +hypotenuse <- function(b,p) +{ + h = sqrt(b^2+p^2) + return(h) +} + +#given: +ab = 150 # tangent to circle + # act as perpendicular height + r = 40 #radius of circle(base) + ao = hypotenuse(r,ab) + print(ao) + \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.5/Ex27_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.5/Ex27_5.R new file mode 100644 index 00000000..c3fbbdb9 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.5/Ex27_5.R @@ -0,0 +1,22 @@ +#page no. 280 +#problem 5 +#formula used: + +deg2rad <- function(deg) {return((deg * pi) / (180))} #degree to radian + +deg2rad_min = function(angle,min) #degree to radian while min are given +{ + deg = ((angle*60)+min)/60 + return(deg2rad(deg)) +} +#part(a) + #given: + d1 = 125 # angle in degree + print(deg2rad(d1)) + + +#part(b) + #given: + d2_angle = 69 # angle in degree and minutes + d2_min = 47 # 69 degree and 47 minutes + print(deg2rad_min(d2_angle,d2_min)) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.6/Ex27_6.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.6/Ex27_6.R new file mode 100644 index 00000000..7c31e6ad --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.6/Ex27_6.R @@ -0,0 +1,15 @@ +#page no. 281 +#problem 6 +#formula used: degrees to minutes +rad2deg <- function(rad) #radian to degree +{return((rad * 180) / (pi))} + + #part(a): + #given: + rad1 = 0.749 + print(rad2deg(rad1)) #in degree + + #part(b): + #given: + rad2 = (3*pi)/4 + print(rad2deg(rad2)) #in degree \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.8/Ex27_8.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.8/Ex27_8.R new file mode 100644 index 00000000..38ca7912 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.8/Ex27_8.R @@ -0,0 +1,13 @@ +#page no. 281 +#problem 8 +#formula used: area of semi circle = area of circle/2 + +area_circle = function(r) +{ + return(pi*r^2) +} + +#given: +r = 14.63 #radius of semicircle +area = (1/2)*area_circle(r) #area of semicircle +print(area) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.9/Ex27_9.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.9/Ex27_9.R new file mode 100644 index 00000000..3a1f1ad7 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.9/Ex27_9.R @@ -0,0 +1,14 @@ +#page no. 282 +#problem 9 +#formula used: area of circle = pi*r^2 + +area_circle = function(r) +{ + return(pi*r^2) +} + +#given: +dia = 35.0 #diameter of circle +r = dia/2 #radius of circle +area = area_circle(r) #area of circle +print(area) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.1/Ex28_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.1/Ex28_1.R new file mode 100644 index 00000000..9300192d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.1/Ex28_1.R @@ -0,0 +1,14 @@ +# page no. 290 +#formula used: volume of cuboid = l*b*h +# : surface area of cuboid = 2*(l*b+b*h+l*h) + +#given: +l = 12 +b = 4 +h = 3 + +volume = l*b*h +print(volume) + +surface_area_of_cuboid = 2*((l*b)+(b*h)+(l*h)) +print(surface_area_of_cuboid) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.11/Ex28_11.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.11/Ex28_11.R new file mode 100644 index 00000000..c925530a --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.11/Ex28_11.R @@ -0,0 +1,15 @@ +#page no.294 +#formula used:volume of pyramid = area of base*perpendicular height/3 +#given: rectangular pyramid +l = 5 # length of rectangular base +b = 6 # breadth of rectangular base +h = 18 # height of rectangular base +vol_rect = l*b*h # Volume of rectangular base +print(vol_rect) +vol_pyramid = vol_rect # volume of pyramid == volume of rectangular metal +L = 6 #length of casted base +B = 10 # breadth of casted base +area_base = L*B # area of base +H = (3*vol_pyramid)/(area_base) #height of pyramid +print(H) + \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.12/Ex28_12.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.12/Ex28_12.R new file mode 100644 index 00000000..c043a048 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.12/Ex28_12.R @@ -0,0 +1,8 @@ +#page no.295 +#Load package -----> measurments +#formula used: volume of cone = (pi*r^2*h)/3 + +r = conv_unit(30, 'mm', 'cm') # radius of cone (mm to cm) +h = conv_unit(80, 'mm', 'cm') # height of cone (mm to cm) +volume_of_cone = (pi*r^2*h)/3 +print(volume_of_cone) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.13/Ex28_13.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.13/Ex28_13.R new file mode 100644 index 00000000..dc38439f --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.13/Ex28_13.R @@ -0,0 +1,20 @@ +#page no.295 +#formula used: volume of cone = (pi*r^2*h)/3 +# total surface area of cone = pi*r(l+r) + +# install.packages("remotes") +# remotes::install_github("cewalters/r-packages") + +r = 5 # radius of cone +h = 12 # height of cone +volume_of_cone = (pi*r^2*h)/3 +print(volume_of_cone) + +hypotenuse <- function (x, y) +{ + sqrt (x ^ 2 + y ^ 2) +} + +l = hypotenuse(r,h) #slant height +TSA = pi*r*(l+r) # total surface area of cone +print(TSA) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.15/Ex28_15.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.15/Ex28_15.R new file mode 100644 index 00000000..5842a0bf --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.15/Ex28_15.R @@ -0,0 +1,12 @@ +#page no.296 +#formula used: volume of sphere = (4*pi*r^3)/3 +# surface area of sphere = 4*pi*r^2 + +area = 201.1 # surface area of sphere +r = sqrt(area/(4*pi)) +print(r) + +dia = 2*r #diameter of sphere +print(dia) +volume = (4*pi*r^3)/3 #volume of sphere +print(volume) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.18/Ex28_18.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.18/Ex28_18.R new file mode 100644 index 00000000..ed025362 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.18/Ex28_18.R @@ -0,0 +1,11 @@ +#page no. 299 +# formula used : volume of hemisphere = (volume of sphere)/2 +# = (2*pi*r^3)/3 +# surface area of hemisphere=((surface area of sphere)/2)+area of circle +# = (2*pi*r^2)+(pi*r^2) +dia = 5.0 #diameter of hemisphere +r = dia/2 +vol = (2*pi*r^3)/3 #volume of hemisphere +print(vol) +area = (2*pi*r^2)+(pi*r^2)#surface area of hemisphere +print(area) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.23/Ex28_23.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.23/Ex28_23.R new file mode 100644 index 00000000..a966fb83 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.23/Ex28_23.R @@ -0,0 +1,42 @@ +#page no. 300 +# formula used:volume of hemisphere =(2*pi*r^3)/3 +# volume of cone = (pi*r^2*h)/3 +# volume of cylinder = pi*r^2*h +# surface area of hemisphere=(2*pi*r^2)+(pi*r^2) +# curved surface area of cylinder= 2*pi*r*h +# curved surface area of cone = pi*r*l +# <-----boiler----top-hemisphere +# middle-cylinder +# bottom-cone + +len = 8 #length of cylinder +dia = 6 # diameter of cylinder +r = dia/2 +h = 4 # height of cone +vol_h = (2*pi*r^3)/3 #volume of hemisphere +print(vol_h) + +vol_Co = (pi*r^2*h)/3#volume of cone +print(vol_Co) + +vol_Cy = pi*r^2*len#volume of cylinder +print(vol_Cy) + +vol_boiler = vol_Co + vol_Cy + vol_h +print(vol_boiler) + + +hypotenuse <- function (x, y) +{ + sqrt (x ^ 2 + y ^ 2) +} + +l = hypotenuse(r,h) #slant height + + +sa_h =(2*pi*r^2)#surface area of hemisphere +sa_Co =pi*r*l #curved surface area of cone +sa_Cy =2*pi*r*len#curved surface area of cylinder + +sa_total = sa_h + sa_Co + sa_Cy # total surface area of boiler +print(sa_total) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.24/Ex28_24.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.24/Ex28_24.R new file mode 100644 index 00000000..dd83aa05 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.24/Ex28_24.R @@ -0,0 +1,10 @@ +#page no. 302 +# formula used: volume of frustum = pi*h*((r^2+R^2+R*r))/3 + +D = 6 #diameter at bigger end +R = D/2 +d = 4 #diameter at smaller end +r = d/2 +h = 3.6 +vol = pi*h*((r^2+R^2+R*r))/3 #volume of frustum +print(vol) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.29/Ex28_29.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.29/Ex28_29.R new file mode 100644 index 00000000..71f6cf1e --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.29/Ex28_29.R @@ -0,0 +1,21 @@ +#page no. 302 +# formula used: volume of frustum = pi*h*((r^2+R^2+R*r))/3 +# volume of cylinder = pi*r^2*h + +D = 25 #diameter at bigger end +R = D/2 +d = 12 #diameter at smaller end +r = d/2 +H = 30 #height of tower +h = 12 #height of cylinder +l = H-h # height of frustum +vol_Cy = pi*R^2*h #volume of cylinder +print(vol_Cy) +vol_f = pi*l*((r^2+R^2+R*r))/3 #volume of frustum +print(vol_f) + +vol_tower = vol_Cy + vol_f +print(vol_tower) + +vol_air_space = 0.6 * vol_tower +print(vol_air_space) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.4/Ex28_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.4/Ex28_4.R new file mode 100644 index 00000000..ed74b56d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.4/Ex28_4.R @@ -0,0 +1,11 @@ +#page no.291 +#formula used: volume of cylinder = pi*r^2*h +# total surface area = 2*pi*r*(h+r) + +dia = 12 #diameter of cylinder +r = dia/2 +h = 20 #height of cylinder +volume = pi*r^2*h +print(volume) +TSA = 2*pi*r*(h+r) #total surface area of cylinder +print(TSA) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.5/Ex28_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.5/Ex28_5.R new file mode 100644 index 00000000..8e49ec9b --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.5/Ex28_5.R @@ -0,0 +1,10 @@ +#page no.291 +#formula used: volume of cylinder = (area of cross-section)*length + +out_dia = 25#outer diameter of pipe +in_dia = 12 #inner diameter of pipe +h = 2.5*100 #lenght of pipe (converted meter to centimeter) +area_of_cross_section = ((pi*out_dia^2)/4)-((pi*in_dia^2)/4) +print(area_of_cross_section) +volume = (area_of_cross_section)*h +print(volume) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.9/Ex28_9.R b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.9/Ex28_9.R new file mode 100644 index 00000000..2c089aab --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH28/EX28.9/Ex28_9.R @@ -0,0 +1,7 @@ +#page no. 294 +# formula used: volume of pyramid = area of base*perpendicular height/3 +#given: square pyramid +l = 6 # side of square base +h = 16 # perpendicular height +volume = ((l*l)*h)/3 +print(volume) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.1/Ex33_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.1/Ex33_1.R new file mode 100644 index 00000000..fe251936 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.1/Ex33_1.R @@ -0,0 +1,11 @@ +#Page no. 356 +#Function used: mean() +# median() + +x<-c(2,3,7,5,5,13,1,7,4,8,3,4,3) #our Data Set + +mean_result = mean(x) #Computing Mean +print(mean_result) + +median_result = median(x)#Computing Median +print(median_result) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.2/Ex33_2.R b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.2/Ex33_2.R new file mode 100644 index 00000000..be3bb910 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.2/Ex33_2.R @@ -0,0 +1,11 @@ +#Page no. 356 +#Function used: mean() +# median() + +x<-c(27.90,34.70,54.40,18.92,47.60,39.68) #our Data Set + +mean_result = mean(x) #Computing Mean +print(mean_result) + +median_result = median(x)#Computing Median +print(median_result) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.3/Ex33_3.R b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.3/Ex33_3.R new file mode 100644 index 00000000..553a0968 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.3/Ex33_3.R @@ -0,0 +1,18 @@ +#page no. 357 +#Function used:with(),mean(),readLines(),gsub() + + +table_data <- "(value) (frequency) + (20.5,20.9] 3 + (21.0,21.4] 10 + (21.5,21.9] 11 + (22.0,22.4] 13 + (22.5,22.9] 9 + (23.0,23.4] 2" +L <- readLines(textConnection(table_data))#read line from connection +DF <- read.table(text = gsub("[^0-9.]", " ", L), skip = 1, as.is = TRUE)#gsub replaces all occurrences + +x <- with(DF, rep((V1 + V2)/2, V3))#computing the intermediate values + +mean_result=mean(x) +print(mean_result) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.4/Ex33_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.4/Ex33_4.R new file mode 100644 index 00000000..6803a0af --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.4/Ex33_4.R @@ -0,0 +1,38 @@ +#page no. 357 +#Function used:with(),mean(),readLines(),gsub() + + +table_data <- "(value) (frequency) +(14.5,15.5] 5 +(16.5,17.5] 8 +(18.5,19.5] 16 +(20.5,21.5] 12 +(22.5,23.5] 6 +(24.5,25.5] 3" +L <- readLines(textConnection(table_data))#read line from connection +DF <- read.table(text = gsub("[^0-9.]", " ", L), skip = 1, as.is = TRUE)#gsub replaces all occurrences + +x <- with(DF, rep((V1 + V2)/2, V3))#computing the intermediate values + +mean_result=mean(x) +print(mean_result) + +median_result=median(x) +print(median_result) + +y <- table(x) +mode_result = names(y)[which(y==max(y))] +print(mode_result) + +hist(x) +abline(v = mean_result, + col = "royalblue", + lwd = 2) + +abline(v = median_result, + col = "red", + lwd = 2) + +abline(v = mode_result, + col = "orange", + lwd = 2) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.5/Ex33_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.5/Ex33_5.R new file mode 100644 index 00000000..8502fef0 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.5/Ex33_5.R @@ -0,0 +1,6 @@ +#page no. 359 +#function used:var(),sqrt() + +x<-c(5,6,8,4,10,3)#data set +sd.result = sqrt(var(x))#calculating the Standard Deviation +print(sd.result)#result \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.6/Ex33_6.R b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.6/Ex33_6.R new file mode 100644 index 00000000..4fc1747e --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH33/EX33.6/Ex33_6.R @@ -0,0 +1,18 @@ +#page no. 359 +#Function used:with(),var(),sqrt(),readLines(),gsub() + + +table_data <- "(value) (frequency) +(20.5,20.9] 3 +(21.0,21.4] 10 +(21.5,21.9] 11 +(22.0,22.4] 13 +(22.5,22.9] 9 +(23.0,23.4] 2" +L <- readLines(textConnection(table_data))#read line from connection +DF <- read.table(text = gsub("[^0-9.]", " ", L), skip = 1, as.is = TRUE)#gsub replaces all occurrences + +x <- with(DF, rep((V1 + V2)/2, V3))#computing the intermediate values + +sd.result = sqrt(var(x))#calculating the Standard Deviation +print(sd.result)#result \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.1/Ex34_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.1/Ex34_1.R new file mode 100644 index 00000000..843e91ce --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.1/Ex34_1.R @@ -0,0 +1,16 @@ +#page no.363 + +n = 20 # no. of men +w = 33 # no. of women +total = n+w # total no. of people + +prob_of_men = n/total +print(prob_of_men) + +prob_of_women = w/total +print(prob_of_women) + +if((prob_of_men + prob_of_women)==1) +{ + print("no error") +} \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.2/Ex34_2.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.2/Ex34_2.R new file mode 100644 index 00000000..9245904a --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.2/Ex34_2.R @@ -0,0 +1,15 @@ +#page no. 363 + +#Load package ------> dice +library(dice) + + +## Probability of rolling no 4's when rolling three six-sided dice + +E=getEventProb(nrolls = 3, # number of dice rolls to make + ndicePerRoll = 1,# number of dice to use in each dice roll + nsidesPerDie = 6,# number of sides on each die + eventList = list(4), + orderMatters = FALSE) + +print(E) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.3/Ex34_3.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.3/Ex34_3.R new file mode 100644 index 00000000..6a125e44 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.3/Ex34_3.R @@ -0,0 +1,17 @@ +#page no. 364 +#problem 3 + +n = 10 # number of horses +win <- function(a,b)# a--->number of winner in race + # b---> total number of particpants +{ + winner <- a/b + return(winner) +} +#part(a) +prob_of_winning = win(1,n) +print(prob_of_winning) + +# part(b) +prob_of_two_races = win(1,n) * win(1,n) +print(prob_of_two_races) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.4/Ex34_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.4/Ex34_4.R new file mode 100644 index 00000000..11b94c85 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.4/Ex34_4.R @@ -0,0 +1,18 @@ +#page no. 364 +#problem 4 +#given: +prob_temp = 1/20#probability of failing due to temperature +prob_vib = 1/25 #probability of failing due to vibration +prob_hum = 1/50 #probability of failing due to humidity + +#part(a) +prob_a = prob_temp * prob_vib # fails--> temperature and vibration +print(prob_a) + +#part(b) +prob_b =prob_vib + prob_hum # fails--> humidity or vibration +print(prob_b) + +#part(c) +prob_c = (1-prob_temp) * (1-prob_hum) # NOT_fails--> temperature and humidity +print(prob_c) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.5/Ex34_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.5/Ex34_5.R new file mode 100644 index 00000000..52248966 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.5/Ex34_5.R @@ -0,0 +1,22 @@ +# page no. 365 +#problem 5 +#given: +n = 100 #total number of capacitors +n_t = 73 # capacitors within req. tolerance values +n_bt = 17 # capacitors within req. tolerance values below +n_at = n-(n_t+n_bt) #capacitors within req. tolerance values above + +probability <-function(a,b) +{ + prob = a/b + return(prob) +} + +#part(a) ----> probability with replacement +prob_n_t = probability(n_t,n) * probability(n_t,n) +print(prob_n_t) + +# part(b) ------> probability one below and second above tolerance values +# without replacement +prob_a_b = probability(n_bt,n) * probability(n_at,n-1) +print(prob_a_b) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.6/Ex34_6.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.6/Ex34_6.R new file mode 100644 index 00000000..d58bee7d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.6/Ex34_6.R @@ -0,0 +1,22 @@ +#page no. 366 +#problem 6 + +n = 40 #total number of components +n_d = 5 # number of defective components +n_g = n - n_d #number of good components + +probability <-function(a,b) +{ + prob = a/b + return(prob) +} + +#part(a) +#with replacement (probability of good) +prob_a = probability(n_g,n) * probability(n_g,n) +print(prob_a) + +#part(b) +#without replacement(probability of good) +prob_b = probability(n_g,n) * probability(n_g-1,n-1) +print(prob_b) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.7/Ex34_7.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.7/Ex34_7.R new file mode 100644 index 00000000..357f687f --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.7/Ex34_7.R @@ -0,0 +1,26 @@ +#page no. 366 +#problem 7 + +n = 40 #total number of components +n_d = 5 # number of defective components +n_g = n - n_d #number of good components + +probability <-function(a,b) +{ + prob = a/b + return(prob) +} + +prob_def = probability(n_d,n) +print(prob_def) +prob_good = probability(n_g,n) +print(prob_good) +#part(a) +#with replacement (probability of one defective component ) +prob_a = (prob_def * prob_good) + (prob_good * prob_def) +print(prob_a) + +#part(b) +#without replacement(probability of one defective component) +prob_b = (prob_def * probability(n_g,n-1))+(prob_good * probability(n_d,n-1)) +print(prob_b) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.8/Ex34_8.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.8/Ex34_8.R new file mode 100644 index 00000000..74042c82 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.8/Ex34_8.R @@ -0,0 +1,9 @@ +#page no.= 366 + +b = 74 #no. of brass washers +s = 86 #no. of steel washers +a = 40 #no. of aluminium washers +t = b+s+a # total no. of washers + +probability = (s/t)*((s-1)/(t-1))*((s-2)/(t-2))#probability that all three are steel washers +print(probability) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.9/Ex34_9.R b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.9/Ex34_9.R new file mode 100644 index 00000000..2d3bd63d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH34/EX34.9/Ex34_9.R @@ -0,0 +1,18 @@ +#page no. 366 +#problem 9 + + +b = 74 #no. of brass washers +s = 86 #no. of steel washers +a = 40 #no. of aluminium washers +t = b+s+a # total no. of washers +a_n = t - a # no. of not aluminium washers + +prob<-function(a,b) +{ + probability = a/b + return(probability) +} +# probability without replacement that no aluminium washer drwan +prob_n_alum = prob(a_n,t) *prob(a_n-1,t-1)*prob(a_n-2,t-2) +print(prob_n_alum) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.11/Ex35_11.R b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.11/Ex35_11.R new file mode 100644 index 00000000..b114395e --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.11/Ex35_11.R @@ -0,0 +1,12 @@ +#page no.376 +#problem 11 + +#load package ----->deriv +library(Deriv) +#funtion used: D()-------> derivative function w.r.t variable +#given: +# (3*x^2-5*x)/2*x ----->((3*x)/2) - (5/2) # expression after solving +y=expression(((3*x)/2) - (5/2)) + +result = D(y,'x') # differentiation w.r.t 'x' +print(result) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.12/Ex35_12.R b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.12/Ex35_12.R new file mode 100644 index 00000000..a7d0f3d9 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.12/Ex35_12.R @@ -0,0 +1,9 @@ +#page no.377 +#problem 12 +#load package ----->deriv +library(Deriv) +#funtion used: D()-------> derivative function w.r.t variable +#given: +y=expression((2*x^3/5)-(4/x^3) + (4*sqrt(x^5))+7) + +D(y,'x') # differentiation w.r.t 'x' \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.16/Ex35_16.R b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.16/Ex35_16.R new file mode 100644 index 00000000..b7943b5c --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.16/Ex35_16.R @@ -0,0 +1,9 @@ +#page no.379 +#problem 16 +#load package ----->deriv +library(Deriv) +#funtion used: D()-------> derivative function w.r.t variable +#given: +y=expression(7*sin(2*x) - 3*cos(4*x)) #sin and cos function derivatives + +D(y,'x') # differentiation w.r.t 'x' \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.25/Ex35_25.R b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.25/Ex35_25.R new file mode 100644 index 00000000..f1c7f575 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.25/Ex35_25.R @@ -0,0 +1,11 @@ +#page no.382 +#problem 25 +#load package ----->deriv +library(Deriv) +#funtion used: D()-------> derivative function w.r.t variable +#given: +y=expression(2*x^3/3 - 4/x^2 + 1/2*x -sqrt(x)) #sin and cos function derivatives + +D1=D(y,'x') # 1st order differentiation w.r.t 'x' +D2=D(D1,'x')# 2nd order differentiation w.r.t 'x' +print(D2) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.6/Ex35_6.R b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.6/Ex35_6.R new file mode 100644 index 00000000..aaa5fe2e --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.6/Ex35_6.R @@ -0,0 +1,9 @@ +#page no.376 +#problem 6 +#load package ----->deriv +library(Deriv) +#funtion used: D()-------> derivative function w.r.t variable +#given: +y=expression(5*sqrt(x)) + +D(y,'x') # differentiation w.r.t 'x' \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.9/Ex35_9.R b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.9/Ex35_9.R new file mode 100644 index 00000000..2338b74e --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH35/EX35.9/Ex35_9.R @@ -0,0 +1,9 @@ +#page no.376 +#problem 9 +#load package ----->deriv +library(Deriv) +#funtion used: D()-------> derivative function w.r.t variable +#given: +y=expression(((2*x^4)/3)-(4/x^3)+9) + +D(y,'x') # differentiation w.r.t 'x' \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.18/Ex36_18.R b/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.18/Ex36_18.R new file mode 100644 index 00000000..a098f867 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.18/Ex36_18.R @@ -0,0 +1,8 @@ +#page no. 392 +#problem 18 +#function: integrate(expression,lower,upper) --->in-built function +f = function(x) (4-x^2) #function defination --->expression + +lower_limit = -2 +upper_limit = 3 +integrate(f,lower_limit,upper_limit) #evaluating the integral value over limits diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.20/Ex36_20.R b/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.20/Ex36_20.R new file mode 100644 index 00000000..62053f58 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.20/Ex36_20.R @@ -0,0 +1,8 @@ +#page no. 392 +#problem 20 +#function: integrate(expression,lower,upper) --->in-built function +f = function(x) (x^3-5*x+1) #function defination --->expression + +lower_limit = -1 +upper_limit = 1 +integrate(f,lower_limit,upper_limit) #evaluating the integral value over limits diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.22/Ex36_22.R b/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.22/Ex36_22.R new file mode 100644 index 00000000..e257638d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.22/Ex36_22.R @@ -0,0 +1,8 @@ +#page no. 393 +#problem 22 +#function: integrate(expression,lower,upper) --->in-built function +f = function(x) (3*sin(2*x)) #function defination --->expression + +lower_limit = 0 +upper_limit = pi/2 +integrate(f,lower_limit,upper_limit) #evaluating the integral value over limits diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.24/Ex36_24.R b/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.24/Ex36_24.R new file mode 100644 index 00000000..708ca20d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH36/EX36.24/Ex36_24.R @@ -0,0 +1,8 @@ +#page no. 393 +#problem 24 +#function: integrate(expression,lower,upper) --->in-built function +f = function(x) (4*exp(2*x)) #function defination --->expression + +lower_limit = 1 +upper_limit = 2 +integrate(f,lower_limit,upper_limit) #evaluating the integral value over limits diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.10/Ex37_10.R b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.10/Ex37_10.R new file mode 100644 index 00000000..8cf5a234 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.10/Ex37_10.R @@ -0,0 +1,21 @@ +#page no. 405 +#problem 10 +#function: +term = function(a,n,d) # to find term value +{ + return(a+((n-1)*d)) +} +#given: +a6 = 17 #6th term of sequence---->(a+5d=17) +a13 = 38 #13th term of sequence---->(a+12d=38) + +# using matrix method X=A(inverse)*B +# we will find a(first value) and d(common difference) values + +A = array(data = c(1,1,5,12),dim = c(2,2)) +B = c(17,38) +X = solve(A,B) # calculating a and d +a = X[1] #first number of sequence +d = X[2] # common difference of AP(airthmetic progression) +a19 = term(a,19,d) # n = 19, to find 19th term of sequence +print(a19) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.12/Ex37_12.R b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.12/Ex37_12.R new file mode 100644 index 00000000..f2f92590 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.12/Ex37_12.R @@ -0,0 +1,15 @@ +#page no.406 +#problem 12 +#formula used: Sn = (n/2)*(2a+(n-1)d) -->sum of n terms in AP +#function: +Sn = function(n,a,d) #function --->sum of n terms +{ + return((n/2)*(2*a+(n-1)*d)) +} +#given: +n = 12 +seq = c(5,9,13,17) +a = seq[1] #first term of sequence +d = seq[2]-seq[1] # common difference +sum_ap = Sn(n,a,d) # sum of n-terms +print(sum_ap) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.14/Ex37_14.R b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.14/Ex37_14.R new file mode 100644 index 00000000..8860f3b2 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.14/Ex37_14.R @@ -0,0 +1,15 @@ +#page no. 406 +#problem 14 +#formula used: Sn = (n/2)*(2a+(n-1)d) -->sum of n terms in AP +# a = [2*Sn/n-(n-1)d]/2 +#function: +find = function(Sn,n,d) +{ + return((((2*Sn)/n)-((n-1)*d))/2) +} +#given: +S7 = 35 #sum of 7 terms +n = 7 # number of terms +d = 1.2 # common difference +find_a = find(S7,n,d) # first term of sequence +print(find_a) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.16/Ex37_16.R b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.16/Ex37_16.R new file mode 100644 index 00000000..44c8d8ac --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.16/Ex37_16.R @@ -0,0 +1,46 @@ +#page no.407 +#problem 16 +#load package ---->pastecs,----->dyplr +library(dplyr) +library(pastecs) +#funtion used: + +term_n = function(a,d,an) #function ---> to find number of terms +{ + return(((an-a)/d)+1) +} + +Sn = function(n,a,d) #function --->sum of n terms +{ + return((n/2)*(2*a+(n-1)*d)) +} + +#given:(0 to 207) AP divisible by 3 + +a1 = 0 #starting of range +e1 = 207 #end of range + +result <- vector("numeric") # prepare a container to store value +# divisible by 3 from (0 to 207) +for (i in c(a1:e1)) +{ + if (i%%3 == 0) + { + result[i] <- i + } +} + +seq = complete.cases(result) #removing the NA values from vector + +seq1 = c(result[seq]) #creating new vector + +seq2 = array(data = c(seq1)) #sequence (3,6,9....207) + #creating for accessing the + # values divisible by 3 + +a = seq2[1] #first number of sequence +d = seq2[2] - seq2[1] #common difference +an = last(seq2) +n = term_n(a,d,an) +sum_terms = Sn(n,a,d) #sum of n-terms in AP +print(sum_terms) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.20/Ex37_20.R b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.20/Ex37_20.R new file mode 100644 index 00000000..163b0d28 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.20/Ex37_20.R @@ -0,0 +1,18 @@ +#page no.409 +#problem 20 +#formula used: an = ar^(n-1) +#function: +find_r = function(an,a,n) #function to find common ratio + {return((an/a)**(1/(n-1)))} +#given: +a = 12 #first term of GP +a5 = 55 #5th term of GP (ar^4) +n = 5 #fith term given +r = find_r(a5,a,n) #common ratio + +#part(a) +a8 = a*r^7 +print(a8) +#part(b) +a11 = a*r^10 +print(a11) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.22/Ex37_22.R b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.22/Ex37_22.R new file mode 100644 index 00000000..192322cc --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.22/Ex37_22.R @@ -0,0 +1,15 @@ +#page no.409 +#problem 22 +#formula used: an = ar^(n-1) +# sum = a(1-r^n)/(1-r) +#function: +Sn= function(a,r,nn) #function to find ---> sum of n-terms +{return(a*(1-r^n)/(1-r))} + +#given: +seq = c(72.0,57.6,46.08) # GP sequence given +a = seq[1] #1st term of sequence +r = seq[2]/seq[1] # common ratio of sequence +n = 9 # 9 terms +sum_n = Sn(a,r,n) #sum of 9 terms +print(sum_n) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.23/Ex37_23.R b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.23/Ex37_23.R new file mode 100644 index 00000000..0365cf1b --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.23/Ex37_23.R @@ -0,0 +1,14 @@ +#page no.409 +#problem 23 +#formula used: an = ar^(n-1) +# S2inf=a/(1-r) +#function: +S2inf= function(a,r) + {return(a/(1-r))} + +#given: +seq = c(3,1,1/3) # GP sequence to infinity....... +a = seq[1] #1st term of sequence +r = seq[2]/seq[1] +sum_inf = S2inf(a,r) #sum to infinity +print(sum_inf) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.4/Ex37_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.4/Ex37_4.R new file mode 100644 index 00000000..2fc85ef6 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH37/EX37.4/Ex37_4.R @@ -0,0 +1,19 @@ +#page no. 404 +#problem 4 +#given: +term = function(n) # to find term value + { + return(3*n+1) +} + # first four term of the sequence will be a1,a2,a3,a4 +a1 = term(1) +a2 = term(2) +a3 = term(3) +a4 = term(4) + +cat("1st term::",a1) +cat("2nd term::",a2) +cat("3rd term::",a3) +cat("4th term::",a4) + + diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.1/Ex5_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.1/Ex5_1.R new file mode 100644 index 00000000..e9e1d0ce --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.1/Ex5_1.R @@ -0,0 +1,7 @@ +#page no.36 +#problem 1 +#laod package ------->formattable +library(formattable) +#function used: percent() +n = 0.015 #decimal to percentage +percent(n) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.10/Ex5_10.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.10/Ex5_10.R new file mode 100644 index 00000000..b0f3602d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.10/Ex5_10.R @@ -0,0 +1,19 @@ +#page no.37 +#problem 10 +#function: +#percentage of given quantity +percent_of_quantity = function(x,y) # x---->percenatge, y----->quantity +{ + return((percent2deci(x))*y) +} + +percent2deci = function(x) +{ + return(x/100) +} + +#given: +p = 27 #percentage +n = 65 # amount of money +result = percent_of_quantity(p,n) +print(result) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.12/Ex5_12.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.12/Ex5_12.R new file mode 100644 index 00000000..bd18d448 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.12/Ex5_12.R @@ -0,0 +1,20 @@ +#page no.38 +#problem 12 +#function: +#percentage of given quantity +percent_of_quantity = function(x,y) # x---->percenatge, y----->quantity +{ + return((percent2deci(x))*y) +} + +percent2deci = function(x) +{ + return(x/100) +} + +#given: +cost = 190 #base price of ipod +VAT = 20 # VAT percentage +VAT1 = percent_of_quantity(VAT,cost) +result = VAT1 + cost #total cost of iPod (VAT+BASE price) +print(result) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.14/Ex5_14.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.14/Ex5_14.R new file mode 100644 index 00000000..2bcba223 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.14/Ex5_14.R @@ -0,0 +1,15 @@ +#page no.38 +#problem 14 +#load package ---->measurements +library(measurements) +#functions: +percent_one_wrt_second = function(x,y) +{ + return(percent(x/y)) +} +#given: +t1 = 47 #time in minutes +t2 = 2 #time in hours +t2 = conv_unit(t2,'hr','min') +result = percent_one_wrt_second(t1,t2) +print(result) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.15/Ex5_15.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.15/Ex5_15.R new file mode 100644 index 00000000..6636c188 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.15/Ex5_15.R @@ -0,0 +1,12 @@ +#page no. 38 +#problem 15 +#function: +percent_change = function(n,o) #n----> new value, o----> original value +{ + return(percent((n-o)/o)) +} +#given: +new_value = 52 #resistor value +original_value = 45 #resistor value increases +change = percent_change(new_value,original_value) +print(change) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.18/Ex5_18.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.18/Ex5_18.R new file mode 100644 index 00000000..6457c222 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.18/Ex5_18.R @@ -0,0 +1,14 @@ +#page no. 39 +#problem 18 +#function: +per_error = function(err,val) #err-->error, val ---> correct value +{ + return(percent(err/val)) +} + +#given: +cal_vol = 50 #calculated voltage +ac_vol = 50.4 #actual voltage +error = ac_vol - cal_vol # error in measurements +result = per_error(error,ac_vol) #percentage error +print(result) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.21/Ex5_21.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.21/Ex5_21.R new file mode 100644 index 00000000..b0b5b75a --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.21/Ex5_21.R @@ -0,0 +1,15 @@ +#page no. 40 +#problem 21 +#formula used:(new value/100-+change%)*100% +#function: +original_value_profit = function(new,change) #new----> new value, change in percentage +{ + return((new/(100+change))*100) + +} + +#given: +c = 40 #change in percentage (profit) +SP = 630# selling price ---->new value +result = original_value_profit(SP,c) #cost to dealer +print(result) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.23/Ex5_23.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.23/Ex5_23.R new file mode 100644 index 00000000..67b55368 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.23/Ex5_23.R @@ -0,0 +1,8 @@ +#page no. 40 +#problem +#formula used: new value = (100 + %increase)*original value/100 +#given: +inc = 6.5 #price increased in percentage +cost = 2400 #original cost of boiler +new_price = (((100 + inc)*cost)/100) #new price of boiler +print(new_price) \ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.4/Ex5_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.4/Ex5_4.R new file mode 100644 index 00000000..39bdfbbc --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.4/Ex5_4.R @@ -0,0 +1,10 @@ +#page no.36 +#problem 4 +#function used: +percent2deci = function(x) +{ + return(x/100) +} +#given: +n = 17.5 # percentage +print(percent2deci(n)) diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.7/Ex5_7.R b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.7/Ex5_7.R new file mode 100644 index 00000000..fde3d0cd --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH5/EX5.7/Ex5_7.R @@ -0,0 +1,10 @@ +#page no.36 +#problem 7 +#laod package ------->formattable +library(formattable) +#function used: percent() +n1 = 57/79 #fraction to percentage +n2 = 49/67 #fraction to percentage + +percent(n1) +percent(n2) -- cgit