initial commit / add all books

27 files changed, 445 insertions, 0 deletions

diff --git a/149/CH4/EX4.10/ques10.sce b/149/CH4/EX4.10/ques10.sce
new file mode 100755
index 000000000..604fbf59d
--- /dev/null
+++ b/149/CH4/EX4.10/ques10.sce
@@ -0,0 +1,37 @@
+clc

+disp(' y^(1/m)+y^-(1/m)=2x  ');

+disp(' OR y^(2/m)-2xy^(1/m)+1');

+disp('OR y=[x+(x^2-1)]^m and y=[x-(x^2-1)]^m ');

+

+syms x m

+disp('For y=[x+(x^2-1)]^m ');

+ y=(x+(x^2-1))^m

+disp('we have to prove (x^2-1)y(n+2)+(2n+1)xy(n+1)+(n^2-m^2)yn ') ;

+//n=input('Enter the order of differentiation ");

+disp('calculating  yn for various values of n');

+for n=1:4

+  

+  //yn=diff(F,x,n)

+  F=(x^2-1)*diff(y,x,n+2)+(2*n+1)*x*diff(y,x,n+1)+(n^2-m^2)*diff(y,x,n);

+  disp(n); 

+  disp('the expression for yn is ');

+  disp(F);

+  disp('Which is equal to 0 ');

+

+end

+disp('For y=[x-(x^2-1)]^m ');

+ y=(x-(x^2-1))^m

+disp('we have to prove (x^2-1)y(n+2)+(2n+1)xy(n+1)+(n^2-m^2)yn ') ;

+//n=input('Enter the order of differentiation ");

+disp('calculating  yn for various values of n');

+for n=1:4

+  

+  //yn=diff(F,x,n)

+  F=(x^2-1)*diff(y,x,n+2)+(2*n+1)*x*diff(y,x,n+1)+(n^2-m^2)*diff(y,x,n);

+  disp(n); 

+  disp('the expression for yn is ');

+  disp(F);

+  disp('Which is equal to 0 ');

+

+end

+disp('Hence proved');

diff --git a/149/CH4/EX4.11/ques11.sce b/149/CH4/EX4.11/ques11.sce
new file mode 100755
index 000000000..31a496d87
--- /dev/null
+++ b/149/CH4/EX4.11/ques11.sce
@@ -0,0 +1,11 @@
+clc

+disp('for roles theorem F9x) should be differentiable in (a,b) and f(a)=f(b)');

+disp(' Here f(x)=sin(x)/e^x');

+disp('');

+syms x

+y=sin(x)/%e^x;

+

+y1=diff(y,x);

+disp(y1);

+disp('putting this to zero we get tan(x)=1 ie x=pi/4');

+disp('value pi/2 lies b/w 0 and pi. Hence roles theorem is verified');

diff --git a/149/CH4/EX4.16/ques16.sce b/149/CH4/EX4.16/ques16.sce
new file mode 100755
index 000000000..21ec43618
--- /dev/null
+++ b/149/CH4/EX4.16/ques16.sce
@@ -0,0 +1,16 @@
+//ques16

+disp('Maclaurins series');

+disp('f(x)=f(0)+xf1(0)+x^2/2!*f2(0)+x^3/3!*f3(0)+......');

+syms x a

+//function y=f(a)

+  y=tan(a);

+//endfunction

+n=input('enter the number of expression in series : ');

+a=1;

+t=eval(y);

+a=0;

+for i=2:n

+  y1=diff(y,'a',i-1);

+  t=t+x^(i-1)*eval(y1)/factorial(i-1);

+end

+disp(t)

diff --git a/149/CH4/EX4.17/ques17.sce b/149/CH4/EX4.17/ques17.sce
new file mode 100755
index 000000000..4ff07ee8d
--- /dev/null
+++ b/149/CH4/EX4.17/ques17.sce
@@ -0,0 +1,16 @@
+//ques16

+disp('Maclaurins series');

+disp('f(x)=f(0)+xf1(0)+x^2/2!*f2(0)+x^3/3!*f3(0)+......');

+syms x a

+

+  y=%e^(sin(a));

+  n=input('enter the number of expression in seris : ');

+  a=0;

+t=eval(y);

+a=0;

+for i=2:n

+  y1=diff(y,'a',i-1);

+   t=t+x^(i-1)*eval(y1)/factorial(i-1);

+end

+disp(t)

+

diff --git a/149/CH4/EX4.18/ques18.sce b/149/CH4/EX4.18/ques18.sce
new file mode 100755
index 000000000..2fac6438f
--- /dev/null
+++ b/149/CH4/EX4.18/ques18.sce
@@ -0,0 +1,16 @@
+//ques18

+disp('Maclaurins series');

+disp('f(x)=f(0)+xf1(0)+x^2/2!*f2(0)+x^3/3!*f3(0)+......');

+syms x a

+

+  y=log(1+(sin(a))^2);

+  n=input('enter the number of differentiation involved in  maclaurins series : ');

+  a=0;

+t=eval(y);

+a=0;

+for i=2:n

+  y1=diff(y,'a',i-1);

+   t=t+x^(i-1)*eval(y1)/factorial(i-1);

+end

+disp(t)

+

diff --git a/149/CH4/EX4.19/ques19.sce b/149/CH4/EX4.19/ques19.sce
new file mode 100755
index 000000000..87b407982
--- /dev/null
+++ b/149/CH4/EX4.19/ques19.sce
@@ -0,0 +1,16 @@
+//ques19

+disp('Maclaurins series');

+disp('f(x)=f(0)+xf1(0)+x^2/2!*f2(0)+x^3/3!*f3(0)+......');

+syms x a b

+

+  y=%e^(a*asin(b));

+  n=input('enter the number of expression in seris : ');

+  b=0;

+t=eval(y);

+

+for i=2:n

+  y1=diff(y,'b',i-1);

+   t=t+x^(i-1)*eval(y1)/factorial(i-1);

+end

+disp(t)

+

diff --git a/149/CH4/EX4.20/ques20.sce b/149/CH4/EX4.20/ques20.sce
new file mode 100755
index 000000000..ef7798090
--- /dev/null
+++ b/149/CH4/EX4.20/ques20.sce
@@ -0,0 +1,6 @@
+//ques20 

+disp('Advantage of scilab is that we can calculate log1.1 directly without using Taylor series');

+disp(' Use of taylor series are given in subsequent examples');

+y=log(1.1);

+disp('log(1.1)= ');

+disp(log(1.1));
\ No newline at end of file
diff --git a/149/CH4/EX4.21/ques21.sce b/149/CH4/EX4.21/ques21.sce
new file mode 100755
index 000000000..e26c9c70f
--- /dev/null
+++ b/149/CH4/EX4.21/ques21.sce
@@ -0,0 +1,17 @@
+//ques21

+disp('Taylor series');

+disp('f(x+h)=f(x)+hf1(x)+h^2/2!*f2(x)+h^3/3!*f3(x)+......');

+disp('To finf the taylor expansion of tan-1(x+h)')

+syms x h

+

+  y=atan(x);

+  n=input('enter the number of expression in seris : ');

+  

+t=y;

+

+for i=2:n

+  y1=diff(y,'x',i-1);

+   t=t+h^(i-1)*(y1)/factorial(i-1);

+end

+disp(t)

+

diff --git a/149/CH4/EX4.22/ques22.sce b/149/CH4/EX4.22/ques22.sce
new file mode 100755
index 000000000..cdc77ff0c
--- /dev/null
+++ b/149/CH4/EX4.22/ques22.sce
@@ -0,0 +1,27 @@
+//ques22

+disp('Here we need to find find the limit of f(x) at x=0')

+syms x

+y=(x*%e^x-log(1+x))/x^2;

+//disp('The limit at x=0 is : ');

+//l=limit(y,x,0);

+//disp(l)

+f=1;

+while f==1

+yn=x*%e^x-log(1+x);

+yd=x^2;

+yn1=diff(yn,'x',1);

+yd1=diff(yd,'x',1);

+x=0;

+a=eval(yn1);

+b=eval(yd1);

+if a==b then

+  yn=yn1;

+  yd=yd1;

+else

+  f=0;

+

+end

+end

+h=a/b;

+disp(h);

+  

diff --git a/149/CH4/EX4.32/ques32.sce b/149/CH4/EX4.32/ques32.sce
new file mode 100755
index 000000000..85964808f
--- /dev/null
+++ b/149/CH4/EX4.32/ques32.sce
@@ -0,0 +1,12 @@
+//ques 32

+disp('Equation of tangent');

+syms x a y;

+f=(a^(2/3)-x^(2/3))^(3/2);

+s=diff(f,x);

+

+Y1=s*(-x)+y;

+X1=-y/s*x;

+g=x-(Y1-s*(X1-x));

+disp('Equation is g=0 where g is');

+disp(g);

+

diff --git a/149/CH4/EX4.34/ques34.sce b/149/CH4/EX4.34/ques34.sce
new file mode 100755
index 000000000..215eca563
--- /dev/null
+++ b/149/CH4/EX4.34/ques34.sce
@@ -0,0 +1,10 @@
+//ques34

+disp('Equation of tangent');

+syms x a t y

+xo=a*(cos(t)+t*sin(t));

+yo=a*(sin(t)-t*cos(t));

+s=diff(xo,t)/diff(yo,t);

+y=yo+s*(x-xo);

+disp('y=');

+disp(y);

+

diff --git a/149/CH4/EX4.35/ques35.sce b/149/CH4/EX4.35/ques35.sce
new file mode 100755
index 000000000..54b58540c
--- /dev/null
+++ b/149/CH4/EX4.35/ques35.sce
@@ -0,0 +1,17 @@
+//ques35

+disp("The two given curves are x^=4y and y^2=4x which intersects at (0,0) and (4,4)');

+disp('for (4,4)');

+x=4;

+syms x

+y1=x^2/4;

+y2=2*x^(1/2);

+m1=diff(y1,x,1);

+m2=diff(y2,x,1);

+x=4;

+m1=eval(m1);

+m2=eval(m2);

+

+disp('Angle between them is(radians) :-');

+t=atan((m1-m2)/(1+m1*m2));

+disp(t);

+

diff --git a/149/CH4/EX4.37/ques37.sce b/149/CH4/EX4.37/ques37.sce
new file mode 100755
index 000000000..fb932fa96
--- /dev/null
+++ b/149/CH4/EX4.37/ques37.sce
@@ -0,0 +1,26 @@
+//ques37

+syms a t

+x=a*(cos(t)+log(tan(t/2)));

+y=a*sin(t);

+s=diff(x,t,1)/diff(y,t,1);

+disp('length of tangent ');

+l=y*(1+s)^(0.5);

+disp(l);

+disp('checking for its dependency on t')

+

+f=1

+t=0;

+k=eval(l);

+for i=1:10

+  t=i;

+  if(eval(l)~=k)

+    f=0;

+  end

+end

+if(f==1)

+  disp("verified and equal to a");

+  disp('subtangent');

+  m=y/s;

+  disp(m);

+   

+    
\ No newline at end of file
diff --git a/149/CH4/EX4.39/ques39.sce b/149/CH4/EX4.39/ques39.sce
new file mode 100755
index 000000000..2b549d92b
--- /dev/null
+++ b/149/CH4/EX4.39/ques39.sce
@@ -0,0 +1,14 @@
+//ques39

+clc

+disp('Angle of intersection');

+disp('point of intersection of r=sint+cost and r=2sint is t=pi/4 ');

+disp('tanu=dQ/dr*r');

+syms Q ;

+

+r1=2*sin(Q);

+r2=sin(Q)+cos(Q);

+u=atan(r1*diff(r2,Q,1));

+Q=%pi/4;

+u=eval(u);

+disp('The angle at point of intersection in radians is : ');

+disp(u);

diff --git a/149/CH4/EX4.4.1/ques4_1.sce b/149/CH4/EX4.4.1/ques4_1.sce
new file mode 100755
index 000000000..972cc4ad8
--- /dev/null
+++ b/149/CH4/EX4.4.1/ques4_1.sce
@@ -0,0 +1,17 @@
+//ques4.1

+//clear

+//cd SCI

+//cd ("..")

+//cd ("..")

+//exec symbolic.sce 

+clc

+disp(' we have to find yn for F=cosxcos2xcos3x ');

+syms x

+F=cos(x)*cos(2*x)*cos(3*x);

+n=input('Enter the order of differentiation ");

+disp('calculating  yn ');

+yn=diff(F,x,n)

+disp('the expression for yn is ');

+disp(yn);

+

+

diff --git a/149/CH4/EX4.41/ques41.sce b/149/CH4/EX4.41/ques41.sce
new file mode 100755
index 000000000..f8bfcf53c
--- /dev/null
+++ b/149/CH4/EX4.41/ques41.sce
@@ -0,0 +1,16 @@
+//ques41

+clc

+disp('tanu=dQ/dr*r');

+syms Q a;

+

+r=2*a/(1-cos(Q));

+

+u=atan(r/diff(r2,Q,1));

+u=eval(u);

+p=r*sin(u);

+syms r;

+Q=acos(1-2*a/r);

+

+//cos(Q)=1-2*a/r;

+p=eval(p);

+disp(p);

diff --git a/149/CH4/EX4.43/ques43.sce b/149/CH4/EX4.43/ques43.sce
new file mode 100755
index 000000000..79ac06619
--- /dev/null
+++ b/149/CH4/EX4.43/ques43.sce
@@ -0,0 +1,11 @@
+//ques43

+syms a t

+x=a*(t+sin(t));

+y=a*(1-cos(t));

+s2=diff(y,t,2)/diff(x,t,2);

+s1=diff(y,t,1)/diff(x,t,1);

+

+r=(1+s1^2)^(3/2)/s2;

+disp('The radius of curvature is : ');

+disp(r);

+

diff --git a/149/CH4/EX4.46/ques46.sce b/149/CH4/EX4.46/ques46.sce
new file mode 100755
index 000000000..aa123fa14
--- /dev/null
+++ b/149/CH4/EX4.46/ques46.sce
@@ -0,0 +1,11 @@
+//ques46

+disp('radius of curvature');

+syms a t

+r=a*(1-cos(t));

+r1=diff(r,t,1);

+l=(r^2+r1^2)^(3/2)/(r^2+2*r1^2-r*r1);

+syms r;

+t=acos(1-r/a);

+l=eval(l);

+disp(l);

+disp('Which is proportional to r^0.5');

diff --git a/149/CH4/EX4.47/ques47.sce b/149/CH4/EX4.47/ques47.sce
new file mode 100755
index 000000000..5775b1e4d
--- /dev/null
+++ b/149/CH4/EX4.47/ques47.sce
@@ -0,0 +1,14 @@
+//qus47

+disp('The centre of curvature');

+syms x a y

+y=2*(a*x)^0.5;

+y1=diff(y,x,1);

+y2=diff(y,x,2);

+xx=x-y1*(1+y1)^2/y2;

+yy=y+(1+y1^2)/y2;

+disp('the coordinates x,y are resp :');

+

+disp(xx);

+disp(yy);

+

+

diff --git a/149/CH4/EX4.48/ques48.sce b/149/CH4/EX4.48/ques48.sce
new file mode 100755
index 000000000..d24dccc2d
--- /dev/null
+++ b/149/CH4/EX4.48/ques48.sce
@@ -0,0 +1,14 @@
+//ques48

+disp('centre of curvature of given cycloid ');

+syms a t

+x=a*(t-sin(t));

+y=a*(1-cos(t));

+y1=diff(y,t,1);

+y2=diff(y,t,2);

+xx=x-y1*(1+y1)^2/y2;

+yy=y+(1+y1^2)/y2;

+

+disp('the coordinates x,y are resp :');

+disp(xx);

+disp(yy);

+disp('which another parametric equation of cycloid ');

diff --git a/149/CH4/EX4.5/ques5.sce b/149/CH4/EX4.5/ques5.sce
new file mode 100755
index 000000000..2a705b8e5
--- /dev/null
+++ b/149/CH4/EX4.5/ques5.sce
@@ -0,0 +1,17 @@
+//ques4.1

+//clear

+//cd SCI

+//cd ("..")

+//cd ("..")

+//exec symbolic.sce 

+clc

+disp(' we have to find yn for F=cosxcos2xcos3x ');

+syms x

+F=x/((x-1)*(2*x+3));

+n=input('Enter the order of differentiation :  ");

+disp('calculating  yn ');

+yn=diff(F,x,n)

+disp('the expression for yn is ');

+disp(yn);

+

+

diff --git a/149/CH4/EX4.52/ques52.sce b/149/CH4/EX4.52/ques52.sce
new file mode 100755
index 000000000..a4128a8bc
--- /dev/null
+++ b/149/CH4/EX4.52/ques52.sce
@@ -0,0 +1,10 @@
+//error

+//ques52

+disp('To find the maxima and minima of given function put f1(x)=0');

+syms x

+//x=poly(0,'x');

+f=3*x^4-2*x^3-6*x^2+6*x+1;

+k=diff(f,x);

+x=poly(0,'x');

+k=eval(k);

+

diff --git a/149/CH4/EX4.6/ques6.sce b/149/CH4/EX4.6/ques6.sce
new file mode 100755
index 000000000..8eeda78a0
--- /dev/null
+++ b/149/CH4/EX4.6/ques6.sce
@@ -0,0 +1,17 @@
+//ques4.1

+//clear

+//cd SCI

+//cd ("..")

+//cd ("..")

+//exec symbolic.sce 

+clc

+disp(' we have to find yn for F=cosxcos2xcos3x ');

+syms x a 

+F=x/(x^2+a^2);

+n=input('Enter the order of differentiation :  ");

+disp('calculating  yn ');

+yn=diff(F,x,n)

+disp('the expression for yn is ');

+disp(yn);

+

+

diff --git a/149/CH4/EX4.61/ques61.sce b/149/CH4/EX4.61/ques61.sce
new file mode 100755
index 000000000..5a6537265
--- /dev/null
+++ b/149/CH4/EX4.61/ques61.sce
@@ -0,0 +1,13 @@
+//ques 61

+clc

+disp('to find the assymptote of given curve ');

+syms x y

+f=x^2*y^2-x^2*y-x*y^2+x+y+1;

+//a=degrees(f,x);

+f1=coeffs(f,x,2);

+disp('assymptotes parallel to x-xis is given by f1=0 where f1 is :');

+disp(factor(f1));

+f2=coeffs(f,y,2);

+disp('assymptotes parallel to y-axis is given by f2=0 and f2 is :');

+disp(factor(f2));

+ 
\ No newline at end of file
diff --git a/149/CH4/EX4.7/ques7.sce b/149/CH4/EX4.7/ques7.sce
new file mode 100755
index 000000000..cf107c984
--- /dev/null
+++ b/149/CH4/EX4.7/ques7.sce
@@ -0,0 +1,17 @@
+//ques4.1

+//clear

+//cd SCI

+//cd ("..")

+//cd ("..")

+//exec symbolic.sce 

+clc

+disp(' we have to find yn for F=cosxcos2xcos3x ');

+syms x a 

+F=%e^(x)*(2*x+3)^3;

+//n=input('Enter the order of differentiation :  ");

+disp('calculating  yn ');

+yn=diff(F,x,n)

+disp('the expression for yn is ');

+disp(yn);

+

+

diff --git a/149/CH4/EX4.8/ques8.sce b/149/CH4/EX4.8/ques8.sce
new file mode 100755
index 000000000..8b19bb92f
--- /dev/null
+++ b/149/CH4/EX4.8/ques8.sce
@@ -0,0 +1,23 @@
+//ques4.1

+//clear

+//cd SCI

+//cd ("..")

+//cd ("..")

+//exec symbolic.sce 

+clc

+disp(' y=(sin^-1)x) --sign inverse x ');

+syms x

+y=(asin(x))^2;

+disp('we have to prove (1-x^2)y(n+2)-(2n+1)xy(n+1)-n^2yn ') ;

+//n=input('Enter the order of differentiation ");

+disp('calculating  yn for various values of n');

+for n=1:4

+  

+  F=(1-x^2)*diff(y,x,n+2)-(2*n+1)*x*diff(y,x,n+1)-(n^2+a^2)*diff(y,x,n);

+  disp(n); 

+  disp('the expression for yn is ');

+  disp(F);

+  disp('Which is equal to 0 ');

+

+end

+disp('Hence proved');

diff --git a/149/CH4/EX4.9/ques9.sce b/149/CH4/EX4.9/ques9.sce
new file mode 100755
index 000000000..364058990
--- /dev/null
+++ b/149/CH4/EX4.9/ques9.sce
@@ -0,0 +1,24 @@
+//ques4.1

+//clear

+//cd SCI

+//cd ("..")

+//cd ("..")

+//exec symbolic.sce 

+clc

+disp(' y=e^(a(sin^-1)x)) --sign inverse x ');

+syms x a

+y=%e^(a*(asin(x)));

+disp('we have to prove (1-x^2)y(n+2)-(2n+1)xy(n+1)-(n^2+a^2)yn ') ;

+//n=input('Enter the order of differentiation ");

+disp('calculating  yn for various values of n');

+for n=1:4

+  

+  //yn=diff(F,x,n)

+  F=(1-x^2)*diff(y,x,n+2)-(2*n+1)*x*diff(y,x,n+1)-(n^2+a^2)*diff(y,x,n);

+  disp(n); 

+  disp('the expression for yn is ');

+  disp(F);

+  disp('Which is equal to 0 ');

+

+end

+disp('Hence proved');