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Diffstat (limited to 'getting_started_with_symbolics/script.rst')
| -rw-r--r-- | getting_started_with_symbolics/script.rst | 68 |
1 files changed, 53 insertions, 15 deletions
diff --git a/getting_started_with_symbolics/script.rst b/getting_started_with_symbolics/script.rst index 93bcde6..5df89fa 100644 --- a/getting_started_with_symbolics/script.rst +++ b/getting_started_with_symbolics/script.rst @@ -140,7 +140,7 @@ Pause the video here, try out the following exercise and resume the video. .. R11 - Define following expressions as symbolic expressions in Sage. +Define following expressions as symbolic expressions in Sage. 1. x^2+y^2 #. y^2-4ax @@ -195,7 +195,7 @@ constants. For this we have to pass an argument -- digits. Apart from the constants Sage also has a lot of built-in functions like ``sin``, ``cos``, ``log``, ``factorial``, ``gamma``, ``exp``, -``arcsin`` etc ... +``arctan`` which stands for arctangent etc ... Lets try some of them out on the Sage notebook. @@ -218,13 +218,13 @@ Pause the video here, try out the following exercise and resume the video. .. R18 - Find the values of the following constants upto 6 digits precision +Find the values of the following constants upto 6 digits precision 1. pi^2 #. euler_gamma^2 - Find the value of the following. +Find the value of the following. 1. sin(pi/4) #. ln(23) @@ -233,10 +233,15 @@ Pause the video here, try out the following exercise and resume the video. {{{continue from paused state}}} {{{ show slide showing solution 2 }}} - + .. R19 The solutions are on your screen. + + n(pi^2,digits=6) + n(sin(pi/4)) + n(log(23,e)) + <pause for sometime,then continue> .. R20 @@ -273,7 +278,9 @@ Evaluating this function f for the value x=pi returns pi/2. We can also define functions that are not continuous but defined piecewise. Let us define a function which is a parabola between 0 -to 1 and a constant from 1 to 2 . Type the following +to 1 and a constant from 1 to 2 .We shall use the function ``Piecewise`` +which returns a piecewise function from a list of pairs. +Type the following .. L23 :: @@ -335,13 +342,13 @@ Pause the video here, try out the following exercise and resume the video. .. R28 - Define the piecewise function. +Define the piecewise function. f(x)=3x+2 when x is in the closed interval 0 to 4. f(x)=4x^2 between 4 to 6. - Sum of 1/(n^2-1) where n ranges from 1 to infinity. +Sum of 1/(n^2-1) where n ranges from 1 to infinity. .. L29 @@ -351,11 +358,23 @@ Pause the video here, try out the following exercise and resume the video. .. R29 The solution is on your screen + +var(’x’) +h(x)=3*x+2 +g(x)= 4*x^2 +f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x) +f + +var(’n’) +f=1/(n^2-1) +sum(f(n), n, 1, oo) + <pause for sometime,then continue> .. R30 -Moving on let us see how to perform simple calculus operations using Sage +Moving on let us see how to perform simple calculus operations +using Sage For example lets try an expression first @@ -414,7 +433,8 @@ Many a times we need to find factors of an expression, we can use the .. R35 -One can simplify complicated expression by using the function ``simplify``. +One can simplify complicated expression by using the +function ``simplify``. .. L35 :: @@ -457,7 +477,7 @@ correct .. R39 -as we can see when we substitute the value the answer is almost = 0 showing +As we can see when we substitute the value the answer is almost = 0 showing the solution we got was correct. Pause the video here, try out the following exercise and resume the video. @@ -470,16 +490,16 @@ Pause the video here, try out the following exercise and resume the video. .. R40 - Differentiate the following. +Differentiate the following. 1. sin(x^3)+log(3x) , degree=2 #. x^5*log(x^7) , degree=4 - Integrate the given expression +Integrate the given expression sin(x^2)+exp(x^3) - Find x +Find x cos(x^2)-log(x)=0 Does the equation have a root between 1,2. @@ -491,6 +511,18 @@ Pause the video here, try out the following exercise and resume the video. .. R41 The solution is on your screen + +var(’x’) +f(x)= x^5*log(x^7) +diff(f(x),x,5) + +var(’x’) +integral(x*sin(x^2),x) + +var(’x’) +f=cos(x^2)-log(x) +find_root(f(x)==0,1,2) + <pause for sometime,then continue> .. R42 @@ -536,11 +568,17 @@ Pause the video here, try out the following exercise and resume the video. .. L46 {{{continue from paused state}}} -{{{ show slide showing solution 4 }}} +{{{ show slide showing solution 5 }}} .. R47 The solution is on your screen + +var(’x,y,z’) +A=matrix([[x,0,1],[y,1,0],[z,0,y]]) +A.det() +A.inverse() + <pause for sometime,then continue> .. L48 |