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Diffstat (limited to 'getting-started-with-symbolics/script.rst')
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diff --git a/getting-started-with-symbolics/script.rst b/getting-started-with-symbolics/script.rst index b41ab87..e03d85c 100644 --- a/getting-started-with-symbolics/script.rst +++ b/getting-started-with-symbolics/script.rst @@ -4,7 +4,7 @@ .. By the end of this tutorial, you will be able to .. 1. Defining symbolic expressions in sage. -.. # Using built-in costants and functions. +.. # Using built-in constants and functions. .. # Performing Integration, differentiation using sage. .. # Defining matrices. .. # Defining Symbolic functions. @@ -37,7 +37,7 @@ During the course of the tutorial we will learn {{{ Show outline slide }}} * Defining symbolic expressions in sage. -* Using built-in costants and functions. +* Using built-in constants and functions. * Performing Integration, differentiation using sage. * Defining matrices. * Defining Symbolic functions. @@ -73,26 +73,32 @@ So let us try :: var('x,alpha,y,beta') x^2/alpha^2+y^2/beta^2 -taking another example +taking another example :: var('theta') - sin^2(theta)+cos^2(theta) + sin(theta)*sin(theta)+cos(theta)*cos(theta) +Similarly, we can define many algebraic and trigonometric expressions using sage . -Similarly, we can define many algebraic and trigonometric expressions -using sage . +Following is an exercise that you must do. -Sage also provides a few built-in constants which are commonly used in -mathematics . +%% %% Define following expressions as symbolic expressions +in sage? + + 1. x^2+y^2 + #. y^2-4ax + +Please, pause the video here. Do the exercise and then continue. + +The solution is on your screen. + + +Sage also provides a few built-in constants which are commonly used in mathematics . -example : pi,e,infinity , Function n gives the numerical values of all these - constants. +example : pi,e,infinity , Function n gives the numerical values of all these constants. -{{{ Type n(pi) - n(e) - n(oo) - On the sage notebook }}} +{{{ Type n(pi) n(e) n(oo) On the sage notebook }}} @@ -131,6 +137,24 @@ lets try some of them out on the sage notebook. log(e,e) +Following is are exercises that you must do. + +%% %% Find the values of the following constants upto 6 digits precision + + 1. pi^2 + #. euler_gamma^2 + + +%% %% Find the value of the following. + + 1. sin(pi/4) + #. ln(23) + +Please, pause the video here. Do the exercises and then continue. + +The solutions are on your screen. + + Given that we have defined variables like x,y etc .. , We can define an arbitrary function with desired name in the following way.:: @@ -157,13 +181,16 @@ screen var('x') - h(x)=x^2 g(x)=1 + h(x)=x^2 + g(x)=1 f=Piecewise(<Tab> {{{ Show the documentation of Piecewise }}} :: - f=Piecewise([[(0,1),h(x)],[(1,2),g(x)]],x) f + f=Piecewise([[(0,1),h(x)],[(1,2),g(x)]],x) + f + @@ -184,9 +211,7 @@ For a convergent series , f(n)=1/n^2 we can say :: var('n') function('f', n) - f(n) = 1/n^2 - sum(f(n), n, 1, oo) @@ -200,6 +225,18 @@ Lets us now try another series :: This series converges to pi/4. +Following are exercises that you must do. + +%% %% 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. + +Please, pause the video here. Do the exercise(s) and then continue. + Moving on let us see how to perform simple calculus operations using Sage For example lets try an expression first :: @@ -267,6 +304,22 @@ correct :: as we can see when we substitute the value the answer is almost = 0 showing the solution we got was correct. +Following is an (are) exercise(s) that you must do. + +%% %% Differentiate the following. + + 1. sin(x^3)+log(3x) , degree=2 + #. x^5*log(x^7) , degree=4 + +%% %% Integrate the given expression + + sin(x^2)+exp(x^3) + +%% %% Find x + cos(x^2)-log(x)=0 + Does the equation have a root between 1,2. + +Please, pause the video here. Do the exercises and then continue. @@ -286,8 +339,18 @@ Now lets do some of the matrix operations on this matrix A.inverse() +Following is an (are) exercise(s) that you must do. + +%% %% Find the determinant and inverse of : + + A=[[x,0,1][y,1,0][z,0,y]] + +Please, pause the video here. Do the exercise(s) and then continue. + + + -{{{ Part of the notebook with summary }}} +{{{ Show the summary slide }}} So in this tutorial we learnt how to |