st-scripts: comparison getting-started-with-symbolics/script.rst

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 .. ----------
 .. 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.
 .. # Simplifying and solving symbolic expressions and functions.
 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.
 * Simplifying and solving symbolic expressions and functions.
 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
+%% %%  Define following expressions as symbolic expressions
-mathematics .
+in sage?
-example : pi,e,infinity , Function n gives the numerical values of all these
+1. x^2+y^2
-constants.
+#. y^2-4ax
-{{{ Type n(pi)
+Please, pause the video here. Do the exercise and then continue.
-	n(e)
-	n(oo)
+The solution is on your screen.
-On the sage notebook }}}
+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.
+{{{ Type n(pi) n(e) n(oo) On the sage notebook }}}
 If you look into the documentation of function "n" by doing
 sin(pi/2)
 arctan(oo)
 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.::
 ::
 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
 We can also define functions which are series
 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)
 Lets us now try another series ::
 sum(f(n), n, 1, oo)
 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 ::
 f.substitute(phi=root)
 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.
 Lets us now try some matrix algebra symbolically ::
 ::
 A.det()
 A.inverse()
+Following is an (are) exercise(s) that you must do.
-{{{ Part of the notebook with summary }}}
+%% %% 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.
+{{{ Show the summary slide }}}
 So in this tutorial we learnt how to
 * We learnt about defining symbolic expression and functions.

changeset 442	a9b71932cbfa
parent 376	3e947a3fa83e
child 458	9a1c5d134feb