--- a/getting-started-with-symbolics/script.rst Wed Nov 10 12:23:40 2010 +0530
+++ b/getting-started-with-symbolics/script.rst Wed Nov 10 17:19:54 2010 +0530
@@ -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 @@
{{{ 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 @@
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 .
-Sage also provides a few built-in constants which are commonly used in
-mathematics .
+Following is an exercise that you must do.
-example : pi,e,infinity , Function n gives the numerical values of all these
- constants.
+%% %% 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.
-{{{ Type n(pi)
- n(e)
- n(oo)
- On the sage notebook }}}
+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.
+
+{{{ Type n(pi) n(e) n(oo) On the sage notebook }}}
@@ -131,6 +137,24 @@
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 @@
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 @@
var('n')
function('f', n)
-
f(n) = 1/n^2
-
sum(f(n), n, 1, oo)
@@ -200,6 +225,18 @@
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 @@
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 @@
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