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39 * Performing Integration, differentiation using Sage. |
39 * Performing Integration, differentiation using Sage. |
40 * Defining matrices. |
40 * Defining matrices. |
41 * Defining symbolic functions. |
41 * Defining symbolic functions. |
42 * Simplifying and solving symbolic expressions and functions. |
42 * Simplifying and solving symbolic expressions and functions. |
43 |
43 |
44 Amongst a lot of other things, Sage can do Symbolic Math and we shall |
44 In addtion to a lot of other things, Sage can do Symbolic Math and we shall |
45 start with defining symbolic expressions in Sage. |
45 start with defining symbolic expressions in Sage. |
46 |
46 |
47 Hope you have your Sage notebook open. If not, pause the video and |
47 Have your Sage notebook opened. If not, pause the video and |
48 start you Sage notebook. |
48 start you Sage notebook right now. |
49 |
49 |
50 On the sage notebook type:: |
50 On the sage notebook type:: |
51 |
51 |
52 sin(y) |
52 sin(y) |
53 |
53 |
62 sin(y) |
62 sin(y) |
63 |
63 |
64 Sage simply returns the expression. |
64 Sage simply returns the expression. |
65 |
65 |
66 Sage treats ``sin(y)`` as a symbolic expression. We can use this to do |
66 Sage treats ``sin(y)`` as a symbolic expression. We can use this to do |
67 symbolic maths using Sage's built-in constants and expressions. |
67 symbolic math using Sage's built-in constants and expressions. |
68 |
68 |
69 Let us try out a few examples. :: |
69 Let us try out a few examples. :: |
70 |
70 |
71 var('x,alpha,y,beta') |
71 var('x,alpha,y,beta') |
72 x^2/alpha^2+y^2/beta^2 |
72 x^2/alpha^2+y^2/beta^2 |
285 f.substitute(phi=root) |
285 f.substitute(phi=root) |
286 |
286 |
287 as we can see when we substitute the value the answer is almost = 0 showing |
287 as we can see when we substitute the value the answer is almost = 0 showing |
288 the solution we got was correct. |
288 the solution we got was correct. |
289 |
289 |
290 Following is an (are) exercise(s) that you must do. |
290 Following are a few exercises that you must do. |
291 |
291 |
292 %% %% Differentiate the following. |
292 %% %% Differentiate the following. |
293 |
293 |
294 1. sin(x^3)+log(3x) , degree=2 |
294 1. sin(x^3)+log(3x) , degree=2 |
295 #. x^5*log(x^7) , degree=4 |
295 #. x^5*log(x^7) , degree=4 |