/
firststeps.wxm
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firststeps.wxm
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/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 12.04.0 ] */
/* [wxMaxima: title start ]
First Steps in Maxima
[wxMaxima: title end ] */
/* [wxMaxima: section start ]
symbolic algebra
[wxMaxima: section end ] */
/* [wxMaxima: input start ] */
(x+2*y)^4;
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
expand(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
factor(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: section start ]
differentiation
[wxMaxima: section end ] */
/* [wxMaxima: input start ] */
diff(sin(x)*cos(x), x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
trigsimp(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
diff(%,x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
diff(sin(x)*cos(x),x,2);
/* [wxMaxima: input end ] */
/* [wxMaxima: section start ]
finite fourier sums
[wxMaxima: section end ] */
/* [wxMaxima: input start ] */
trigreduce(sin(x)^5);
/* [wxMaxima: input end ] */
/* [wxMaxima: section start ]
integration
[wxMaxima: section end ] */
/* [wxMaxima: input start ] */
integrate((x+1)/(x^3-8),x);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
can avoid being asked questions with assumptions
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
assume(m>4);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
integrate(x^m*(a+b*x)^3,x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
diff(%,x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
factor(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
integrate(x/(x^3+1),x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
diff(%,x);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
eek!, but help is at hand
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
ratsimp(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: subsect start ]
another example of integration, differentiation, simplification
[wxMaxima: subsect end ] */
/* [wxMaxima: input start ] */
integrate(exp(a*x)*sin(x)*cos(x),x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
diff(%,x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
ratsimp(%);
/* [wxMaxima: input end ] */
/* [wxMaxima: subsect start ]
giving it a hand
[wxMaxima: subsect end ] */
/* [wxMaxima: input start ] */
fn(x):=1/((x-3)^4+1/2);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
int: integrate(fn(x),x);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
failzor! can change variables by hand
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
inty: changevar(int,x-3-y,y,x);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
I don't get this bit:
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
ev(inty,integrate);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
now back substitute
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
sfx: %, y=x-3;
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
and try various simplifications
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
sfx2: ratsimp(sfx);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
sfx3: radcan(sfx2);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
sfx4: logcontract(sfx3);
/* [wxMaxima: input end ] */
/* [wxMaxima: comment start ]
looks like that's about as good as it gets
[wxMaxima: comment end ] */
/* [wxMaxima: input start ] */
wxplot2d([fn,sfx4],[x,0,10]);
/* [wxMaxima: input end ] */
/* [wxMaxima: subsect start ]
look under the hood, as it were
[wxMaxima: subsect end ] */
/* [wxMaxima: input start ] */
integrate(1/(x^3+1), x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
diff(%, x);
/* [wxMaxima: input end ] */
/* [wxMaxima: input start ] */
ratsimp(%);
/* [wxMaxima: input end ] */
/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$