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32 lines
1.4 KiB
Plaintext
32 lines
1.4 KiB
Plaintext
clear all
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; Some symbolic differentiation examples follow.
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; Take the derivative of the absolute value function:
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|x|
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derivative ; The result is the sign function sgn(x), which gives the sign of x.
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repeat echo *
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; Mathomatic can differentiate anything that doesn't require symbolic logarithms.
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y=e^(1+1/x)
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derivative ; The first order derivative is:
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derivative ; The second order derivative is:
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expand fraction ; Perhaps easier to read:
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repeat echo *
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; A Taylor series demonstration:
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y=x_new^n ; x_new is what we want, without using the root operator.
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x_new ; It is easily solved for in Mathomatic.
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y ; But we want an algorithm to compute it without using non-integer exponentiation.
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taylor x_new, 1, x_old ; build the (nth root of y) iterative approximation formula
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solve verifiable x_new ; solve for the output variable
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; That is the convergent nth root approximation formula.
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copy ; "calculate x_old 10000" tests this formula, if you would like to see for yourself.
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replace x_old x_new with x ; make x_old (input) and x_new (output) the same
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x ; make sure the formula was correct by solving for x
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repeat echo *
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; Another Taylor series demo:
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e^x ; enter the exponential function
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taylor x, 10, 0 ; generate a 10th order taylor series of the exponential function
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laplace x ; do a Laplace transform on it
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simplify ; show the structure of the result
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laplace inverse x ; undo the Laplace transform
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compare with 10 ; check the result
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