Skip to main content
J
JohnArcher10-Marble
10-Marble
December 16, 2014
Solved

Use and properties of the Series command.

  • December 16, 2014
  • 6 replies
  • 3017 views

Good morning, all.

I need some guidance on the use of the Series command.

I uinderstand the stricture of not expanding a Talyors Series too far, but I have a quotient with numerator and denonminator having many terms involving exp(x), cosh(x) etc, all based upon the exponential property. These should be solvable using expansions of exp(x) and the binomial theorem.

Does Mathcad 15 or Prime have such built-in functionality built into Series to avoid Taylor?

My equations contain data spanning dc to nanoseconds and I need more than a three term expansion.

Practically the quotient expands into a ratio of terms involving root(s), the coomplex variable. After rationaliziing, I find thr LHP roots of the denominator and use a contour integral solution.

I really need some help, here. Still pushing boundaries and learning at age 79!

Thanks, John Archer.

Best answer by StuartBruff

Have you tried using the symbolic rewrite keyword to express your initial result in terms of exp?

Is there a simpler way of deriving the expression (are you using Laplace, for example)?

Stuart

6 replies

R
RichardJ19-Tanzanite
19-Tanzanite
December 16, 2014

I'm not sure what you mean by "avoiding Taylor". The symbolic series keyword expands a function as a Taylor series. If you need more than three terms use Taylor,N, where N is the power of the highest term. Does that solve your problem?

series.png

J
JohnArcher10-MarbleAuthor
10-Marble
December 17, 2014

Thanks ror tour prompt reply, Richard.

Because of the circuit properties (high speed transitions on mis-terminated tramsmission lines for arc fault suppression) the denominator and numerator of my quotient each produce a series in mutiples of root(s), which cleans up after Simplification. A 15th order Series command finally produces an 8th order quotient and a result that makes sense. I know that I will later need at least twice this resolution for the second half of the process. Mathcad 15 is very slow for very high order series involving cosh or sinh and complex arguements.

Mathcad Help and my books warn of errors if a series expansion is pushed too far. How do I determine "too far"?

Exp(x) is a fundamental series that does not depend on anyone's series approximation method. By inference, are sine and cosh, with complex arguements, also immune to expansion errors using Mathcad if expanded correctly? Would 64bit Prime give a better or faster result than 32bit Mathcad 15?

I already have a provisional patent on this device and will file for the full patent shortly. Before i spend several thousand dollars of my retirement money on this application, I want to make sure that I am doing things correctly.

Sorry to be a pain, but I am a creative magnetics engineer, not a math wizaerd.

John Archer

S
StuartBruff23-Emerald VAnswer
23-Emerald V
December 17, 2014

Have you tried using the symbolic rewrite keyword to express your initial result in terms of exp?

Is there a simpler way of deriving the expression (are you using Laplace, for example)?

Stuart

Terms & ConditionsAccessibility statement