Maple worksheets on Fourier series
Approximation of functions:
The following Maple worksheets can be downloaded.
They are all compatible with Classic Worksheet Maple 10.
Preliminaries: even and odd functions, adding sine and cosine graphs - FRprelim.mws
- Even and odd functions.
- Examples of even functions.
- Examples of odd functions.
- Products and composites of even and odd functions.
- Integral formulas involving even and odd functions.
- Adding sine and cosine graphs.
An introduction to Fourier series - FRintro.mws
- Introductory examples
- Dot product of functions and orthogonal functions
- The Fourier series coefficients
More period 2*Pi Fourier series examples - FRexamp.mws
- Convergence of a Fourier series
Fourier series for general period 2*Pi functions - FRexamp2.mws
- Integrating a periodic function over a complete period.
- Fourier series coefficients for general periodic functions with period 2*Pi
Fourier series for general periodic functions .. I - FRgen.mws
- Fourier of general periodic functions
- Fourier series .. summary
Fourier series for general periodic functions .. 2 - FRgen2.mws
- Fourier series coefficients for general periodic functions
A procedure for constructing Fourier series: FourierSeries - FRproc.mws
- A procedure for constructing truncated Fourier series: FourierSeries
The procedure attempts to construct a general formula for the coefficients, but if this fails, individual coefficients are calculated separately. When integrals cannot be determined analytically, they are calculated numerically.
Fourier sine and cosine series - FRsincos.mws
- Fourier sine series coefficients
- Fourier cosine series coefficients
Half-range Fourier series - FRhalf.mws
- Half-range sine and cosine series
Fourier series of some functions with infinite discontinuities - FRmore.mws
Fourier series and Chebyshev series - FRcheb.mws
- Chebyshev polynomials
- Introductory example of a Chebyshev series
- More xamples
Further symmetry properties related to Fourier series - FRsym.mws
- Functions which are even or odd with respect to an interval (my terminology)
- Pseudo-even and pseudo-odd functions (my terminology again)
- The Fourier series of a pseudo-even function
- The Fourier series of a pseudo-odd function
- Simplification of the integral formulas for the Fourier series of pseudo-even and pseudo-odd functions
- associated "half-range" type series
DE's with a periodic forcing function and Fourier series - FRDE.mws
- An example of forced damped oscillations
- Forced damped oscillations with a non-sinusoidal periodic forcing function
Fourier series for piecewise linear functions- FRpwlin.mws
- A procedure for constructing a piecewise linear function through given points: convert(.., pwlinear,x)
The complex Fourier series - FRcomplex.mws
- Formulas for the coefficients in the complex Fourier series
- Orthogonality of the functions in the complex Fourier series
- The complex Fourier series via the orthogonality properties
Procedures for Fourier series and Fourier transforms - fourier.zip
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