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
- Examples

More period 2*Pi Fourier series examples- FRexamp.mws

- Convergence of a Fourier series
- Examples

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
- Examples

Fourier series for general periodic functions .. I- FRgen.mws

- Fourier of general periodic functions
- Fourier series .. summary
- Examples

Fourier series for general periodic functions .. 2- FRgen2.mws

- Fourier series coefficients for general periodic functions
- Examples

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
- Examples
- Fourier cosine series coefficients
- Examples

Half-range Fourier series- FRhalf.mws

- Half-range sine and cosine series
- Examples

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)- Examples

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