Maple worksheets on the convergence of Fourier series |

Approximation of functions:

- Taylor Series
- Fourier Series
- Convergence of Fourier Series
- Bernstein polynomials and polynomial approximation

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Convergence of sequences of functions- FRconvg.mws

- Pointwise and uniform convergence of a sequences of functions
- Examples of pointwise and uniform convergence

Parseval's formula and the Riemann-Lebesgue lemma- FRparsvl.mws

- Approximation of functions by truncated Fourier series
- Mean square error
- Mean square error via the complex Fourier series
- Parseval's formula
- Parseval's formula for a complex valued function
- The Riemann-Lebesgue lemma I
- The Riemann-Lebesgue lemma II

Differentiation of Fourier series- FRdiff.mws

- The coefficients in the Fourier series of the derivative of a periodic function
- Rate of decay of Fourier coefficients
- The Fourier series of two infinitely differentiable periodic functions
- The Fourier series of a twice continuously differentiable periodic function
- The Fourier series of a once continuously differentiable periodic function

Dirichlet's theorem on the convergence of Fourier series- FRdirich.mws

- Absolutely integrable functions
- The Dirichlet kernel
- 1st convergence result
- 2nd convergence result
- Putting the results together - Dirichlet's theorem

Cesaro summation of Fourier series- FRcesaro.mws

- The Cesaro limit of a sequence
- Cesaro summability of a series
- Cesaro summation of Fourier series
- Examples

Fejer's theorem on the convergence of Fourier series- FRfejer.mws

- The Fejer kernel
- Some properties of the Fejer kernel
- Fejer's theorem