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

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