Mathematical transforms:

• Laplace transforms
• Fourier transforms

The following Maple worksheets can be downloaded.

They are all compatible with Classic Worksheet Maple 10.

Introduction to Fourier transforms - FRtrans.mws

• Explanation of the Fourier transform via a limiting process 
• The real and imaginary parts of a Fourier transform
• Examples of Fourier transforms

Some properties of the Fourier transform - FRtrans2.mws

• Shifting and symmetry properties of the Fourier transform
• Examples

Differentiation formulas for the Fourier transform - FRTdiff.mws

• Differentiation formulas for the Fourier transform
• Examples

Approximations for Fourier integrals - FRTint.mws

• Fourier integrals
• Examples

Fourier transforms of Hermite functions - FRTherm.mws

• The Schrodinger wave equation
• Hermite polynomials
• Solutions for the Schrodinger equation
• Fourier transforms of Hermite functions

The Dirac delta function - delta.mws

• The Dirac delta function
• The sampling property of the Dirac delta function
• The Dirac delta function as a limit of a general class of functions

Distributions - distrib.mws

• Test functions
• Weak convergence
• Construction of test functions
• The concept of a distribution
• Operations with distributions
• Functions as distributions

Heaviside's step function - step.mws

• The integral of the Dirac delta function
• The step function as a distribution
• The integral property of the Heaviside step function

The Fourier transform of the delta function and the step function - FRTdelta.mws

• The Fourier transform of the delta function
• The Fourier transform of the step function

Convolution and the Fourier transform - convolution.mws

• The convolution of two functions
• The convolution theorem
• Examples

The derivative of the Dirac delta function - diff_delta.mws

• The derivative of the Dirac delta function

The Fourier transform of periodic functions - FRTprdc.mws

• The Fourier transform of a periodic function.
• The Fourier transforms of  cos ax and sin ax.
• The Fourier transforms of  cos³ ax.
• The Fourier transform of a train of pulses.
• The Fourier transform of | sin x |.

The discrete fast Fourier transform - FFTintro.mws

• Derivation of the discrete Fourier transform and its inverse
• Formulas for the discrete Fourier transform and its inverse
• The fast Fourier transform algorithm
• First versions of the fast Fourier transform algorithm
• Examples

A procedure for the discrete fast Fourier transform - FFTproc.mws

• Economical fast Fourier transform of real data
• Procedures for discrete Fourier transforms and inverse transforms: fft, ifft
• Comparison of a discrete Fourier transform and Fourier transform coefficients
• Adding noise to periodic data, smoothing data

Procedures for Fourier series and Fourier transforms - fourier.zip

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