Maple worksheets on Laplace transforms |

Mathematical transforms:

- Laplace transforms
- Fourier transforms

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Integration prerequisites for Laplace transforms- intparts.mws

- Integration by parts
- Improper integrals

The Laplace transform-laplace.mws

- Introduction to the Laplace transform
- Laplace transforms of some standard functions
- Linearity of the Laplace transform operator

The inverse Laplace transform-invlaplace.mws

- The inverse Laplace transform operator.
- Some examples of inverse Laplace transforms.
- Provisional table of inverse Laplace transforms.

The Laplace transform method for solving some first order DE's-lapDE.mws

- The differentiation formula: L[f '(t)] = s L[f(t)] - f(0).
- Examples to illustrate the differentiation formula.
- Examples of solving 1st order DE's by the Laplace transform method.

Using partial fractions to find inverse Laplace transform-invlaplace2.mws

- Partial fractions and inverse Laplace transforms.
- Examples.
- Examples of solving 1st order DE's by the Laplace transform method.
- Partial fraction expansions involving irreducible quadratic factors in the denominator.
- More examples of solving 1st order DE's by the Laplace transform method.

The shift formula for the Laplace Transform-shift.mws

- The shift formula: If L[f(t)] = F(s), then L[exp(a t) f(t)] = F(s - a).
- Inverse Laplace transforms using the shift formula.
- Partial fraction expansions for the case of repeated factors in the denominator.
- More examples of solving 1st order DE's by the Laplace transform method.

Solving 2nd order DE's by the Laplace transform method-lapDE2.mws

- Extension of the differentiation formula for the Laplace transform operator.
- Examples of solving 2nd order DE's by the Laplace transform method.

More formulas for Laplace Transforms-morelap.mws

- An integration formula for the inverse Laplace transform operator.
- A 2nd differentiation formula for the Laplace transform.
- A 2nd integration formula for the Laplace transform.
- More standard Laplace transforms.
- Some standard inverse Laplace transforms.

Laplace transforms of piecewise functions-piecewise.mws

- The unit step function H(t-a) and its Laplace transform.
- The second shift formula: L[H(t-a) f(t)] = exp(-a s) L[f(t+a)].
- Examples of finding Laplace transforms using the 2nd shift formula.
- Finding Laplace transforms of piecewise functions.
- Inverse version of the second shift formula.

Differential equations involving piecewise functions-lapDE3.mws

- Differential equations arising from L-R and R-C series circuits
- Examples of differential equations involving piecewise functions

Laplace transforms of piecewise periodic functions-periodic.mws

- Periodic functions
- General method for finding Laplace transforms of periodic functions.
- Examples of Laplace transforms of piecewise periodic functions:

- Laplace transform of a square wave
- Laplace transform of a sawtooth wave
- Laplace transform of a triangular wave
- Laplace transform of the full-wave rectification of a sine wave
- Laplace transform of the half-wave rectification of a sine wave
- Laplace transform of a parabolic wave

Differential equations involving piecewise periodic functions-lapDE4.mws

- Laplace transforms of periodic functions as infinite sums.
- Differential equations with a piecewise periodic "forcing function":

- A first order DE with a square-wave "forcing function"
- A first order DE with a half-wave rectified sine wave "forcing function"
- A first order DE with a triangular wave "forcing function"

Another differential equation involving a piecewise periodic function-lapDE5.mws

- The Laplace transform of an alternating triangular wave.
- A 2nd order differential equation with an alternating triangular wave "forcing function".

Yet another differential equation involving a piecewise periodic function-lapDE6.mws

- The Laplace transform of an alternating trapezoidal wave.
- 2nd order differential equations with an alternating trapezoidal wave "forcing function".

A procedure for solving some 1st order differential equations by the Laplace transform method-desolveLP.mws

- A procedure for solving first order DE's by using Laplace transforms -
desolveLP.- Examples

A procedure for solving some 2nd order differential equations by the Laplace transform method-desolveL2.mws

- A procedure for solving 2nd order DE's by using Laplace transforms -
desolveL2.- Examples

Procedures for differential equations- DEsol.zip