LaTeX source for engineering maths methods

houghton@maths.tcd.ie

Problem Sheets

Laplace Transforms

Z Transforms

Problem Sheet 6: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob6.tex and soln6.tex. Taking the Z-transform, the shift theorems.
Problem Sheet 7: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob7.tex and soln7.tex. Solving difference equations.

Systems of differential equations

Problem Sheet 8: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob8.tex and soln8.tex, tanks.eps (a eps of tanks for the mixing problem). Revising eigenvectors. Mixing problems.
Problem Sheet 9: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob9.tex and soln9.tex. Revising eigenvectors. Solving linear systems.
Problem Sheet 10: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob10.tex and soln10.tar (tar file including eps of nodes). Phase diagrams and stationary points.
Problem Sheet 11: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob11.tex and soln11.tar (tar file including eps of nodes). More phase diagrams and stationary points.
Problem Sheet 12: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob12.tex and soln12.tar (tar file including eps of nodes). Drawing spirals, only one eigenvector.
Problem Sheet 13: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob13.tex and soln13.tex. Inhomogeneous equations.

Linearization

Problem Sheet 14: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob14.tex and soln14.tar (tar file including eps of phase diagram). Linearization.
Problem Sheet 15: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob15.tex and soln15.tar (tar file including eps of phase diagram). More linearization.

Series solutions

Problem Sheet 16: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob16.tex and soln16.tex. Series solutions.
Problem Sheet 17: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob17.tex and soln17.tex. More series solutions, method of Frobenius.
Problem Sheet 18: Question 1 is about Legendre polynomials.

Vector calculus

Problem Sheet 18: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob18.tex and soln18.tex. Legendre polynomials, revision of vectors.
Problem Sheet 19: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob19.tex and soln19.tex, 16April2001.eps (an eps showing (sin^3t,cos^3t)), curve11apr2001.epsi (an eps showing a corkscrew spiral). Revision of vectors, lengths of curves.
Problem Sheet 20: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob20.tex and soln20.tex The gradient.
Problem Sheet 21: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob21.tex and soln21.tex The div and curl.
Problem Sheet 22: pdf or ps. Solutions pdf, small pdf, ps or small ps. prob22.tex and soln22.tex The Gauss theorem.

Notes on Z-transforms

Table of Z-transforms. pdf or ps. Ztnew.tex
Notes on Z-transforms, part 1. pdf, ps, short pdf or short ps. note1.tex.
Notes on Z-transforms, part 2. pdf, ps, short pdf or short ps. note2.tex.
Notes on Z-transforms, part 3. pdf, ps, short pdf or short ps. note3.tex.
Notes on Z-transforms, part 4. pdf, ps, short pdf or short ps. note4.tex.

Notes on Laplace transforms

Table of Laplace transforms. pdf or ps laplacet-03-04.tex

Laplace transform of cosh(at)cosh(bt). pdf or ps. 12Oct2001.tex This is an example of using the first shift theorem.
A long example of solving a second order problem using Laplace transforms. pdf, short pdf, ps or short ps 19Oct2001.tex
Examples with complex roots, pdf, short pdf, ps or short ps 6Nov2002.tar includes epsi plot of solution.

Simple example with Heaviside function. pdf or ps 6Nov2001.tex
Another Heaviside function example and a Dirac delta function example, pdf or ps or short pdf or short ps. 18Nov2003.tex

The convolution cost*cost. pdf or ps.
Another convolution example. pdf or ps. 12Nov2002.tex

The Laplace transform of a periodic function. pdf or ps.
The Laplace transform of a saw tooth function. pdf, ps, short pdf or short ps. soln5.tex.