TRINITY COLLEGE DUBLIN
Engineering Mathematics V (for JS Engineering, option for JS MSISS)
Mathematics Course 3E1 (lecturer: Richard M. Timoney from January 2003)
Notes
Tutorial sheets
Topics
There is a syllabus
in the
online course
descriptions at
http://www.maths.tcd.ie/pub/official/CoursesNow.
 Recap on vector calculus, Greens theorem
and divergence (Gauss') theorem [January 15th, 2003]
 Further recap on vector caclulus,
use of diveregence theorem to derive heat equation [February 2,
2003]
 Picture for introductory linear
programming example [February 26, 2003]
 Lecture notes for 2nd April, 2003
(on graphs).
 Lecture notes for 9th April,
2003 (on basic ideas from complex analysis, start of power series
and radius of convergence).
 Lecture notes for 30th April,
2003 to end of course (on complex integration, Cauchy's theorem and
related topics).
 Hilary Tutorial 1 [January 813, 2003]

Simple PDE problems.
 Hilary Tutorial 2 [January 15February 3,
2003]

Example use of divergence theorem, separation of variables solution
for Heat equation.
 Hilary Tutorial 3 [February 510,
2003]

Wave equation with boundary conditions where one end is fixed and the
other free.
 Hilary Tutorial 4 [February 1217,
2003]

Use of initial conditions (for a wave equation). Nodal lines for a 2D
wave equation of a rectangular region.
 Hilary Tutorial 5 [February 1924,
2003]

Circular drum and Laplacian in polar coordinates.
 Hilary Tutorial 6 [February 26  March 3,
2003]

Types of PDEs (elliptic, hyperbolic, parabolic). Setup linear
programming example.
 Hilary/Trinity Tutorial 7 [March 5  31,
2003]

Simplex algorithm, simple graph theory.
 Trinity Tutorial 8 [April 2  7, 2003]

Graphs, Dijkstra's algorithm.
 Trinity Tutorial 9 [April 9  14, 2003]

Mapping properties of 1/z and z + 1/z. CR equations for log z.
 Trinity Tutorial 10 [April 23  28, 2003]

Trigonometric and hyperbolic functions (complex case), log z. Also
further problems on power series and complex integration.
 Solutions to further problems on power
series and complex integration.
For past examination papers, see the College archive of
exam papers (under Engineering, JS, Engineering Mathematics V).
Updated May 15th, 2003
Richard M. Timoney