Wed, 21 Jan 2009, 10:34:05 EST
Created on: Sat, 27 Dec 2008, 20:15:39 EST
EGM 6322 Principles of Engineering Analysis 2,
Dr. L. Vu-Quoc
Partial differential equations (elliptic, parabolic, hyperbolic),
exact solution methods, approximate analytical solution methods.
The objectives of this course is to develop analytical methods
to solve partial differential equations with applications in many
areas of engineering (solids, fluids, electromagnetics, heat).
Text and other resources:
Overview on analytical methods of solving PDEs, caveat for PDEs
Nonlinear, quasilinear, linear PDEs.
Classification of second-order PDEs.
Transformation methods: Reduction to first-order systems, changing variables, curvilinear
coordinates, Euler transformation, Kirchhoff transformation, von Mises transformation, Prandtl
transformation, hodograph transformation, Legendre transformation.
Separation of variables, free-boundary problems
Exact methods for both ODEs and PDEs:
method of undertermined coefficients,
eigenfunction expansions (with advanced application to singularity computation),
method of images,
integral transforms (for finite and infinite intervals),
Exam methods for PDEs:
Conformal mappings for 2-D Laplace equation,
Poisson formula to solve Laplace equation on a circle (with application in conformal mappings),
Duhamel's principle for linear parabolic and hyperbolic PDEs,
method of characteristics for hyperbolic PDEs,
exact solutions for the wave equation,
method of descent for hyperbolic PDEs,
hodograph transformation (application in fluid mechanics),
Legendre transformation (also application in dynamics and thermodynamics),
Approximate analytical methods:
Multiple scales, application to singularity computation (fracture mechanics, fluid
mechanics, electromagnetics), advanced application of eigenfunction expansions.
Tentatively, homework/projects and class participation including bonuses (50%),
Exam 1 (25%), Exam 2 (25%).
Adjustments to this grade determination and to the weights could be made during the course in
consultation with the students.
Handbook of Differential Equations,
Third Edition, Academic Press, 1998.
QA371.Z88 1989, 2 copies, one for in-library use.
L. Lapidus and G.F. Pinder,
Numerical Solution of Partial Differential Equations in Science and Engineering
Q172 .L36 1982
W.E. Boyce and R.C. DiPrima,
Elementary Differential Equations and Boundary Value Problems,
QA371 .B773 2001
Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation
Partial Differential Equations in Mechanics 2 : The Biharmonic Equation, Poisson's Equation (Vol 2) (Soft Cover)
QA805 .S45 2000
Homework / Projects:
There will be HW assignments, which are to be solved following
Cooperative Learning Techniques.
HW should be thought of as mini
projects, which include ``hand solution'' with the help of
Matlab and the use of the Matlab codes that come with
Students will also be asked to develop their own Matlab codes.
For a tutorial on how to use Matlab, see
for more details.
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