Catalog data:
(Systems of) first order equations, Laplace transforms, series solution, Sturm-Liouville
and partial differential equations. |
Course year:
BSc 2nd year
Semester: 2A
Hours p/w: 4
Other hours:
Assessment: Written
Assessm.period(s): 2A, 2B
(see academic calendar) |
Prerequisites: |
Follow
up: |
Detailed
description of topics:
First order differential equations,
linear equations, separable equations, exact equations and integrating factors,
homogeneous equations. Higher order linear equations, fundamental solution and the
Wronskian, the method of undetermined coefficients, the method of variation of parameters.
Systems of first order linear equations, homogeneous linear systems with constant
coefficients, complex and repeated eigenvalues, fundamental matrices, nonhomogeneous
linear systems.
The Laplace transform, solution of
initial value problems, impulse functions, the convolution integral. Series solution of
second order linear equations, regular singular points, Bessel's
equation.
Partial differential equations and
Fourier series. Solution of heat conduction problems, the wave equation, Laplace's
equation. Sturm-Liouville boundary value problems, eigenvalue and eigenfunctions. Series
of orthogonal functions.
|
Course
material:
Elementary differential equations and boundary
value problems 5th/6th edition, William E.\ Boyce, Richard C.\ DiPrima, John Wiley &
Sons, Inc. ISBN 0-471-57019-2
|
References
from literature:
Elementary differential equations and boundary
value problems 5th/6th edition , William E.\ Boyce, Richard C.\ DiPrima, John Wiley \&
Sons, Inc. ISBN 0-471-57019-2
|
Remarks
(specific information about assesment, entry requirements, etc.): |
Goals:
To introduce the basic techniques to solve
differential equations, as used in mechanical engineering and marine technology.
|
Computer
use: |
Laboratory
project(s):
Maple and Matlab.
|
Design
content: |
Percentage
of design: 0% |