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:
wi135wb |
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:
The student must be able to:
-
Distinguish ordinary & partial differential equations
-
Distinguish linear & nonlinear ordinary differential
equations
-
Solve linear first-order differential equations
-
Solve separable, exact and homogeneous first-order
differential equations
-
Find simple integrating factors
-
Solve homogeneous linear differential equations with
constant coefficients
-
Determine particular solutions for inhomogeneous linear
differential equations by means of the method of indeterminate
coefficients
-
Determine of particular solutions of inhomogeneous linear
differential equations by means of the method of variation of constants
-
Solve simple differential equations by means of the
Laplace transform
-
Solve simple integral equations by means of convolution
integrals
-
Solve homogeneous systems of linear differential
equations with constant coefficients
-
Determine particular solutions of inhomogeneous systems
of linear differential equations by means of the method of indeterminate
coefficients
-
Determine particular solutions of inhomogeneous systems
of linear differential equations by means of the method of variation of
constants
-
Determine stability properties of solutions of simple
nonlinear autonomous systems of differential equations
-
Find the Fourier (cosine and/or sine) series of a
function
-
Solve a simple heat or diffusion equation by means of the
method of separation of variables
-
Solve a simple wave equation by means of the method of
separation of variables
-
Solve a simple Laplace or potential equation by means of
the method of separation of variables
|
Computer
use: |
Laboratory
project(s):
Maple and Matlab.
|
Design
content: |
Percentage
of design: 0% |