## Syllabus  Math 527 -- Fall 2006

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All section numbers refer to the course text: Greenberg, Advanced Engineering Mathematics, 2nd edition.
The due dates for handing in assignments will be given in class.
THIS SYLLABUS IS SUBJECT TO CHANGE AS THE SEMESTER PROGRESSES; reload this page frequently to make sure you are not reading an out-of-date, cached version.

5.1, 5.2 Course overview; Laplace transforms, introduction. Problems
Read Entrance guide and try the problems
5.3, 5.4 Laplace transforms and applications to ode. Problems
Solutions, problem set 1
5.5, 5.6, 4.1, 4.2 Laplace transforms and applications to ODE Problem Set 2
4.2  Taylor series, radius of convergence. Problem Set 2
4.3  Method of Frobenius. Problem Set 2
Solutions, problem set 2
Solution to problem 7 e) in section 4.2
4.3, 4.5 (Gamma function only) Method of Frobenius Fully worked example Problem Set 3
4.3 and 4.6 Method of Frobenius, Bessel functions;
4.6 Bessel functions Problem Set 4
9, 10/3 7.2--7.3 Phase plane; phase portraits, singular points, stability.
10, 10/5 7.3 Elementary singularities; examples.
11, 10/10 7.4 Phase plane applications.
Worked example of phase portrait
analysis of a nonlinear planar system.

12, 10/12 FIRST EXAM, IN CLASS Review problems for exam
13, 10/17 7.3 Phase portraits of linear systems, continued
14, 10/19 7.4 Phase portraits of nonlinear system
15, 10/24 7.5 Limit Cycles
16, 10/26 9.6--9.10 Introduction to vector spaces; vector spaces of functions;
inner product; orthonormal bases.

17, 10/31 17.1--17.2 Vector spaces of functions; best approximation
Intro to Fourier Series.
Handout on Gram-Schmidt

18; 11/2 17.3 Introduction to Fourier series.
19, 11/7 17.4--17.6 Half and quarter range expansions;
Manipulating Fourier series.

20, 11/9 17.7, 11.3 Symmetric matrices. Sturm-Liouville theory.
Lecture Notes for this lecture
Worked example of Fourier series calculations

21, 11/14 17.8 More Sturm-Liouville theory.
22, 11/16 Exam II November 16 Review problems
Review problem solutions, part I
Review problem solutions, part II
23, 11/21 18.1--18.3 Separation of variables;
application of Sturm-Liouville theory.

24, 11/28 18.1--18.3 Separation of variables continued;
Review.

25, 11/30 17.9,17.10, 18.4 Fourier integral and Fourier transform.
26, 12/5 18.4 Fourier transform method continued.
27, 12/7 19.1--19.2 The wave equation.
28, 12/12 19.1--19.2 The wave equation.