Lecture  Readings  Topics  Assignments 

1  5.1, 5.2  Course overview; Laplace transforms, introduction.  Problems Read Entrance guide and try the problems 
2  5.3, 5.4  Laplace transforms and applications to ode.  Problems Solutions, problem set 1 
3  5.5, 5.6, 4.1, 4.2  Laplace transforms and applications to ODE  Problem Set 2 
4  4.2  Taylor series, radius of convergence.  Problem Set 2 
5  4.3  Method of Frobenius.  Problem Set 2 Solutions, problem set 2 Solution to problem 7 e) in section 4.2 
6  4.3, 4.5 (Gamma function only)  Method of Frobenius Fully worked example  Problem Set 3 
7  4.3 and 4.6  Method of Frobenius, Bessel functions;  
8  4.6  Bessel functions  Problem Set 4 
9, 10/3  7.27.3  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  9.69.10  Introduction to vector spaces; vector spaces of functions; inner product; orthonormal bases. 

17, 10/31  17.117.2  Vector spaces of functions; best approximation Intro to Fourier Series. Handout on GramSchmidt 

18; 11/2  17.3  Introduction to Fourier series.  
19, 11/7  17.417.6  Half and quarter range expansions; Manipulating Fourier series. 

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

21, 11/14  17.8  More SturmLiouville theory.  
22, 11/16  Exam II  November 16  Review problems Review problem solutions, part I Review problem solutions, part II 
23, 11/21  18.118.3  Separation of variables; application of SturmLiouville theory. 

24, 11/28  18.118.3  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  19.119.2  The wave equation.  
28, 12/12  19.119.2  The wave equation. 