Lecture  Readings  Topics  Assignments  

1  5.1, 5.2  Course overview; Laplace transforms, introduction.  5.2: 1, 58, 10;Solutions Entrance problems Entrance problems solutions 

2  5.3, 5.4  Laplace transforms and applications to ode.  5.3: 1, 3b,e,f 10a,c,d; 5.4: 1a,b,d,g,h,j,l,m,q,r,s,v Hand in 5.4 1(h),(l),(m) Solutions 

3  5.5, 5.6, 4.1, 4.2  Dirac delta functions and Laplace transforms.  5.5: 1a,b,g, 5a,b,d,f 5.6: 1a,c,d,e,i Hand in: 5.5: 5(f); 5.6: 1(c),(d), (e) Solutions 

4  4.2  Taylor series, radius of convergence.  4.2: 1,3,9 Hand in 1(c), (j); 3(e),(l) Solutions 

5  4.3  Method of Frobenius.  4.3 1, 2, 3, 6; Hand in 1(b)(n), 2(a), 6(b) Solutions 

6  4.5, 4.6  Method of Frobenius, continued Fully worked example from lecture  4.3 1, 2, 3, 6; Hand in 1(b)(n), 2(a), 6(b)  
7  4.6 continued, 7.12.  Bessel and Hankel functions;  4.6: 13, 57, 12a)d); Hand in 2, 6(a), 12(b) Solutions. 

8  7.27.3  Phase plane; phase portraits, singular points, stability.  7.2: 1,4,5,10; 7.3: 1. Hand in 7.2: 4(b), 5(d), 10. Solutions.  
9  7.3  Elementary singularities; examples.  7.3: 1, 9, 11. Hand in 9(a), (b): Solutions.  
10  7.4  Phase plane applications. Worked example of phase portrait analysis of a nonlinear planar system. 
7.4: 2(a)(e), (j)(n); Hand in 2(c) (e) Sketch a graph of the trajectories near each singular point, if you have enough information to do so. Solutions. 

11  7.5  Limit cycles; van der Pol equation; Exam 1 review.  7.5 4. Hand in 4(c). Solutions.  
Some review problems  
12  October 11!  EXAM #1.  
13  Handout [pp. 500519], Web notes of Prof. Chan 
Regular and singular perturbation expansions.  Problem in Prof. Chan's notes; Hand this problem in. Handout: 25.8, 25.9, 25.10 Solutions. 

14  Catch up  
15; Oct. 20.  9.69.10  Introduction to vector spaces; vector spaces of functions; inner product; orthonormal bases. 
9.6: 1, 1012, 14; 9.9: 11. 12 (b,c). Hand in 9.6: 12, 9.9:
11 Solutions 

16; Oct. 25  17.117.2  Vector spaces of functions; best approximation.  17.2: 5(ah), 12(all). Hand in 5 (b),(d), 12(j),(l).  
17; Oct. 27.  17.3  Introduction to Fourier series.  17.3: 1, 4(a,c,g,l), 8. Hand in 1, 4(a,c,g,l) Solutions 

18; Nov. 1;  17.417.6  Half and quarter range expansions; Manipulating Fourier series. 
17.4 2(ad); 17.5: 2(a,b), 17.6: 2(ad) Hand in 17.4: 2(b,d), 17.5: 2(b), 17.6: 2(a,b,c). Solutions, 17.4 Solutions, 17.5, 17.6 

19; Nov. 3.  17.7, 11.3  Symmetric matrices. SturmLiouville theory.  11.3: 1(a,b,e), 15(a,b); 17.7: 1(all), 8, 9(ac) Hand in 1(cf), 9(ac) Solutions, 17.7  
20; Nov. 8.  17.8  More SturmLiouville theory.  17.8: 2(ad),4,5; Hand in 2(a,b), 4, 5 Solutions, part I Solutions, part II 

21; Nov. 10.  18.118.3  Separation of variables; application of SturmLiouville theory. 
18.3: 6(ah)  
22; Nov. 15  Exam II  November 15  
23; Nov. 17.  18.118.3  Separation of variables continued; Review. 
18.3: 4 Solutions, to 18.3, 4,6  
24  17.9,17.10, 18.4  Fourier integral and Fourier transform.  17.10: 3, 4, 6(b,f,j,l), 12
Solutions 18.3: 15, 16 (b)(d), 17 (b) Hand in 18.3: 6 (b); 17.10: 6, 12 

25  18.4  Fourier transform method continued.  18.4: 6, 8, 10; 18.3: 19 Hand in 18.4, 10 and 18.3, 19 on Dec. 8 Solutions  
26  19.119.2  The wave equation.  
27  19.119.2  The wave equation.  19.2; 5(b),(c), 6, 8 19.4; 2(a), 7 

28  Review 