Syllabus and homework problems for Math 421

Date	Section	Topics	Homework problems
9/4	4.1	Definition of the Laplace transform	1, 5, 7, 13, 23, 35
9/8	4.2	The Inverse Transform and Transform of Derivatives	7, 11, 23, 31, 35, 39
9/11	4.3	Translation Theorems	3, 7, 9, 11, 15, 19, 37, 41, 45, 47, 49-54, 67
9/15	4.4	Additional Operational Properties	3, 7, 11, 13, 19a, 27, 33, 37, 39
9/18	4.5	Dirac Delta Function	1, 3, 9
9/22	4.6	Solving Systems of Linear Equations	1, 7, 9, 11
9/25	7.6	Vector spaces
9/25	8.8	The Eigenvalue Problem	5, 13, 19
9/29	8.10	Orthogonal Matrices	7, 13, 15
10/2	8.12	Diagonalization	5, 13, 15, 23
10/6	8.15	Method of Least Squares	2, 4, 8
10/6	3.9	Linear Models: Boundary-Value Problems	11, 15
10/9	12.1	Orthogonal Functions	3, 7, 17
10/13	Catch up and review
10/16	First midterm exam
10/20	12.2	Fourier Series	1, 5, 9, 15, 17, 21 Problem 21 is Parseval's Formula
10/23	12.3	Fourier Sine and Cosine Series	3, 5, 7, 13, 19, 23, 29, 35
10/27	12.4	Complex Fourier Series and Frequency Spectrum	5
10/27	12.5	Sturm-Liouville Problem	1
10/30	12.6	Bessel and Legendre Series
11/3	13.1	Separable Partial Differential Equations	16, 22
11/6	13.2	Classical Equations and Boundary-Value Problems	1, 3, 5, 9
11/10	13.3	Heat Equation	1, 3, 4
11/10	13.4	Wave Equation	1, 3, 5, 14, 15, 18 Problem 14 gives d'Alembert's solution to the wave equation.
11/13	13.5	Laplace's Equation	5, 7, 15
11/13	13.8	Fourier Series in Two Variables	1, 3
11/17	Catch up and review
11/20	Second midterm exam
11/24	13.8	Fourier Series in Two Variables
11/24	13.6	Nonhomogeneous BVPs
11/25	13.6	Nonhomogeneous BVPs	10, 14, 18.
12/1	14.1	Laplace's Equation in Polar Coordinates	1, 3, 7
12/4	15.2	Applications of the Laplace Transform	5, 9
12/8	Review
12/16	Final exam, Tuesday, December 16, 12:00--3:00 pm