Syllabus and homework problems for Math 421

Syllabus and homework problems for Math 421

DateSection Topics Homework problems
9/24.1 Definition of the Laplace transform 1, 5, 7, 13, 23, 35
9/74.2 The Inverse Transform and Transform of Derivatives 7, 11, 23, 31, 35, 39
9/94.3 Translation Theorems 3, 7, 9, 11, 15, 19, 37, 41, 45, 47, 49-54, 67
9/144.4 Additional Operational Properties 3, 7, 11, 13, 19, 27, 33, 37, 39, 51
9/164.5 Dirac Delta Function 1, 3, 9
9/214.6 Solving Systems of Linear Equations 1, 7, 9, 11
9/23 7.6 Vector spaces
8.1Matrix Algebra 17, 23, 29, 35, 37
8.2 Systems of Linear Algebraic Equations 5, 9, 11, 37
9/28 8.3 Rank of a Matrix 5. 7. 9, 13, 17
8.4 Determinants 19, 21, 25, 27
8.5 Properties of Determinants 5, 11, 13, 23, 31, 33
9/308.6 Inverse of a Matrix 7, 25, 27, 31, 51, 53
8.7 Cramer's Rule 1, 9
10/5 8.8 The Eigenvalue Problem 5, 13, 15
10/7 8.10 Orthogonal Matrices 7, 13, 15
8.12 Diagonalization 5, 13, 15, 23
10/12 Catch up and review
10/14 First midterm exam
10/19 3.9 Linear Models: Boundary-Value Problems 11, 15
12.1 Orthogonal Functions 3, 7, 17
10/21 12.2 Fourier Series 1, 5, 9, 15, 17, 21
Problem 21 is Parseval's Formula
10/26 12.3 Fourier Sine and Cosine Series 3, 5, 7, 13, 19, 23, 29, 35
10/28 12.4 Complex Fourier Series and Frequency Spectrum 3, 5
12.5 Sturm-Liouville Problem 1
11/213.1 Separable Partial Differential Equations 3, 11, 15
11/4 13.2 Classical Equations and Boundary-Value Problems 1, 3, 5, 9
11/913.3 Heat Equation 1, 3, 4
13.4 Wave Equation 1, 3, 5, 12, 15
Problem 12 gives d'Alembert's solution to the wave equation.
11/11 13.5 Laplace's Equation 5, 7, 15
13.8 Fourier Series in Two Variables 1, 3
11/16 Catch up and review
11/18 Second midterm exam
11/23 13.8 Fourier Series in Two Variables
13.6 Nonhomogeneous BVPs
11/30 13.6 Nonhomogeneous BVPs 1, 5, 13, 17
12/2 14.1 Laplace's Equation in Polar Coordinates 1, 3, 7
12/7 15.2 Applications of the Laplace Transform 3, 9
12/9 Review
12/16 Final Exam