Syllabus and homework problems for Math 421

Syllabus and homework problems for Math 421

DateSection Topics Homework problems
9/44.1 Definition of the Laplace transform 1, 5, 7, 13, 23, 35, 37
9/94.2 The Inverse Transform and Transform of Derivatives 7, 11, 19, 23, 31, 35, 39
9/114.3 Translation Theorems 3, 9, 11, 15, 19, 25, 37, 41, 45, 47, 49-54, 67
9/164.4 Additional Operational Properties 3, 7, 11, 13, 21, 27, 33, 37, 39
9/184.5 Dirac Delta Function 1, 3, 9
9/234.6 Systems of Linear Differential Equations 1, 7, 9, 11
9/25 7.6 Vector spaces
8.1Matrix Algebra 17, 23, 29, 35, 37
8.2 Systems of Linear Algebraic Equations 5, 9, 11, 17
9/30 8.3 Rank of a Matrix 5, 7, 9, 13, 15
8.4 Determinants 19, 21, 25, 27
8.5 Properties of Determinants 5, 13, 23, 29, 31, 33
10/28.6 Inverse of a Matrix 7, 21, 25, 27, 31, 49, 51, 53
8.7 Cramer's Rule 1, 9
10/7 8.8 The Eigenvalue Problem 5, 13, 15, 19
10/9 8.10 Orthogonal Matrices 7, 13, 15
8.12 Diagonalization 5, 13, 15, 23, 29
10/14 Catch up and review
10/16 First midterm exam
10/21 3.9 Linear Models: Boundary-Value Problems 11, 15
12.1 Orthogonal Functions 3, 7, 11, 17
10/23 12.2 Fourier Series 1, 5, 9, 11, 15, 17
10/28 12.3 Fourier Sine and Cosine Series 3, 5, 7, 13, 19, 23, 29, 35
10/30 12.4 Complex Fourier Series 3, 5
12.5 Sturm-Liouville Problem 1
11/413.1 Separable Partial Differential Equations 3, 11, 15, 17, 21, 23
11/6 13.2 Classical PDEs and Boundary-Value Problems 1, 3, 5, 9
11/1113.3 Heat Equation 1, 3, 4
13.4 Wave Equation 1, 3, 5, 18, 19
Problem 18 gives d'Alembert's solution to the wave equation.
11/13 13.5 Laplace's Equation 5, 7, 15
13.8 Fourier Series in Two Variables
11/18 Catch up and review
11/20 Second midterm exam
11/25 13.8 Fourier Series in Two Variables 1, 3
13.6 Nonhomogeneous BVPs
12/2 13.6 Nonhomogeneous BVPs 2, 3, 14, 18
12/4 14.1 Laplace's Equation in Polar Coordinates 1, 3, 7
12/9 15.2 Applications of the Laplace Transform 2, 17
12/11 Review
12/17 Final Exam