------------------------------------------------------------------------------- Math 421, Spring 2015, Syllabus ------------------------------------------------------------------------------- 01 Tue 1/20 4.1 Definition of the Laplace Transform 02 Fri 1/23 4.2 The Inverse Transform and Transforms of Derivatives 03 Tue 1/27 04 Fri 1/30 4.3 Translation Theorems 05 Tue 2/3 4.4 Additional Operational Properties 06 Fri 2/6 4.5-4.6 Dirac Delta Function, Systems of Linear Diff Eqns 07 Tue 2/10 7.6,8.1-8.2 Vector Spaces, Matrix Algebra, Sys of Lin Eqns 08 Fri 2/13 8.3-8.4 Rank of a Matrix, Determinants 09 Tue 2/17 8.5-8.6 Properties of Determinants, Inverse of a Matrix 10 Fri 2/20 8.7-8.8,8.10 Cramer's Rule, Eigenvalues, Orthogonal Matrices 11 Tue 2/24 8.12 Diagonalization 12 Fri 2/27 12.1-12.2 Orthogonal Functions, Fourier Series 13 Tue 3/3 Midterm 1 14 Fri 3/6 12.3 Fourier Cosine and Sine Series 15 Tue 3/10 12.4 Complex Fourier Series 16 Fri 3/13 12.5 Sturm-Liouville Problem 17 Tue 3/24 13.1-13.2 Separable PDEs, Classical PDEs 18 Fri 3/27 13.3 Heat Equation 19 Tue 3/31 13.4 Wave Equation 20 Fri 4/3 13.5 Laplace's Equation 21 Tue 4/7 13.6 Nonhomogeneous BVPs 22 Fri 4/10 13.7 Orthogonal Series Expansions 23 Tue 4/14 Midterm 2 24 Fri 4/17 13.8 Fourier Series in Two Variables 25 Tue 4/21 14.1 Problems in Polar Coordinates 26 Fri 4/24 15.3 Fourier Integral 27 Tue 4/28 15.4 Fourier Transforms The homework and midterm problems are part of the syllabus as well. Final Exam: Wednesday May 13, 8:00-11:00 AM -------------------------------------------------------------------------------