# Matthew Romney

### MAT 308-01 - Differential Equations with Linear Algebra - Spring 2023

This course meets MW 4:25-5:45 in Frey Hall 217.

Course Syllabus

### Course information

 Office hours: Monday 3:00-4:00pm Wednesday 12:00-1:00pm or by appointment You have the option to come to my office (Math Tower 4101B) or to meet on Zoom: https://stonybrook.zoom.us/j/2482038879?pwd=TDVGcUU4UXhlNHEvdllnckdBb2VpZz09. Let me know in advance if you plan to meet on Zoom. Textbook: Williamson and Trotter, Multivariable mathematics, Fourth edition.

### Course schedule and assignments

Each week’s homework assignment is due Wednesday of the following week at midnight. Homework should be submitted on Brightspace. You are also encouraged to work through as many other problems as you find helpful to understand the material, especially the odd-numbered problems since their answers are mostly in the book.

 Week Date Sections Assignment 1 Jan. 23   Jan. 25 3.1 Linear functions on R^n 3.2 Vector spaces 3.3 Linear functions HW 1 3.1 #4, 12, 16, 20, 33; 3.2 #4, 10, 12, 18, 31; 3.3 #6, 8, 18, 22 2 Jan. 30   Feb. 1 3.4 Image and null-space 3.5 Coordinates and dimension HW 2 3.4 #2, 6, 10, 20, 22; 3.5B #4, 10, 14, 18, 26, 36, 40; 3.5C #2, 13, 14 3 Feb. 6   Feb. 8 3.6 Eigenvalues and eigenvectors 3.7 Inner products HW 3 3.6A #2, 6, 8; 3.6B #4, 8, 12, 16; 3.7A #2, 13, 14; 3.7B #2, 4, 15 4 Feb. 13   Feb. 15 10.1 Direction fields 10.2 Applications 10.3 Linear systems HW 4 10.1A #2, 8, 24 10.2 #8, 14, 24, 28; 10.3 #2, 4, 8, 10, 16, 22 5 Feb. 20   Feb. 22 11.1 Differential operators 11.2 Complex solutions HW 5 11.1 #12, 14, 32, 34, 41; 11.2A #4, 18, 35, 46; 11.2B #2, 4, 14, 20, 52 6 Feb. 27   Mar. 1 11.3 Nonhomogeneous equations 11.4 Oscillations HW 6 11.3B #2, 8, 30, 43; 11.3D #2, 6, 12, 16, 28; 11.4 #2, 4, 12, 14 7 Mar. 6   Mar. 8 Review MIDTERM 1 (3.1-7, 10.1-11.4) 8 Mar. 20   Mar. 22 11.5 Laplace transforms 11.6 Convolution HW 7 11.5 #2, 6, 8, 12, 24, 26; 11.6 #2, 8, 10, 18, 22 9 Mar. 27   Mar. 29 11.7 Nonlinear equations 12.1 Vector fields HW 8 11.7B #2, 8, 14, 18; 11.7C #12; 12.1C #4, 6, 14; 12.1D #2, 5, 6 10 Apr. 3   Apr. 5 12.2 Linear systems 12.3 Applications HW 9 12.2 #6, 8, 10, 12, 24, 28; 12.3 #6, 8, 10, 22 11 Apr. 10   Apr. 12 13.1 Eigenvalues and eigenvectors 13.2 Matrix exponentials HW 10 13.1 #8, 12; 13.2C #4, 12, 16, 24; 13.2D #4, 6, 8, 16; 13.2E #4, 6 12 Apr. 17   Apr. 19 13.3 Nonhomogeneous systems 13.4 Equilibrium and stability HW 11 13.3 #2, 4, 12, 16; 13.4A #4, 10, 14; 13.4B #2, 5, 6, 14 13 Apr. 24   Apr. 26 Review MIDTERM 2 (11.5-7, 12.1-3, 13.1-4) 14 May 1   May 3 14.6 Differential equations 14.7 Power series solutions HW 12 14.6 #2, 4, 6, 8; 14.7 #4, 7, 8 May 16, 2:15-5:00 Final Exam CumulativeAll sections included in Midterms 1, 2plus 14.6-7