MAT 30801  Differential Equations with Linear Algebra  Spring 2023
This course meets MW 4:255:45 in Frey Hall 217.
Course information
Office hours:  Monday 3:004:00pm 
Wednesday 12:001:00pm  
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 oddnumbered 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 nullspace 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 (3.17, 10.111.4) 

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 (11.57, 12.13, 13.14) 

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, 2:155:00  Final Exam  Cumulative All sections included in Midterms 1, 2 plus 14.67 