James Waterman - Spring 2024 MAT308

MAT 308 - Differential Equations with Linear Algebra - Spring 2024

Lectures: MW 4:00pm--5:20pm in Physics P113

Recitation: Th 4:00pm- 4:53pm in Earth & Space 069

Office hours: M 2:00- 3:00pm, Th 1:00-2:00pm or by appointment

Office: Math Tower 3-118

Schedule:

Week # Week of Topics covered

#1 1/22 10.1: 1st order DE, direction fields; 10.2: Separation of variables; 10.3: linear equations, integrating factors

#2 1/29 3.1: Linear Maps/Euclidean spaces; 3.2, 3.3: Vector Spaces and Linear Maps

#3 2/5 3.4, 3.5 Image and Null Space, Coordinates and Dimension; 3.6 Eigenvalues and Eigenvectors

#4 2/12 3.6 Eigenvalues and Eigenvectors; 3.7 Inner Products

#5 2/19 Ch3 & Ch10 Midterm Review; Midterm Wed Feb 21

#6 2/26 11.1, 11.2 Differential Operators, Complex Solutions, Higher Order Eqns; 11.3 Non-homogeneous Eqns

#7 3/4 11.5 Laplace Transform; 11.6 Convolution

#8 3/11 Spring Break

#9 3/18 12.1 Vector Fields; 12.2 Linear Systems

#10 3/25 Planar systems, Jordan Canonical Form (Ch4 and Ch5 of Hirsch, Smale, Devaney or Ch 13)

#11 4/1 Higher dimensional linear systems, Computing Matrix Exponential (Ch6 of Hirsch, Smale, Devaney or Ch 13)

#12 4/8 Midterm Review; Midterm Wed. April 10th

#13 4/15 More computing matrix exponential; power series (14.6)

#14 4/22 power series solutions; Non-linear systems

#15 4/29 No class 4/29; An example, Final Review

Homework:

Due 1/29: 10.1A: 2, 3, 7, 8, 11, 20, 25; 10.1B: 1, 4, 5, 10; 10.2: 4, 9, 18, 19

Due 2/5: 10.2: 22, 26, 28; 10.3: 6, 7, 9, 16; 3.1: 2, 4, 6, 8, 12, 17, 19

Due 2/12: 3.2: 12, 16, 17, 18, 20, 24, 25, 26; 3.3 6, 7, 8, 11, 12, 17, 20, 22, 24; 3.4 8, 9, 10, 11, 12

Due 2/19: 3.4: 21; 3.5B: 4, 15, 41; 3.5C: 3,10; 3.6A: 4,13,14; 3.6B:4,8; 3.7A: 10; 3.7B: 2

Due 2/26: Nothing

Due 3/4: 11.1: #12, 32, 34; 11.2A: #4, 18, 35, 46; 11.2B: #2, 4, 14, 20

Due 3/18: 11.5 #2, 8, 12, 24; 11.6 #2, 8, 10, 22

Due 3/25: Here

Due 4/3: See Gradescope

Due 4/8: See Gradescope

Due 4/15: Nothing

Due 4/22: See Gradescope

Due 5/3: See Gradescope

Final Exam: 5:30pm-8:00pm Monday May 13th

Additional material:

Slope fields:

Phase plane:

Hirsch, Smale, Devaney: