Final Exam Information
- Monday 14 December, 12-2pm in our regular classroom.
- Info/Review
- Table of Laplace Transforms
Announcements
Syllabus
Schedule
This schedule will be updated as necessary throughout the semester. Section numbers refer to the text Differential Equations, J. Brannan & W. Boyce; John Wiley & Sons, 3^{rd} edition, 2015.
Week 1: 8/24-8/28
Mon | Sec 1.1 Notes |
Modeling — How differential equations are used to describe real-world processes. |
Wed | Sec 1.3 Notes |
Definitions, Classification & Terminology — Solutions of differential equations, the order of differential equations, linear vs. nonlinear differential equations. |
Fri | Sec 1.2 Notes Worksheet |
Group Work: Qualitative Methods — Determining the behavior of solutions to a differential equation, without actually solving the equation. |
Week 2: 8/31-9/4
Mon | Sec 2.1 Notes Worksheet |
Group Work: Separable Equations — Solution technique and interval of existence of solutions for first order separable differential equations. |
Wed | Sec 2.2 Notes Worksheet |
Linear Equations — Solving first order linear differential equations using the method of integrating factors. |
Fri | Sec 2.3 Notes |
Modeling with first order differential equations. |
Week 3: 9/7-9/11
Mon | No Class | |
Wed | Sec 2.4/2.5 Notes (sec 2.4) Notes (sec 2.5) Worksheet (sec 2.5) |
Group Work: Two Models of Population Dynamics |
Fri | Sec 2.6 Notes |
Exact first order differential equations. |
Week 4: 9/14-9/18
Mon | Catch-up/Review | |
Wed | Info/Review Key Stats |
Exam 1: Chapters 1 & 2 |
Fri | Sec A1 Notes Homework |
Introduction to Matrices. |
Week 5: 9/21-9/25
Mon | Sec A2 Notes Homework |
Solving systems of linear algebraic equations. |
Wed | Sec A3 Notes Worksheet Homework |
Group Work: Matrix determinants and inverses. |
Fri | Sec A4 Notes Homework |
Eigenvalues and eigenvectors. |
Week 6: 9/28-10/2
Mon | Sec 3.1 Notes |
Complex eigenvalues and eigenvectors, and a “review” of complex arithmetic. |
Wed | Sec 3.2 Notes Worksheet |
Group Work: Introduction to systems of first order linear differential equations. |
Fri | Sec 3.3 Notes (updated 10/5 to correct errors and add information) |
Solving $2 \times 2$ homogenous systems of first order linear differential equations with constant coefficients. Case 1: the coefficient matrix has two distinct real eigenvalues. |
Week 7: 10/5-10/9
Mon | Sec 3.3/3.4 Notes |
Solving $2 \times 2$ homogenous systems of first order linear differential equations with constant coefficients. Case 1 (continued): the coefficient matrix has two distinct real eigenvalues. Case 2: the coefficient matrix has complex eigenvalues |
Wed | Sec 3.4 Worksheet. |
Group Work: Finding solutions to and classifying phase portraits for $2 \times 2$ systems with complex eigenvalues. |
Fri | Sec 3.5 Notes |
Solving $2 \times 2$ homogenous systems of first order linear differential equations with constant coefficients. Case 3: the coefficient matrix has a repeated eigenvalue. |
Week 8: 10/12-10/16
Mon | Catch-up/Review | |
Wed | Info/Review Key Stats |
Exam 2: Appendix, Ch 3 |
Fri | Sec 4.1 Notes |
Introduction to second order differential equations. |
Week 9: 10/19-10/23
Mon | Sec 4.2, 4.3 Notes |
Solutions to second order linear homogenous differential equations with constant coefficients. |
Wed | Sec 4.3 Notes Worksheet |
Group Work: (1) Second order linear homogenous initial value problems, and: (2) the relationship between the solution methods using the characteristic polynomial, and using the associated system. |
Fri | Sec 4.4 Notes |
Undamped harmonic motion: $ay” + cy = 0$, $a,c > 0$. |
Week 10: 10/26-10/30
Mon | Sec 4.4 Notes |
Damped harmonic motion: $ay” + by’ + cy = 0$, $a,b,c > 0$. |
Wed | Sec 4.5 Notes Worksheet |
Group Work: Introduction to the method of undetermined coefficients — the “basic” cases. |
Fri | Sec 4.5 | The method of undetermined coefficients, continued — additional cases. |
Week 11: 11/2-11/6
Mon | Sec 4.6 Notes |
Damped forced vibrations: $ay” + by’ + cy = g(t)$, $a,b,c > 0$, $g(t) = \alpha \cos \omega t$ or $g(t) = \beta \sin \omega t$ |
Wed | Sec 4.6 Worksheet |
Group Work: Undamped forced vibrations: $y” + \omega_0^2 y = A \cos \omega t$ |
Fri | Sec 4.7 Notes |
Variation of parameters. |
Week 12: 11/9-11/13
Mon | Catch-up/Review | |
Wed | Info/Review Key Stats |
Exam 3: Ch 4 |
Fri | Sec 5.1 Notes |
Introduction to the Laplace transform. |
Week 13: 11/16-11/20
Mon | Sec 5.2 Notes |
Properties of the laplace transform. |
Wed | Sec 5.3 Notes Worksheet |
Group Work: Inverse Laplace transform. |
Fri | Sec 5.3 Notes |
Solving differential equations using the Laplace transform. Basic table of Laplace transforms. |
1/23-11/27: Fall Break – no class
Week 14: 11/30-12/4
Mon | Sec 5.5 Notes |
Discontinuous functions (the “on/off” switch). |
Wed | Sec 5.5/5.6 Notes Worksheet |
Group Work: Discontinuous functions (the “on/off” switch) and differential equations with discontinuous forcing functions. |
Fri | Sec 5.5, 5.6, 5.7 Notes |
Discontinuous functions (continued), periodic functions (?), and/or unit impulse function (?). |
Week 15: 12/7-12/11
Mon | Sec 5.5, 5.7 Notes |
Periodic and/or unit impulse functions. |
Wed | Worksheet | Review: Group Work. |
Fri | Review |
Final Exam — Monday 14 December, 12-2pm: Ch 5 & Comprehensive — Info/Review