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Final Exam Information


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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, 3rd 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