# Math 383H: A First Course in Differential Equations

Sec 001: Tuesday and Thursday from 11:00-12:15 in Graham Memorial 213

Office Hours: T,Th from 3:30-4:30 pm and W: 10-11 am in PH 314 and by appointment.

Homework will be assigned through WebAssign. You can find the syllabus here.

**Tentative Course Outline**

- Lec 1 (Jan 12): Section 1.1-1.2 Introduction (What are differential equations and why do we care?)
- Lec 2 (Jan 17): Section 1.3-2.1 Classification of ODEs; Method of integrating factors.
- Lec 3 (Jan 19): Section 2.2 and 2.4 Separable Equations; Existence and Uniqueness Theorems
- Lec 4 (Jan 24): Sec 2.3 Modeling with First Order Equations
- Lec 5 (Jan 26): Sec 2.5-2.6 Autonomous Equations and Exact Equations
- Lec 6 (Jan 31): Sec 2.6 and 2.8 Exact Equations and the Existence and Uniqueness Theorem
- Lec 7 (Feb 2): Sec 2.8 and 7.2 The Existence and Uniqueness Theorem;
- Lec 8 (Feb 7): Sec 2.8 Finish Existence and Uniqueness Theorem (maybe start section 3.1)
- Lec 9 (Feb 9): Sec 3.1-3.2 Second order differential equations; linear homogeneous equations with constant coefficients
- Lec 10 (Feb 14): Section 3.3-3.4 Complex and repeated roots of the characteristic equation
- Lec 11 (Feb 16): Section 3.4- 3.5 Repeated roots and inhomogeneous systems
- (Feb 21): Exam 1
- Lec 12 (Feb 23): Sec 3.5,-3.6 Undetermined coefficients and mechanical vibrations
- Lec 13 (Feb 28):3.6-3.7 Unforced and forced mechanical vibrations
- Lec 14 (March 2): Overview of Chapter 4.
- Lec 15 (March 7): 7.2-7.3 Matrix algebra review, linear independence, eigenvalues and eigenvectors.
- Lec 16 (March 9): 7.1 and 7.3 Eigenvalues and eigenvectors for 3×3 matrices; introduction to systems
- (March 14): Spring break– no classes
- (March 16): Spring break — no classes
- Lec 17 (March 21 ): 7.4-7.5 Basic theory of systems of first order linear equations; homogeneous systems with constant coefficients
- Lec 18 (March 23):7.6-7.7 Complex eigenvalues; fundamental matrices
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- Lec 19 (March 23): 5.5-5.6 Series solutions near a regular singular point I-II
- Lec 20 (March 28): Exam II
- Lec 21 (March 30):
- Lec 22 (April 4):
- Lec 23 (April 6): 7.8-7.9 Repeated eigenvalues; non-homogeneous linear systems
- Lec 24 (April 11): 9.1-9.2 The phase plane: linear systems; autonomous systems and stability
- Lec 25 (April 13): 9.3-9.4 Locally linear systems; Competing species
- Lec 26 (April 18): 9.5-9.6 Predator-prey equations;Liapunov’s second method
- Lec 27 (April 20): 9.7-9.8 Periodic Solutions and Limit Cycles; Chaos and strange attractors: the Lorenz Equations.
- Lec 28 (April 25): TBD
- Lec 30 (April 27): TBD — last day of classes.

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