# Math 383: A First Course in Differential Equations

Sec 002: Tuesday and Thursday from 12:30-1:45 in PH 332

Office Hours: T and Th from 2:00-3:00, W from 10- 11 am, and by appointment in PH 314.

Nifty tool for Direction Fields

**Tentative Course Outline**

- Lec 1: Section 1.1-1.2 Introduction (What are differential equations and why do we care?)
- Lec 2: Section 1.3-2.1 Classification of ODEs; Method of integrating factors.
- Lec 3: Section 2.1-2.2 Method of integrating factors continued; Separable equations.
- Lec 4: Section 2.2 and 2.4; Separable equations and Difference between linear and nonlinear equations;
- Lec 5: Section 2.3 Modeling with first order equations.
- Lec 6: Section 2.5 – 2.6 Autonomous equations in population dynamics; Exact equations
- Lec 7: Section 2.6 Exact equations and integrating factors.
- Lec 8: Section 2.6 – 2.7 Exact equations and integrating factor continued; Numerical approximations: Euler’s method.
- Lec 9 : 2.7 Numerical approximations: Euler’s method; review.
- Let 10: Exam 1 (will cover 1.1-2.6)
- Lec 11: Section 7.2 and 7.3 Review of matrices; Linear Algebra.
- Lec 12: Section 7.2-3.1 Linear algebra review; Homogeneous equations with constant coefficients.
- Lec 13: Section 3.1-3.2 Homogeneous equations with constant coefficients continued; Solutions of linear homogeneous equations.
- Lec 14: Section 3.2 – 3.3 Solutions of linear homogeneous equations continued; Complex roots of the characteristic equation.
- Lec 15: Section 3.3 – 3.4 Complex roots of the characteristic equation continued; Repeated roots, reduction of order.
- Let 16: Section 3.4 – 3.5 Repeated roots, reduction of order continued; Non-homogeneous equations, method of undetermined coefficients.
- Lec 17: Section 3.5-3.6 Non-homogeneous equations, method of undetermined coefficients continued; Variation of parameters.
- Lec 18: Section 3.6-3.7: Variation of parameters continued; Mechanical and electrical vibrations.
- Lec 19: Section 3.7 Mechanical and electrical vibrations continued; review.
- Lec 20: Exam 2 (will cover 2.7-3.6).
- Lec 21: Section 4.1-4.2 General theory of nth order linear equations; Homogeneous equations with constant coefficients.
- Lec 22: Section 4.2-4.3 Homogeneous equations with constant coefficients continued; The method of undetermined coefficients.
- Lec 23: Section 4.3-4.4 The method of undetermined coefficients continued; The method of variation of parameters.
- Lec 24: Section 7.1 and 7.4 Basic theory of systems of first order linear equations.
- Lec 25: Section 7.5 Homogeneous systems with constant coefficients.
- Lec 26: Section 9.1 The phase plane: linear systems.
- Lec 27: Section 9.2 Autonomous systems and stability.
- Lec 28: Section 9.3 Locally linear systems.
- Lec 29: 9.4 Competing species; review.

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