Math 20D
Introduction to Differential Equations

Course Syllabus

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COURSE TOPICS:   Ordinary Differential Equations

INSTRUCTOR:   Dr. Daniel Reynolds

TEXTBOOK(S):
  • Boyce and Diprima, Elementary Differential Equations and Boundary Value Problems, 8th Edition, John Wiley and Sons, 2005, Chapters 1-6.
  • Stewart, Calculus: Early Transcendentals, 5th Edition, Brooks/Cole, 2003, Chapter 11.

CATALOG DESCRIPTION:   20D. Introduction to Differential Equations (4)
Infinite series.Ordinary differential equations:exact,separable, and linear; constant coefficients, undetermined coefficients, variations of parameters. Series solutions. Systems, Laplace transforms, technique for engineering sciences. Computing symbolic and graphical solutions using Matlab. Formerly numbered Math. 21D. May be taken as repeat credit for Math. 21D. Prerequisite: Math 20C (or Math 21C) with a grade of C- or better.


TENTATIVE LECTURE SCHEDULE:
Lecture Date Section(s) Topics Covered
1 Jan 9 1.1-1.3 Introduction: Mathematical modeling with ODE, Classification of ODE and PDE
2 Jan 11 2.1 Linear equations; Method of Integrating Factors
3 Jan 13 2.2 Separable Equations
4 Jan 18 2.3, 2.4 Modeling with First Order Equations; Differences Between Linear and Nonlinear Equations
5 Jan 20 2.5 Autonomous Equations and Population Dynamics
Quiz 1, covering sections 1.1-2.2
6 Jan 23 2.6 Exact Equations and Integrating Factors
7 Jan 25 3.1, 3.2 Second Order Linear Equations: Fundamental Solutions of Linear Homogeneous Equations
8 Jan 27 3.3 Linear Independence and the Wronskian
Quiz 2, covering sections 2.3-2.6
9 Jan 30 3.4 Complex Roots of the Characteristic Equation
10 Feb 1 3.5 Repeated Roots; Reduction of Order
11 Feb 3 3.6 Nonhomogeneous Equations; Method of Undetermined Coefficients
Week 5 Feb 6 Mid-Term 1 TOPICS COVERED: Boyce and DiPrima 1.1-3.4.
12 Feb 8 3.7 Variation of Parameters
13 Feb 10 11.1 (S) Sequences: Concepts, Squeeze Theorem, Monotonic Sequence Theorem
14 Feb 13 11.2, 11.3 (S) Series: Geometric and Harmonic Series, Integral Test
15 Feb 15 11.4, 11.5 (S) Comparison and Alternating Series Tests
16 Feb 17 11.6 (S) Absolute convergence, Ratio and Root Tests
Quiz 3, covering sections 3.5-3.7 (B&D), and 11.1 (S)
17 Feb 22 11.8, 11.9 (S) Power Series, Radius of Convergence, Examples
18 Feb 24 11.10 (S) Taylor Series and Remainder Estimate
Quiz 4, covering sections 11.2-11.6
19 Feb 27 11.12 (S) Applications of Taylor Series and Remainder Estimate
20 Mar 1 5.1 Using Power Series to Solve ODEs; Ordinary Points and Singular Points
21 Mar 3 5.2, 5.3 Series Solutions Near an Ordinary Point
Week 9 Mar 6 Mid-Term 2 TOPICS COVERED: Boyce and DiPrima 3.5-3.7, Stewart 11.1-11.12.
22 Mar 8 6.1 The Laplace Transform: Definition of the Laplace Transform
23 Mar 10 6.2 Solution of Initial Value Problems
24 Mar 13 6.3, 6.4 Step Functions; Differential Equations with Discontinuous Forcing Functions
25 Mar 15 6.5 Impulse Functions.
Week 10 Mar 17 Review REVIEW for Final Exam
Week 11 Mar 22 Final Exam TOPICS COVERED: Boyce and DiPrima 1.1-6.2, Stewart 11.1-11.12.