AME 250 – Techniques of Measurement and Data Analysis

AME 321 – Differential Equations and Applied Mathematics - Fall 2002 Syllabus

Period Date Topic B&DiP Text

1 8/19 Policies, Syllabus; DE Introduction: Why DEs?; Chpt. 1

Notation and Classification

2 8/21 Formulating DEs;
1^st Order ODEs: Common Examples; Linear Eqns; Chpt. 2

3 8/28 Separable Eqns; Exact Eqns;

4 9/2 Integrating Factors; Homogeneous Eqns

5 9/4 2^nd Order Linear ODEs: Homogeneous Eqns with Chpt. 3

Constant Coefficients

6 9/9 Reduction of Order; Linear Independence; Nonhomogeneous

Eqns: Methods of Undetermined Coeffs.

7 9/11 Methods of Undetermined Coeffs. Examples;

Variation of Parameters; Classifying Solutions

8 9/16 Higher Order Linear Eqns: General Theory; Chpt. 4

Homogeneous Eqns with Const Coefficients;

9 9/18 EXAM 1

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10 9/30 Methods of Undetermined Coeffs & Variation of Parameters

11 10/2 Systems of 1^st Order Linear Eqns: Chpt. 7

Reduction Method; Review of Matrices;

12 10/7 Systems of Linear Algebraic Eqns:

Linear Independence; Eigenvalues; Eigenvectors;

13 10/9 Basic Theory of Systems of 1^st Order Linear Eqns;

Homogeneous Linear Systems with Const Coeff;

14 10/14 Complex Eigenvalues; Repeated Eigenvalues

15 10/16 Fundamental Matrices; Nonhomogeneous Linear Systems;

16 10/21 Phase Plane and Portraits

17 10/23 EXAM 2

18 10/28 Numerical Methods: Intro, Forward & Backward Euler Methods Chpt. 8

19 10/30 Improved Euler; 3-Term Taylor; Runge Kutta

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20 11/11 Runge-Kutta; Numerical Error; Multi-step Methods;

21 11/13 Systems of 1^st-Order Eqns;

22 11/18 Shooting Method; Method of Lines

23 11/20 EXAM 3

24 11/25 Nonlinear DEs: Phase Plane, Autonomous Systems Chpt. 9(only 9.1, 9.2)

25 11/27 Partial DEs: Introduction; "Famous" PDEs; Chpt. 10

26 12/2 Separation of Variables, Heat Conduction Eqn;

27 12/4 Fourier Series; Convergence Theorem; Even & Odd Functions

28 12/9 The Wave Eqn

29 12/11 Laplace’s Eqn; Closure

12/16 FINAL EXAM

Days for Cooperative Quizzes (On Mondays):

Homework Due Days (On Wednesdays EXCEPT Exam Days and 1^st and Last Wednesdays of the Semester):