Math 325 - Fall 2004 - Course Outline

All section numbers refer to W. E. Boyce's and R. C. DiPrima's "Elementary Differential Equations and Boundary Value Problems", 8th edition.

Week Reading Topics

1 (9/2)       1.2
      1.3 Solutions to some differential equations
Classification of Differential Equations

2 (9/7 - 9/9)       1.3
      2.1
      2.2 Classification of Differential Equations
Linear Equations: Method of Integrating Factors
Separable Equations.

3 (9/14 - 9/16)       2.4
      2.5
      2.6 Differences Between Linear and Nonlinear Equations
Autonomous Equations and Population Dynamics
Exact Equations and Integrating Factors

4 (9/21 - 9/23)       2.8
      * The Existence and Uniqueness Theorem
Prelim 1, September 23

5 (9/28 - 9/30)       3.1
      3.2
      3.3 Homogeneous Equations with Constant Coefficients
Fundamental Solutions of Linear Homogeneous Equations
Linear Independence and the Wronskian

6 (10/5 - 10/7)       3.4
      3.5
      3.6
Complex Roots of the Characteristic Equation
Repeated Roots; Reduction of Order
Nonhomogeneous Equations; Method of Undetermined Coefficients

7 (10/12 - 10/14)       *
      3.7
      4.1 Reading Holiday, October 12
Variation of Parameters
General Theory of n-th Order Linear Equations

8 (10/19 - 10/21)       4.2
      4.3
      4.4
Homogeneous Equations with Constant Coefficients
The Method of Undetermined Coefficients
The Method of Variation of Parameters

9 (10/26 - 10/28)       *
      7.1
      7.2 Prelim II, October 26
Systems of First Order Linear Equations; Introduction
Review of Matrices

10 (11/2 - 11/4)       7.3
      7.4
      7.5
Linear Algebraic Equations; Linear Independence; Eigenvalues, Eigenvectors
Basic Theory of Systems of First Order Linear Equations
Homogeneous Linear Systems with Constant Coefficients

11 (11/9 - 11/11)       7.6
      7.7
      7.8
Complex Eigenvalues
Fundamental Matrices
Repeated Eigenvalues

12 (11/16 - 11/18)       5.1
      *
Review of Power Series
Prelim III, November 18

13 (11/23 - 11/25)       5.2
      5.3
      * Series Solutions Near an Ordinary Point
Series Solutions Near an Ordinary Point
Thanksgiving, November 25

14 (11/30 - 12/2)       10.1
      10.2
      10.3
Two-Point Boundary Value Problems
Fourier Series
The Fourier Series Convergence Theorem

15 (12/7 - 12/9)       10.4
      10.5
Even and Odd Functions
Separation of Variables

Week	Reading	Topics
1 (9/2)	1.2 1.3	Solutions to some differential equations Classification of Differential Equations
2 (9/7 - 9/9)	1.3 2.1 2.2	Classification of Differential Equations Linear Equations: Method of Integrating Factors Separable Equations.
3 (9/14 - 9/16)	2.4 2.5 2.6	Differences Between Linear and Nonlinear Equations Autonomous Equations and Population Dynamics Exact Equations and Integrating Factors
4 (9/21 - 9/23)	2.8 *	The Existence and Uniqueness Theorem Prelim 1, September 23
5 (9/28 - 9/30)	3.1 3.2 3.3	Homogeneous Equations with Constant Coefficients Fundamental Solutions of Linear Homogeneous Equations Linear Independence and the Wronskian
6 (10/5 - 10/7)	3.4 3.5 3.6	Complex Roots of the Characteristic Equation Repeated Roots; Reduction of Order Nonhomogeneous Equations; Method of Undetermined Coefficients
7 (10/12 - 10/14)	* 3.7 4.1	Reading Holiday, October 12 Variation of Parameters General Theory of n-th Order Linear Equations
8 (10/19 - 10/21)	4.2 4.3 4.4	Homogeneous Equations with Constant Coefficients The Method of Undetermined Coefficients The Method of Variation of Parameters
9 (10/26 - 10/28)	* 7.1 7.2	Prelim II, October 26 Systems of First Order Linear Equations; Introduction Review of Matrices
10 (11/2 - 11/4)	7.3 7.4 7.5	Linear Algebraic Equations; Linear Independence; Eigenvalues, Eigenvectors Basic Theory of Systems of First Order Linear Equations Homogeneous Linear Systems with Constant Coefficients
11 (11/9 - 11/11)	7.6 7.7 7.8	Complex Eigenvalues Fundamental Matrices Repeated Eigenvalues
12 (11/16 - 11/18)	5.1 *	Review of Power Series Prelim III, November 18
13 (11/23 - 11/25)	5.2 5.3 *	Series Solutions Near an Ordinary Point Series Solutions Near an Ordinary Point Thanksgiving, November 25
14 (11/30 - 12/2)	10.1 10.2 10.3	Two-Point Boundary Value Problems Fourier Series The Fourier Series Convergence Theorem
15 (12/7 - 12/9)	10.4 10.5	Even and Odd Functions Separation of Variables