Lecture Notes

1/14/08 Introduction and Basic Definitions

1/15/08 Integration Factors

1/17/08 Separable Equations

1/22/08 Applications of First Order ODEs

1/23/08 Existence and Uniqueness Theorems for First Order ODEs

1/25/08 Autonomous Equations (Methods For Deriving Qualitative Information about Solutions)

1/28/08 Exact Equations

Exam 1 / Fall 07Key, Exam 1 / Fall 07

2/4/08 Introduction to Second Order Linear Equations

2/5/08 Fundamental Theory of Second Order Linear Equations (Superposition and the Wronskian)

2/7/08 Linear Independence and the Wronskian

2/8/08 Solving ay’’ + by’ cy = 0 When Roots of the Characteristic Equation are Complex-Valued

2/11/08 Solving ay’’ + by’ + cy = 0 When the Root is Repeated / The Reduction of Order Algorithm

2/12/08 The Method of Undetermined Coefficients

2/14/08 The Method of Variation of Parameters

2/15/08 Mechanical Vibrations I (The Model for An Oscillating Spring Set in Motion)

2/18/08 Mechanical Vibrations II (The Model for An Oscillating Spring With Additional Forces)

Exam 2 / Fall 07Key, Exam 2 / Fall 07

2/26/08 General Theory of Higher Order Linear Equations

2/28/08 Higher Order Homogeneous equations with Constant Coefficients  

2/29/08 The Method of Undetermined Coefficients Applied to Higher order Equations 

3/3/08 The Laplace Transform

3/6/08 Solving Differential Equations with the Laplace Transform

3/10/08 Step Functions and the Laplace Transform

3/11/08 Differential Equations with Discontinuous Forcing Functions

3/13/08 Differential Equations Involving Impulse Functions

3/14/08 The Convolution Integral

3/27/08 Review of Infinite Series

3/28/08 Solving Differential Equations with Infinite Series

4/1/08 Convergence of Series Solutions About Ordinary Points

Key, Exam 3 / Fall 07

4/7/08 Systems of Differential Equations

4/8/08 Introduction to Matrices and Linear Algebra

4/10/08 Systems of First Order Systems of Linear Equations

4/14/08 First Order Systems of Differential Equations

4/15/08 Homogeneous Linear Systems of Differential Equations

4/17/08 Homogeneous Linear Systems with Complex Eigenvalues

4/18/09 Homogeneous Linear Systems with Repeated Eigenvalues

4/21/08 The Fundamental Matrix and Diagonalization

4/24/08 Nonhomogeneous Linear Systems of Ordinary Differential Equations

Practice Final Exam