1/14/08 Introduction and Basic Definitions
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)
Exam 1 / Fall 07 – Key, 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 07 – Key, 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
3/6/08 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
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