Ordinary Differential Equations
Revised: November 2006
Course Description
Modeling, first order differential equations, existence and uniqueness of solutions, systems of differential equations, second order differential equations and Laplace transforms. Three semester hours.
Objectives
1. To formulate differential equations via modeling.
2. To acquire geometric, numeric, and analytic techniques used for solving and/or examining differential equations.
3. To interpret the solutions to differential equations.
Text
D. Blanchard, R. Devaney, and G. Hall. Differential Equations, Third Edition. Thompson Brooks/Cole, 2006.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
- Chapter 1: First-Order Differential Equations. (9 class days)
Modeling, Analytic Techniques, Qualitative Techniques, Numerical Techniques, Existence and Uniqueness, Equilibria, Phase Line, Bifurcations, Linear Equations, and Integrating Factors. - Chapter 2: First-Order Differential Equations. (9 class days)
Modeling via systems, Geometry of Systems, Analytic Methods for Systems, Euler's Method for Systems, and Lorenz Equations. - Chapter 3: Linear Systems. (11 class days)
Linearity Principle, Straight-Line Solutions, Phase Plane for Linear Systems with Real Eigenvalues, Complex Eigenvalues, Repeated and Zero Eigenvalues, Second-Order Linear Equations, Trace-Determinant Plane, and Linear Systems in Three Dimensions. - Chapter 4: Forcing and Resonance. (4 class days)
Forced Harmonic Oscillators, Sinusoidal Forcing, and Undamped Forcing and Resonance. - Chapter 6: Laplace Transforms. (7 class days)
Laplace Transforms, Discontinuous Functions, Second-Order Equations, Delta Function and Impulse Forcing, Convolutions, and Qualitative Theory of Laplace Transforms.