Ordinary Differential Equations
Revised: September 2020
Course Description
Solution techniques and analysis of first order differential equations, linear equations
of higher order, systems of differential equations, and the Laplace Transform technique;
mathematical modeling, numerical methods, existence and uniqueness of solutions.
Prerequisite: MATH 255. Three semester hours.
Student Learning Objectives
By the end of the course students should be able to
- use geometric, numeric, and analytic techniques to solve and/or examine first-order
ordinary differential equations;
- use analytic and transform techniques to solve both homogeneous and nonhomogeneous
linear higher-order ODEs;
- work with systems of differential equations in terms of matrices to find their solutions
using linear algebra techniques;
- formulate differential equations and systems via modeling;
- interpret results from mathematical modeling with ODEs in the context of the original
physical problem; and
- use mathematical software to solve and/or examine differential equations.
Text
Edwards, Penney, and Calvis, Differential Equations and Boundary Value Problems: Computing and Modeling, 5th ed., Pearson.
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 (Slope Fields), Numerical Techniques,
Existence and Uniqueness, Linear First-Order Equations, and Integrating Factors.
- Chapter 2: Mathematical Models and Numerical Method (7 class days)
Population Models, Critical Points, Equilibrium and Stability, Acceleration-Velocity
Models, Euler's Method, and Runge-Kutta Method.
- Chapter 3: Linear Equations of Higher Order. (9 class days)
Second-Order Linear Equations, General Solutions of Linear Equations, Homogeneous
Equations with Constant Coefficients, Mechanical Vibrations, Method of Undetermined
Coefficients, Variation of Parameters.
- Chapter 4: Systems of Differential Equations. (4 class days)
First-Order Systems and Applications, Method of Elimination, Numerical Methods for
Systems.
- Chapter 5: Linear Systems of Differential Equations. (6 class days)
Matrices and Linear Systems, Eigenvalue Method for Homogeneous Systems, Multiple
Eigenvalue Solutions.
- Chapter 7: Laplace Transform Methods. (7 class days)
Laplace Transforms and Inverse Transforms, Transformation of Initial Value Problems,
Translation and Partial Fractions, with Additional Topics as Time Allows