Math 300 Ordinary Differential Equations

Course Syllabus

Prerequisite: Math 206, or consent of the instructor.

• Description
• Objectives
• Syllabus
• Technology
• Assessment
• Text
• Instructor

Description

Theory and methods of solutions of ordinary differential equations and systems of linear differential equations with constant coefficients. Power series solutions, Laplace transforms, and applications.

Objectives

Ordinary Differential Equations is designed as a one semester cousre in basic theory from both quantitative and qualitative methods as illustrated by standard examples from astromony, biology, chemistry, engineering, and physics. On completion of the course the student should be able to:

• Create and analyze mathematical models based on ordinary differential equations;
• Determine the type of a given differential equation, determine the existence of a solution and if a solution can be obtained, select the appropriate anaytical techinique for finding the solution;
• Utliize technology tools to construct slope fields, and numerical solutions;
• Solve Linear Sytems of equations using eigenvalues and eigenvectors;
• Solve differential equations using Laplace transforms;
• Find an infinite series solution to a given differential equation.

Syllabus

1. First-Order Differential Equations.

Differential Equations and Mathematical Models. Integrals as General and Particular Solutions. Slope Fields and Solution Curves. Separable Equations and Applications. Linear First Order Equations. Substitution Methods and Exact Equations.

2. Linear Equations of Higher Order.

Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Nonhomogeneous Equations and Undetermined Coefficients. Forced Oscillations and Resonance. Electrical Circuits. Endpoint Problems and Eigenvalues.

3. Power Series Methods.

Introduction and Review of Power Series. Series Solutions Near Ordinary Points. Regular Singular Points. Method of Frobenius: The Exceptional Cases. Bessel's Equation. Applications of Bessel Functions.

4. Laplace Transform Methods.

Laplace Transforms and Inverse Transforms. Transformation of Initial Value Problems. Translation and Partial Fractions. Derivatives, Integrals, and Products of Transforms. Periodic and Piecewise Continuous Forcing Functions. Impulses and Delta Functions.

5. Linear Systems of Differential Equations.

Linear Systems and Matrices. The Eigenvalue Method for Homogeneous Systems. Second Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Matrix Exponentials and Linear Systems. Nonhomogenous Linear Systems.

6. Numerical Methods.

Numerical Approximation: Euler's Method. A Closer Look at the Euler Method, and Improvements. The Runge-Kutta Method.

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Final

Technology

The Mathlab, CH 5, provides the technology tools required for the course.

Assessment

Homework (60%)

Student Presentation (20%)

Comprehensive Final (20%)

Text

Elementary Differential Equations
by Edwards & Penny , 5e

Instructor

Robert Garry
College Hall 8
University of Hawaii- Hilo
933-0814
rgarry@hawaii.edu

Effective for Summer 2007.