# MAT 311 Differential Equations

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### Course Description

Topics covered include first and second order linear equations including existence and uniqueness theorems, series solutions; nonlinear equations; systems of linear equations. Other topics may include the Laplace transform, qualitative theory.

MAT 311 meets for three hours of lecture per week.

### Prerequisites

MAT 211 and MAT 271 with grade C or better.

### Objectives

After completing MAT 311 the student should be able to

• find the solution for linear and nonlinear first order differential equations using the techniques of separable equations, exact equations, and integrating factors
• find the solution for second order linear differential equations with constant coefficients
• find particular solutions to nonhomogeneous second order equations using the methods of undetermined coefficients and variation of parameters
• find series solutions to second order linear equations with polynomial coefficients near an ordinary point, and near a regular singular point
• solve homogeneous and nonhomogeneous first order linear systems with constant coefficients
• determine existence and uniqueness of solutions of differential equations and systems of equations
• use the above techniques to analyze and solve applied problems.

### Expected outcomes

Students should be able to demonstrate through written assignments, tests, and/or oral presentations, that they have achieved the objectives of MAT 311.

### Method of Evaluating Outcomes

Evaluations are based on homework, class participation, short tests and scheduled examinations covering students' understanding of the topics that are covered in MAT 311.

### Text

Elementary Differential Equations and Boundary Value Problems (3rd. edition), by William E. Boyce and Richard C. DiPrima

#### Sample List of Topics

• First Order Differential Equations
• Linear Equations
• Nonlinear Equations
• Separable Equations
• Exact Equations
• Integrating Factors
• Homogeneous Equations
• Existence and Uniqueness Theorem
• Second Order Linear Differential Equations
• Fundamental Solutions for the Homogeneous Equation
• Linear Independence
• Reduction of Order
• Homogeneous Equations with Constant Coefficients
• Complex Roots
• The Nonhomogeneous Problem
• The Method of Undetermined Coefficients
• The Method of Variation of Parameters
• Series Solutions of Second Order Linear Equations
• Series Solutions near an Ordinary Point
• Series Solutions near a Regular Singular Point
• Euler Equations
• Systems of First Order Linear Equations
• Solution of Linear Systems by Elimination
• Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
• Basic Theory of Systems of First Order Linear Equations
• Homogeneous Linear Systems with Constant Coefficients
• Complex Eigenvalues
• Repeated Eigenvalues
• Fundamental Matrices
• Nonhomogeneous Linear Systems

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in MAT 311. The instructor determines the relative weights of these factors.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

### Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.