# A Course in Functional Differential Equations

Math 485 Topics in Functional Differential Equations, 3 units

The Mathematics of Control Theory, Robots, Epidemics, and Pollution Management SONOMA STATE UNIVERSITY, Salazar Hall 2014
SPRING SEMESTER 2004
Wednesday evenings 6 - 8:50 PM , Instructor: C. E. Falbo

We will be using a book which is written for this course and whose contents are listed below. The chapters are short and each one will take about two weeks to cover. This will be a seminar type of class with plenty of student activity. I will discuss the code needed to write programs in C or in Mathematica for solving the problems.

Prerequisites: A Course in Differential Equations (Calculus III) and some experience with computer programming.

### CONTENTS

Chapter 1 Introduction to Functional Differential Equations

1.1 What is a Functional Differential Equation?
1.2 Type of FDE's
1.3 Systems of FDE's
EXERCISES

Chapter 2. FDE'S with linear delays

2.1 Simple delays t - d
2.2 The Method of Steps
2.3 Accelerated delays mt - d
2.4 Applications
EXERCISES

Chapter 3. Relation to Partial Differential Equations

3.1 Fires & Explosions
3.2 Classification of PDE's
3.3 Solving quasi-linear PDE's
EXERCISES

Chapter 4. FDE's with Nonlinear Delays

4.1 Increasing functions h(t) - d
4.2 Method of Steps for Nonlinear Delays
4.3 Finding Inverses of h(t)
EXERCISES

Chapter 5 FDE's with Idempotent Arguments

5.1 Idempotent functions u(u(t)) = t
5.2 Decreasing Functions Through the Origin
5.3 Applied Models Requiring Reverse Time Equations
EXERCISES

Chapter 6 Systems of FDE's and PDE's

6.1 Methods of Characteristics
6.2 Nonhomogenous Equations
6.3 Equations used in Robotics
6.4 Other Applications
EXERCISES

Chapter 7 FDE's With Fixed Point Arguments

7.1 Decreasing Functions about a Fixed Point
7.2 Periodic Functions
EXERCISES

Chapter 8 Second Order PDE's of Physics

8.1 Separation of Variables
8.2 Fourier Series Solutions
8.3 Orthogonal Functions
EXERCISES

Appendices

I. Tabular Integration by Parts
II. Eigenvectors
III. LaPlace Transforms