# 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*