Graphical and Numerical Solution of Differential Equations (UMAP)

By the end of this module students will have learned how to: 1) draw a tangent field for a given first order differential equation; 2) sketch several possible solutions through a given tangent field; 3) solve a first order differential equation by a graphical application of Euler's Method; 4) carry out a numerical solution of a differential equation by Euler's Method, either by hand, by using a calculator or by a computer; 4) given a verbal description of a simple situation that can be described by means of first order differential equation, write such an equation; and 6) given an equation, a graph, or a table of data points, determine whether they represent solutions to a given differential equation.

Table of Contents:

CHAPTER 1: THE OPTICAL FILTER

CHAPTER 2: THE SAGGING BEAM PROBLEM

CHAPTER 3: THE FISH POND PROBLEM

CHAPTER 4: MODELING THE OPTICAL FILTER PROBLEM

CHAPTER 5: MODELING THE SAGGING BEAM PROBLEM
Quiz #1

CHAPTER 6: PROFESSOR ARCLET TO THE RESCUE

CHAPTER 7: TANGENT FIELDS, AND SOLUTIONS TO DE'S
Quiz #2

CHAPTER 8 : THE FISH POND PROBLEM SOLVED WITH A TANGENT FIELD

CHAPTER 9: SOLVING DIFFERENTIAL EQUATIONS GRAPHICALLY
Quiz #3

CHAPTER 10: A GRAPHICAL SOLUTION TO THE FILTER PROBLEM

CHAPTER 11: SOLVING DIFFERENTAL EQUATION NUMERICALLY
Quiz #4

CHAPTER 12: A NUMERICAL SOLUTION TO THE SAGGING BEAM PROBLEM

CHAPTER 13: THAT EXAM AGAIN
That Exam

APPENDICES
A: Answers to Quiz #1
B: Answers to Quiz #2
C: Answers to Quiz #3
D: Answers to Quiz #4
E: Answers to That Exam