Math 275

Differential Equations

Instructor

Chuck Iverson (http://www.civerson.com, iverson@smccd.edu)

Class Location and Meeting Times

Building 22, Room 118 
9:45-11:00 am TTh

Prerequisites

Physics 250 and Math 252, both with a grade of C or better.

Materials

  • Differential Equations (2nd Edition) by Polking, Boggess and Arnold (ISBN: 0-13-143738-0)

Grading

Your grade will be based on:

  • Homework and Exercises (30%)
  • Exams and Quizzes (70%)

Course Description

One motivation in the development of Calculus was to express the fundamental principles that govern many phenomena in our everyday lives in the language of differential equations. The resulting equations involve rates of change and can be used to predict the future behavior of physical, biological, economic and other systems. This course focuses on the formulation of differential equations and the interpretation of their solutions. Solutions are analyzed from three different points of view: qualitatively (by the use of slope fields, graphs, vector fields, phase planes), numerically (using spreadsheets, calculators and various computer programs), and analytically (finding explicit solutions when possible).

Homework

Reading the textbook and doing the assigned exercises are the most important work students can do between classes to insure understanding of concepts and to develop skill in applying problem solving techniques. Consequently, exercises and labs are collected and contribute 30% to the final grade. Late assignments get a maximum of half credit. Each set of exercises or problems must have the following information printed at the top, right corner of the page: student name, section number, page numbers, exercise numbers and date. For example:

  • Your Name
  • Section 1.5
  • pp. 57-59 (1-29, odd)
  • 9/25/08

Exams

Frequent quizzes, two midterm exams and a final exam on the last three chapters will be given during the semester. Each midterm exam will cover two chapters. The final exam will cover three chapters. You may have one sheet of notes for each chapter covered. See the tentative schedule below for the dates of the exams.

Make-Up Exams

A make-up exam will be offered to any student who scores less than his or her homework average on a particular exam. Before taking a make-up exam, a student must meet with me to review his or her original exam. A make-up exam score will be limited to a student's current homework average. A make-up exam score will replace an original exam score only if the make-up exam score is higher.

Expectations

I can help you succeed in this class, but I can't succeed for you. In this class you're expected to be responsible for your own academic success.

  • That means you are expected to attend class and to arrive on time (2 lates equals 1 absence, 7 absences leads to a drop).
  • If you're going to miss class, you should notify me ahead of time, either by phone or email.
  • You are expected to contribute to class discussions and to ask questions when something is not clear.
  • You are expected to do your homework assignments before the class when they are due and to seek help from me or your classmates or Nancy Ward if you are having difficulty completing them.
  • You should check WebAccess (http://smccd.mrooms.net/) for assignments and class notes if you miss class.
  • You are expected to see me during office hours for additional help or to take make-up exams.
WebAccess

All class assignments, exam solutions and special notes will be posted on the web after class (with links on WebAccess). You are invited to share questions, answers, ideas, opinions, and suggestions by posting them on WebAccess.

Instructor's Fall 2008 Class Schedule

My class schedule, below, shows when and where I'm on campus. The best way to contact me if I'm not on campus is via email. I check my email several times a day. I have my email automatically sorted by the first 4 characters in the subject field. For this class, the subject line of the email should begin with M275.

F08Schedule

Tentative Topic Schedule

TuesdayThursday
8/19 - 1.1 DE Models
1.2 Derivatives
1.3 Integration
8/21 - 2.1 DE Solutions
2.2 Separable Equations
8/26 - 2.3 Models of Motiion 8/28 - 2.4 Linear Equations
9/2 - 2.5 Mixing Problems 9/5 - 2.6 Exact DEs
9/9 - 2.7 Solution Existence and Uniqueness
2.8 Initial Conditions
9/11 - 2.9 Autonomous Equations and Stability
9/16 - 3.1 Modeling Population Growth
3.2 Models and the Real World
9/18 - 3.3 Personal Finance
3.4 Electrical Circuits
9/23 - Chapter 1-3 Review 9/25 - Chapter 1-3 Exam
9/30 - 4.1 Definitions and Examples
4.2 Second-Order Equations and Systems
10/2 - 4.3 Linear, Homogeneous Equations with Constant Coefficients
4.4 Harmonic Motion
10/7 - 4.5 Undetermined Coefficients 10/9 - 4.6 Variation of Parameters
10/14 - 4.7 Forced Harmonic Motion 10/16 - 5.1 Laplace Transform Definition
5.2 Properties of Laplace Transforms
10/21 - 5.3 Inverse Laplace Transforms
5.4 Solving DEs with Laplace Transforms
10/23 - 5.5 Discontinuous Forcing Terms
10/28 - 5.6 Delta Functions
10/30 - 5.7 Convolutions
5.8 Summary
11/4 - Chapter 4-5 Review 11/6 - Chapter 4-5 Exam
11/11 - 11.1 Power Series 11/13 - 11.2 Power Series
11/18 - 8.1 Definitions and Examples
8.2 Geometric Interpretation of Solutions
11/20 - 8.3 Qualitative Analysis
8.4 Linear Systems
11/25 - 8.5 Properties of Linear Systems 11/27 - Thanksgiving Holiday
12/2 - 9.1 Overview of the Technique
12/5 - 9.2 Planar Systems
12/9 - 9.3 Phase-Plane Portraits 12/11 - 9.4 The Trace-Determinant Plane

12/18 - 11:10-1:40 Exam on Chapters 8, 9, 11