Math 275

Differential Equations

Instructor

  • Chuck Iverson
  • Office Hours: MESA/Learning Center
  • Office: 18-108
  • Office Phone: (650) 306-3253
  • Email: iverson@smccd.edu
  • Web Page: http://www.civerson.com

Class Location and Meeting Times

  • Building 16, Room 108
  • 12:45-2:00 pm MW

Prerequisite

  • Math 252 with a grade of C or better

Materials

  • Differential Equations (2nd Edition) by Polking (ISBN 9780131437388)

Grading

  • Homework (25%)
  • Exams and Quizzes (70%)
  • Class Participation (5%)

Course Description

Study of vectors, systems of linear equations, the algebra of matrices, determinants, eigenvalues and eigenvectors, vector spaces, inner products and least-squares.

Sample Student Learning Objectives

  • Correctly classify differential equations by degree (first-order, second-order, ...) and type (linear/nonlinear, ordinary/partial, homogeneous/driven).
  • Correctly develop a differential equation to model a particular system.
  • Correctly determine whether a given function is a solution to a differential equation.
  • Correctly use standard methods (integrating factors, undetermined coefficients, variation of parameters, Laplace Transforms, power series, numerical methods) to find a solution to an initial-value-problem.

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 contribute significantly to the final grade. One by-arrangement hour of tutorials and exercises in the Math Lab is also required per week.

Class Notes and Assignments

http://www.civerson.com/M275/

Exams and Quizzes

Frequent quizzes, two midterm exams and a final exam will be given during the semester. Each midterm exam will cover several chapters. You may have one sheet of notes for each exam. See the tentative schedule below for the dates of the exams. Quizzes may be given during the first 15 minutes of each class, based on the material discussed in the previous class. The average of your top ten quiz scores will count as one exam score.

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.

Software

We'll be using Matlab (or SysquakeLE), Graphing Calculator and GeoGebra extensively in class to aid your understanding, to simplify routine calculations and to allow us to examine more interesting topics. It's not necessary to have these programs at home, but it may be useful. SysquakeLE (http://www.calerga.com/download/index.html) is cross-platform, free and duplicates many of Matlab's facilities for use in this class. Graphing Calculator, in particular, is an immensely helpful and easy-to-use math program that can be used through all math courses offered at Cañada College, and it will help you to visualize what's going on with vectors, lines and surfaces in two and three dimensions. To encourage students in mathematics, the creator of the program offers special student rates: $20 for a one-year rental or $60 (educational discount -- equivalent to two large pizzas, but so much better for you): http://www.pacifict.com/Order.html. I personally use this program every day. I recently learned about GeoGebra (http://www.geogebra.org/cms/), another free and very useful program.

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, more than 4 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 a tutor if you are having difficulty completing them.
  • You should check the class notes and assignments link (top right of this page) if you miss class. All class assignments, exam solutions, sample code and special notes will be posted at this web site after class.
  • You are expected to see me during office hours for additional help or to take make-up exams.

Instructor's Fall 2011 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.

fall2011Schedule

Tentative Topic Schedule

Tuesday Thursday
8/18 - 1.1 DE Models
1.2 Derivatives
1.3 Integration
8/23 - 2.1 DE Solutions
2.2 Separable Equations		 8/25 - 2.3 Models of Motion
8/30 - 2.4 Linear Equations 9/01 - 2.5 Mixing Problems
9/06 - 2.6 Exact DEs 9/08 - 2.7 Solution Existence and Uniqueness
2.8 Initial Conditions
9/13 - 2.9 Autonomous Equations and Stability 9/15 - 3.1 Modeling Population Growth
3.2 Models and the Real World
9/20 - 3.3 Personal Finance
3.4 Electrical Circuits		 9/21 - Review of Chapters 1-3
9/27 - Exam on Chapters 1-3 9/29 - 4.1 Definitions and Examples
4.2 Second-Order Equations and Systems
10/04 - 4.3 Linear, Homogeneous Equations with Constant Coefficients
4.4 Harmonic Motion		 10/06 - 4.5 Undetermined Coefficients
10/11 - 4.6 Variation of Parameters 10/13 - 4.7 Forced Harmonic Motion
10/18 - 5.1 Laplace Transform Definition
5.2 Properties of Laplace Transforms		 10/20 - 5.3 Inverse Laplace Transforms
5.4 Solving DEs with Laplace Transforms
10/25 - 5.5 Discontinuous Forcing Terms 10/27 - 5.6 Delta Functions
11/01 - 5.7 Convolution
5.8 Summary		 11/03 - Review of Chapters 4-5
11/08 - Exam on Chapters 4-5 11/10 - 11.1 Power Series
11/15 - 11.2 Power Series 11/17 - 8.1 Definitions and Examples
8.2 Geometric Interpretation of Solutions
11/22 - 8.3 Qualitative Analysis
8.4 Linear Systems		 11/24 - Thanksgiving Holiday
11/29 - 8.5 Properties of Linear Systems
9.1 Overview of the Technique		 12/01 - 9.2 Planar Systems
9.3 Phase-Plane Portraits
12/06 - 9.4 The Trace-Determinant Plane 12/08 - Review of Chapters 8, 9 and 11
12/13 - No Class 12/15 - 11:10-1:40
Final Exam


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