MATH 23: Differential Equations

Fall Term, 2003

Dr. S. Pauls

Text: Elementary Differential Equations and Boundary Value Problems, 7^th edition. Boyce and DiPrima

Course Details MWF 10:00am-11:05am x-hour Tuesday 12:00pm – 12:50pm Classroom:  Bradley 104

Instructor Information Office: 404 Bradley Phone: 646-1047 email: scott.pauls@dartmouth.edu Office Hours:  Monday 12:30pm-1:30pm, Thursday 1pm-2pm

Link to Homework Assignments

Overview

In this course we will cover some of the techniques used to solve differential equations, building on the techniques covered in math 3, 8, and 13. These include but are not limited to separation of variables, constant coefficient methods, the method of undetermined coefficients, variation of parameters, applications of linear algebraic methods to systems of equations, series solutions, Fourier series solutions and transform methods. The objective of mastering these techniques is to apply them to differential equations which model physical or “real world” situations. Although we will see numerous applications of this type throughout the semester, the main goal of the course is to apply the techniques to three of the most important differential equations in physics: the Laplace equation, the heat equation and the wave equation.

Course Structure and Expectations

Exams: This course will have one take home midterm exam handed out October 25^th and due November 1^st. There will also be a final exam, scheduled by registrar. As the registrar has yet to schedule final exams, no student should leave the Hanover area before the 11^th of December. No exceptions or arrangements will be made for students who do not make their travel arrangements appropriately.

Reading Assignments: There will be regular reading assignments for the course. You are expected to read the relevant sections before coming to the class in which we discuss this material.

Homework: There will be regular homework assignments. Usually, there will be problems assigned at the end on one class period which will be due at the beginning of the next class.

Quizzes: I reserve the right to give an unspecified number of quizzes throughout the term. These quizzes may or may not be announced. Unannounced quizzes tend to correlate inversely to the amount of assigned reading the class is completing.

Grading

The course grade breaks down roughly as follows:

Midterm: 25% 

Final Exam: 50% 

Homework and Quizzes: 25% 

Depending on the number of quizzes, the contribution of homework and quizzes to the final grade may be raised or lowered. If a change occurs, I will explain the change completely in class.

Rough Syllabus

Week 1: First and second order linear ODEs, review of separable equations, constant coefficientmethods, modeling of physical systems, etc. (Chapter 2 and the beginning of chapter 3)

Week 2: End of chapter three and chapter 4, including method of undetermined coefficients and variation of parameters. Applications to physical systems associated to vibrations.

Week 3: Chapter 5, power series and series solutions. Be prepared – review series and power series!

Week 4: More series solutions and beginning of systems of equations (chapter 7)

Week 5: Review of necessary linear algebra, techniques for homogeneous linear system with constant coefficients. (More of chapter 7)

Week 6: More complicated systems of linear equations, phase planes (parts of chapters 9 and 10)

Week 7: Fourier series, introduction to partial differential equations and separation of variables (Chapter 10)

Week 8: Applications of separation of variables to the Heat and Wave equations.

Week 9: More wave equation and applications to Laplace’s equation.

Week 10: Supplemental topics and/or catch-up.