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
xhour Tuesday

Instructor Information
Phone: 6461047 email: scott.pauls@dartmouth.edu Office Hours: Monday 12:30pm1:30pm, Thursday 1pm2pm 
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
Course Structure and Expectations
Exams: This course will have one take home midterm
exam handed out
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
Week 10: Supplemental
topics and/or catchup.