**MATH 23:
Differential Equations**

**Dr. S. Pauls**

__Text__: *Elementary Differential Equations and
Boundary Value Problems, 7 ^{th} edition. *Boyce and DiPrima

MWF x-hour Tuesday |
Office: 404 Bradley Phone: 646-1047 Blitz: scott.pauls@dartmouth.edu Office Hours: Monday 3-4pm, Tues 2-3pm, Friday 10-11am |

__Overview__

In this course we will cover
some of the techniques used to solve differential equations, building on the
techniques covered in math 5, 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 *no student should
leave the **Hanover** area before the 14 ^{th} of
March. *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: 100 points

Final Exam: 150 points

Homework: 100 points

Quizzes/Misc: 50 points

Total: 400 points

Depending on the number of quizzes, the contribution of 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 coeef
methods, 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 catch-up.