Series and Boundary Value Problems

Office Hours

Donovan 2283:

Monday 3:00 -- 5:00 PM Thursday 4:00 -- 5:00 PM Friday 10:00 -11:00 AM

Or by appointment

TEXTBOOK: Dennis G. Zill: Differential Equations with Boundary-Value Problems, 5^th edition, Brooks/Cole Publishing Company

DESCRIPTION: This course is a continuation of MAT330 (Differential Equations). Since the topic of infinite series is not covered in MAT 322, we will be covering this topic in this course. After this, the focus of the course will be to use series techniques (including Fourier series) for the purpose of solving linear ordinary and partial differential equations, specifically focusing on those that occur in engineering and physics applications.

PREREQUISITES: MAT 330 or equivalent

1. Infinite Series (Ch.8 of Larson & Hostetler or any other calculus text)
   • Sequences, Series, tests of convergence
   • Power Series
   • Taylor and Maclaurin series
2. ODEs with Variable Coefficients (4.7, Ch.6)
   • Cauchy - Euler equation
   • Power series solutions
   • Solutions around ordinary and singular points
   • Bessel and Legendre equations
3. Orthogonal Functions & Fourier Series (Ch.11)
   • Periodic Functions, Trigonometric series, Dirichlet conditions
   • Fourier Series, complex form of Fourier series
   • Sturm-Liouville problem
4. Boundary Value Problems (Ch.12)
   • Separable partial differential equations
   • Heat, wave and Laplace's equations
5. The Fourier Transform (Ch.14)
   • Fourier cosine and sine integrals
   • Fourier transforms
   • Application to boundary value problems

Homework:
There will be problems assigned from the textbook each week. Indicated problems will be collected and graded. No late submissions are accepted! Also, we will use Computer Algebra systems such as Maple or Mathematica. Becoming familiar with them will be part of the homework assignments.

EVALUATION
There will 2 in class exams and a final exam. First exam will be on Thursday February 26, the second will be on Tuesday April 6, and the final will be during the week of May 10, 2004. These dates are subject to change. All exams are closed book and no calculators permitted. Any cheating will result in F grade!

• 15 % for assignments
• 25 % for each partial exam
• 35 % for final exam (cumulative)

Optional topics:
Extra credit during exam can be earned by solving the "Bonus Question" containing the material from the optional topics.

Make-ups:
Make up for an exam will be permitted only if there is a legitimate reason for the absence, and if I am notified before the exam.

Grades:

A+:	96-100%		C+:	70-74%
A:	92-95%		C:	65-69%
A-:	88-91%		C-:	60-64%
B+:	84-87%		D+:	55-59%
B:	79-83%		D:	50-54%
B-:	75-78%