# Spring 2007

 Instructor Dr. Thomas M. Fiore Email Office hours Mondays 1:30-2:30, Wednesdays 3:00-4:00, and by appointment. All office hours are in Room 318, Eckhart Hall. Class Meeting Times MWF 12:30-1:20, Room 016, Albert Pick Hall for International Studies, 5828 S. University Ave. Textbooks Elementary Differential Equations and Boundary Value Problems: Eighth Edition, by William E. Boyce and Richard DiPrima, Complex Variables: Second Edition, by Stephen D. Fisher. Exams In-Class Exam I: Wednesday, April 11th Solutions In-Class Exam II: Friday, May 4th Solutions Final: Thursday, June 7th, 4-6, in Stuart 101 Syllabus Topics Covered Direction fields, classification of differential equations, integrating factors, separable equations, modeling, linear versus nonlinear equations, population dynamics, exact equations, Euler's method, existence and uniqueness theorem, Picard's Iteration Method, difference equations, second order homogeneous equations with constant coefficients, fundamental solution sets, Wronskians, linear independence, characteristic equation and solutions, method of undetermined coefficients, variation of parameters, vibrations, higher order equations, power series review, power series solutions near an ordinary point, power series solutions near a regular singular point, Laplace transform and initial value problems, step functions, equations with discontinuous forcing functions, Dirac delta-function, convolution, geometry of the complex plane (circles and lines), triangle inequality, open subsets, curves, complex functions, complex sequences, complex power series, complex exponential and trigonometric functions, line integrals, Green's Theorem, analytic and harmonic functions, Cauchy-Riemann equations, Cauchy's Theorem, Cauchy's Formula, isolated singularities, Residue Theorem, and applications to definite integrals.

Homework: Homework is due at the beginning of class on Wednesdays. All exercises are in Boyce and DiPrima, until we use Fisher later in the quarter. Use Mathematica or MatLab for the exercises marked with a "mouse symbol" in the text, and hand in the printouts.