AE 525a/ME 525 Spring 2003
www.usc.edu/dept/engineering/mecheng/meclasses_dravinski/ME525S03.html
Time and Place: T,Th 5-6:15 PM, OHE 100
Instructor: M. Dravinski
Office Hours: T,Th 2-4 PM, OHE 430 I, 213-740-0493, mdravins@usc.edu
Grader: Z. Chen, M 2-5, Th 1-5, VHE 202, 213-740-8253, zhengxic@usc.edu
Texts:
Homework: Due to each Tuesday. No late homeworks.
Exams: Midterm: Th, February 27, 2003, 5-6:15 PM. Final: T, May 6, 2003, 4:30-6:30 PM. Closed books and notes, no calculators. No makeup exams.
Grade: HW(10%) + MD(45%)+FE(45%)
Course Outline
Matrices and Linear Equations (Lct #1, Lct #2, Lct #3, Lct #4, Lct #5, Lct #6)
Linear equations, Gauss-Jordan reduction, matrices, determinants, Cramer’s rule, special matrices, inverse matrix, rank of a matrix, elementary operations, solvability of linear equations, linear vector spaces, linear equations and vector space, eigenvalue problem, orthogonalization of vector sets, quadratic forms, equivalent matrices and transformations, Hermitian matrices, multiple eigenvalues of symmetric matrices, functions of symmetric matrices, least-squares solutions.
Functions of Complex Variables (Lct #8, Lct #9, Lct#10, Lct#11, Lct #12)
Analytic functions, multiple valuedness, branch cuts and Riemann surfaces, Cauchy-Riemann equations, integration in the complex plane, Cauchy theorem, multiple connected regions, Cauchy integral formula, Taylor and Laurent series, isolated singularities, zeros and poles, analytic continuation, residues and their applications, improper integrals, special functions, Laplace and Fourier transforms.