MATH 412
Complex Variables for Applications

Fall Semester 2003

Assignments in the course

TIME OF MEETING: Tue & Thr  9:45 - 11:05
PLACE: HU 0023
INSTRUCTOR: Karin Reinhold,  ES 128A,  phone 442-4641
Office hours:   11:05-11:45 Tues Thrs  or by appt.,  or by e-mail.
TEXT: Fundamental of Complex Analysis, by Saff & Snider, Prentice Hall.


Complex numbers: the algebra of complex numbers, vector and polar representations, modulus and conjugation,commplex exponential, powers and roots, applications to mechanics.
Analytic Functions: functions of a complex variable, limits and continuity, analyticity, Cauchy-Riemann equations, harmonic functions, applications to steady state temperature.
Elementary functions: Exponential, trigonometric and hyperbolic functions, the Log function, complex powers, application to oscillating systems.
Complex integration: Contours and contour integrals, independence of path, Cauchy's integral theorem, Cauchy's integral formula and consequences, application to harmonic functions.
Series: Sequences and series, Taylor Series, power series, Laurent series.
Residue Theory: The residue theorem and applications to certain trig integrals.

TEST SCHEDULE: (tentative)

Sept 23: Exam 1, chapters 1 & 2
Oct 16: Exam 2, chapters 3 & 4
Nov 11: Exam 3, chapter 5
Dec 9: Exam 4, chapter 6
Dec 17: Final Exam 1-3
The above schedule is ambitious, we'll adjust it as we advance thorugh the material of the course. The final grade will be based on homework assignments and the best three scores of your tests. A minimum average of 50% is required to pass the course, not more than one exam can be failed (below 30%), all 4 exams are required to pass the course, plus a final exam.
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