|
|
||||||
|
MAT 709 Complex Function Theory
- I Fall 2007: 3
credits
|
||||||
|
Analytic
functions, conformal mappings, Cauchy’s theorem, power series, Laurent
series, the Riemann mapping theorem, harmonic functions, subharmonic
functions, canonical mappings of multiply connected regions, analytic
continuation. Prerequisite: MAT 657 or MAT 659 or equivalent. |
||||||
|
Taught by |
|
|||||
|
Listserv |
|
|||||
|
Grading |
Tests/HW:
65%; Final: 30%; Attendance: 5% Guaranteed
Grades: A- ( > 90%); B- ( > 80%); C- ( > 70%); |
|||||
|
Lecture Room |
CBC C124 |
|||||
|
Lecture Time |
MW from
1:00p - 2:15p |
|||||
|
Office Hours |
Location: TBE B108; 12:00 P.M. - 02:00 P.M. |
|||||
|
Textbook |
Complex
Analysis (Publisher: Springer, ISBN #978-0-387-95069-3) |
|
Schaum's Outline of
Complex Variables (Paperback) by |
|||
|
Links |
||||||
|
Schedule |
||||||
|
Dates |
Days |
Topics |
Textbook (CA: Complex
Analyis, SO: Schaum’s Outline) |
|||
|
Aug 27 |
M |
Complex
Numbers, representation |
Chapter I
(CA) and Chapter 1 (SO) |
|||
|
W |
Stereographic
projections, functions |
Chapter I
(CA) and Chapter 2 (SO) |
||||
|
Sept 3 |
M |
Labor Day
Recess |
|
|||
|
W |
Riemann
Surfaces, sequences, limits |
Chapter II
(CA) and Chapter 2 (SO) |
||||
|
Sept 10 |
M |
Topology,
analytic fns, Cauchy Riemann, Inverse Map |
||||
|
W |
Harmonic
fns, Conformal Map, Mobius Trans. |
Chapter II
(CA) and Chapter 3 (SO) |
||||
|
Sept 17 |
M |
Line
Integrals, Green's thm, Exact & closed diff. forms |
Chapter III
(CA) |
|||
|
W |
Harmonic
conjugates, mean value thm, max prin., appl. |
|||||
|
Sept 24 |
M |
|
||||
|
W |
Fluid
Dynamics, Heat and Electromagnetics |
Chapter III
(CA) |
||||
|
Oct 1 |
M |
Complex
Line Integrals, Fnd Thm, Cauchy Integral |
Chapter IV
(CA) and Chapter 4-5 (SO) |
|||
|
W |
Liouville’
Thm, Morera’s Thm |
|
||||
|
Oct 8 |
M |
Gaursat’s
Thm, Complex Calculus Notation |
||||
|
W |
Pompeiu’s
Formula |
|||||
|
Oct 15 |
M |
|
||||
|
W |
Infinite
Series, of functions, Power Series |
Chapter V
(CA) and Chapter 6 (SO) |
||||
|
Oct 22 |
M |
Analytic Functions, Exp
at Infinity |
Chapter V
(CA) and Chapter 6 (SO) |
|||
|
W |
Series
Manipulation, Zeros, Analytic Continuation |
Chapter V
(CA) and Chapter 6 (SO) |
||||
|
Oct 29 |
M |
Laurent
Decomposition, Series |
Chapter VI
(CA) and Chapter 6 (SO) |
|||
|
W |
Isolated
Singularities, Partial Fractions |
HW#5 Due ; Chapter VI (CA) and Chapter 6 (SO) |
||||
|
Nov 5 |
M |
Residues,
Rational, Trig, br. Pts. Fns, frac res. |
Chapter VII
(CA) and Chapter 7 (SO) |
|||
|
W |
Argument
Principle, Rouche’s Hurwitz’s Thms |
Chapter
VIII (CA) |
||||
|
Nov 12 |
M |
Veteran’s
Day |
HW#6 Due ; |
|||
|
W |
|
|||||
|
Nov 19 |
M |
Open
Mapping, Inv. Fn thm, winding #, critical pts. |
Chapter
VIII (CA) |
|||
|
W |
Schwarz
Lemma, Hyperbolic Geomtery |
Chapter IX
(CA); |
||||
|
Nov 26 |
M |
Schwarz
Lemma, Hyperbolic Geomtery |
Chapter IX
(CA) HW#7 |
|||
|
W |
Harmonic
Functions and Reflection Principle |
Chapter X (CA) |
||||
|
Dec 3 |
M |
Harmonic
Functions and Reflection Principle |
Chapter X
(CA) and Chapter 10 (SO) |
|||
|
W |
||||||
