Reading List
MATH 6300, Fall 2005
Reading List has been updated to include
material
assigned on
December 8, 2005
Textbooks
Ahlfors, Complex Analysis: nice
standard graduate textbook on complex analysis. Theoretically
inclined
(analysis and algebra).
Ablowitz and Fokas, Complex Analysis:
advanced applied mathematical treatment of complex analysis.
Dettman, Applied Complex Variables:
a relatively inexpensive textbook with a concrete, application-oriented
style
All textbooks are optional. I may suggest readings in
one or the other during the lectures, but many topics can be found in
all
three texts. For those instances in which I cover a topic
not
treated in all the books, I'll have the relevant material scanned into
a PDF file and posted here. So you should have at least one
graduate level complex analysis text, but you can choose the one (or
several) that
suit your taste.
Readings to complement the lectures and homework will be listed
here, organized by topic. Dates
indicate
the class by which you should have read the indicated
material.
Some readings may be announced here before they are announced in class,
in case you want to read ahead. Sometimes, particularly if
I am traveling, you may find some references posted at the library
class
reserves before they are linked here.
I am still trying to figure out how to link directly from this web
page to the class reserve readings, but for now you can go directly to
the library website and access them that way.
Complex Numbers, Arithmetic, Algebra, and
Basic Geometry
- Ahlfors 1.1.1-1.2.3 (09/12/05)
- Ablowitz and Fokas 1.1, 2.2 (09/12/05)
- Dettman 1.1-1.3 (09/12/05)
Stereographic Projection
- Ahlfors 1.2.4 (09/12/05)
- Ablowitz and Fokas 1.2.2 (09/12/05)
- Dettman
1.5 (class reserves) (09/12/05)
- includes discussion of chordal metric
Functions of a Single Complex Variable
- Ahlfors 2.1.1 (09/12/05)
- Ablowitz and Fokas 1.2.1 (09/12/05)
- Dettman 2.1 (09/12/05)
Linear Fractional Transformations
- Ahlfors 3.3 (09/15/05)
- Ablowitz and Fokas 5.7 (09/15/05)
- Dettman 2.4 (09/15/05)
Analytic Functions
- Ahlfors
2.1.1, 2.1.2 (09/26/05) (class reserves)
- includes using z and z-bar formally as independent variables
(rather than x,y)
- Ablowitz and Fokas 1.3, 2.1 (09/26/05)
- Dettman 2.2, 2.3, 2.5 (09/26/05)
Multi-valued Functions, Branch Cuts, and
Riemann Surfaces
- Ahlfors 3.4.3 (09/26/05)
- Ablowitz and Fokas 2.2, 2.3
(class reserves) (09/26/05)
- Dettman 2.6 (09/26/05)
Integration in the Complex Plane
- Ahlfors 4.1, 4.2 (10/03/05)
- Ablowitz and Fokas 2.4-2.6 (10/03/05)
- Dettman 3.1-3.4, 3.6, 3.7 (10/03/05)
Taylor Series and Laurent Series
- Ahlfors 5.1 (10/10/05)
- Ablowitz and Fokas 3.1-3.4 (10/10/05)
- Dettman 4.1-4.4, 4.6 (10/10/05)
Singularities
- Ahlfors 4.3 (10/17/05)
- Ablowitz and Fokas 3.5 (10/17/05)
- Dettman 4.6 (10/17/05)
Mittag-Leffler Expansion and Weierstrass
Product Expansion
- Ahlfors 5.2 (10/20/05)
- Ablowitz and Fokas 3.6 (10/20/05)
Residue Theory of Integration
- Ahlfors 4.5 (10/20/05)
- Ablowitz and Fokas 4.1-4.3 (10/20/05)
- Dettman 5.1-5.2 (10/20/05)
Principle of the Argument and Rouche's
Theorem
- Ahlfors 4.5.2 (11/03/05)
- Ablowitz and Fokas 4.4 (11/03/05)
- Dettman 5.3 (11/03/05)
Series Solutions of Ordinary Differential
Equations
- Ahlfors 8.4.1-8.4.2 (11/14/05)
- Ablowitz and Fokas 3.7 (11/14/05)
- Dettman 7.3-7.6 (11/14/05)
Complex-Valued Functions Defined Through
Integrals
- Ablowitz and Fokas 3.2 (11/14/05)
- Dettman 3.5 (11/14/05)
Conformal Mapping
- Ablowitz and Fokas 5 (11/28/05)
- Ahlfors 3.2, 6 (11/28/05)
- Dettman 6.4 (11/28/05)
Complex Variable Techniques in Fluid
Mechanics
Analytic Continuation
- Ablowitz and Fokas 3.2, 3.5.1 (12/12/05)
- Ahlfors 8.1 (12/12/05)
- Dettman 4.4, 4.5, 4.10 (12/12/05)