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This is an introductory course to Complex Analysis at an undergraduate level. Complex
Analysis, in a nutshell, is the theory of differentiation and integration of functions
with complex-valued arguments *z = x + i y* , where

The text book used for the course is **
Complex Variables (Dover Books on Mathematics) by Flanigan, Francis J**. The book can be purchased through the bookstore or online
via Amazon. It is ot necessarily my favorite book, but it is very cheap and
considering the price it *is* a good book. Incidentally, you should check other
books from the Dover Books on Mathematics series; they are *all* cheap
and worth purchasing.

To easily follow the lectures we will use the computer program *DyKnow*,
available from our homepage. You should bring your laptop charged and ready to
every class.

My office is in Science Building, room 118 D, and you can reach me by phone at
(973) 761-9000 x5167 or - much preferred - via email at `
wachsmut@shu.edu`. My office hours
are Mon & Wed from 11 am to 12 pm

There will be homework assigned during each class, which will be due and collected the next time class meets. No late homework is accepted, except in special circumstances. There will be two exams during the semester, and possibly a final exam during the officially scheduled time. In addition, each person is required to explain a homework problem on the board at least once. While that performance is not graded, it is required for passing the course. The final grade is computed as follows: 45% homework, 45% exams, 10% participation

The course will cover material that is considered standard for an undergraduate complex analysis course:

*1*. Complex Numbers (Basic Algebraic, Vectors and Moduli,Conjugates,Exponentials, Products and Powers, Roots, Regions in the Complex Plane)*2*. Analytic Functions (Limits, Continuity, Derivatives, Cauchy�Riemann Equations, Analytic Functions, Harmonic Functions)*3*. Elementary Functions (Exponential, Logarithm, Complex Exponents, Trigs, Hyperbolic Functions)*4*. Integrals (Definite Integrals, Contour Integrals, Antiderivatives, Cauchy�Goursat Theorem, Cauchy Integral Formula, Liouville's Theorem, Fundamental Theorem of Algebra, Maximum Modulus Principle)*5*. Series (Sequences, Convergence of Series, Taylor Series, Laurent Series, Absolute and Uniform Convergence, Power Series techniques)*6*. Residues and Poles (Residues, Cauchy's Residue Theorem, Residue at Infinity, Zeros of Analytic Functions)

We might also cover excerpts from "Applications of Residues), "Mapping by Elementary Functions", or some "Dynamic Systems", depending on how the course progresses.