The pages refers to the pages in Complex Analysis: An Introduction, Lars V. Ahlfors, McGraw-Hill, 2nd Ed. (1966). These are almost the same as for the 3rd edition but different from the 1st edition. So please try to use the 2nd one. Some copies will be put on reserve in the library.

HW1 : due Wed Sept 17th :

1.2 analytic functions (p28 in the 2nd edition) problems : 1 and 2

1.4 rational function (p33 in the 2nd edition) problems : 1, 2 and 3

2.4 power series (p41 in the 2nd edition) problem : 3

HW2 : due Wed Sept 24th :

p45 : 3,4

(3.4 The Logarithm) p48 : 3, 5,

p73 : 1

HW3 : due October 1st

p78 : 3, 4

p80 : 3,

p82 : 6,

p88 : 6

HW4 : due October 8th

p108 : 4,6

p123 : 2,3,4

HW5 : due October 15th

p130 : 2,3, 5

p133 : 1, 4

If you did not get full grad for pb 3 in page 78, you can try this pb again or ask Sho about it.

HW6 : due October 22nd

p136 : 1,2, 5

p147 : 3, 4

HW7 : due October 29th

p160 : 4, 5, 7

p136 : 3, 4

HW8 : due November 5th

p160 : 8, 9

p164 : 1 , 2, 3

HW9 : due November 12th

p169 : 1, 2, 5

p172 : 1, 3

HW10 : due November 19th (try to do this HW in 2h)

p176 : 2, 3

p182 : 2(just compute P_1 and P_2 ), 5

p184 : 4

HW11 : due November 26th (extended to Dec 1st)

p188 : 1, 4

p191 : 1, 2

p196 : 1

Practice Exam.

Here are more pbs to help you go through the material of the begining of the semester :

p108 : 3, 6

p120 : 1

p123 : 3, 4, 5

p130 : 2,4, 5

p133 : 4

p136 : 1

p160 :

p169 : 1, 3

Office hours of the grader : Sho Tanimoto (tanimoto@cims.nyu.edu) room 1004 : Monday from 1-3 PM or by appointment.

G63.2451.001 COMPLEX VARIABLES (one-term format)

3 points. Fall term.

Mondays, Wednesdays, 9:15-10:30, N. Masmoudi.

Note: Master's students should consult course instructor before registering for this course.

Prerequisites: advanced calculus, or G63.1410 Introduction to Math Analysis. Concurrent registration is not permitted.

Complex numbers, the complex plane. Power series, differentiability of convergent power series. Cauchy-Riemann equations, harmonic functions. conformal mapping, linear fractional transformation. Integration, Cauchy integral theorem, Cauchy integral formula. Morera's theorem. Taylor series, residue calculus. Maximum modulus theorem. Poisson formula. Liouville theorem. Rouche's theorem. Weierstrass and Mittag-Leffler representation theorems. Singularities of analytic functions, poles, branch points, essential singularities, branch points. Analytic continuation, monodromy theorem, Schwarz reflection principle. Compactness of families of uniformly bounded analytic functions. Integral representations of special functions. Distribution of function values of entire functions.

Text: Complex Analysis: An Introduction, Lars V. Ahlfors, McGraw-Hill, 3rd Ed.