University of Arizona | Department of Mathematics | |

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Syllabus | Calendar

Homework: due May 1due Apr 10due Apr 1due Mar 25due Mar 11due Feb 20due Feb 13due Jan 30

PROJ	Visualize Riemann surfaces for the functions F(z) = f(z) + 1/f(z), where f(z) = ((z2 − 1)1/2 − z)1/3, and G(z) = arctan z (with clear indication of branching points (e.g., surface for arcsin z from Wikipedia is incomprehensible)). As an example, here are two visualizations of Riemann surface for √1 − z2 (you can check by tracking how parts I, II, III, and IV are connected that the two pictures give the same surface). Here are visualizations of Riemann surface for arcsin z. This project is for MATH 524 students. MATH 424 students can get 12 points from the project (grading is 6 points per surface, no partial credit). due May 1
HW8	2.6: 2, 5, 6, 8, 11, 13, 18 (see also (not a part of HW8) 5 problems on material of 2.6 with answers)
HW7	2.5: 4, 6, 8, 10 Problem 5: Expand in terms of Laurent series the function 1 / (z − 1) (z + 4) in three different ring shaped domains with z = 0 as the center. (See also (not a part of HW7) 5 problems on Laurent series with answers and 2 examples of finding several first terms in the expansion.)
HW6	2.2: 2, 5, 6, 10 (see also (not a part of HW6) 5 problems on radius of convergence with answers); 2.4: 2, 10, 16
HW5	2.3: 2, 4, 8, 10, 12, 15, 16
HW4	2.1: 2, 6, 8, 16, 20 problem 6: Check where the Cauchy–Riemann equations hold for the function f(z):
HW3	1.5: 2, 3, 4, 6, 12, 20 problem 7 (solution of similar problem, solution of yet another one, see also problem 5 from Spring 2012 Midterm 1(B)): Consider a branch of z1/3 with the cut being a ray from the origin passing through −i, with (−1)1/3 = −1. Find ((1 − i√3) / 2)1/3. problem 8: Compare Log(z5) and 5 Log z. Where do they coincide?
HW2	1.4: 2, 3, 5, 6, 8, 10
HW1	1.1: 1, 2, 3, 5, 6, 13