Math 372: Solutions to Homework - Williams College.
Math 185 - Introduction to Complex Analysis - Spring 2015 Instructor: Jason Murphy. Complex Analysis by Elias Stein and Rami Shakarchi Additional resources: Sets, logic, and mathematical language by George Bergman Complex Analysis by Theodore W. Gamelin Course notes. Syllabus: The official course description includes the following topics: analytic functions of a complex variable, Cauchy's.
Homework set 2: Chapter 1 Exercises 22, 25. Chapter 2 Problem 1. (due on Friday Sept 29 at the beginning of lecture) Homework 2 solutions. Weeks 4 and 5. Practice problems: Chapter 2 Exercises 1-4, 11-15. These are not to be turned in. Homework set 3: Chapter 2 Exercises 11, 12, 14. (due on Friday Oct 13 at the beginning of lecture) Homework 3.
Complex Analysis, by Elias Stein and Rami Shakarchi; Prerequisite. Math 5021; Preview. We plan to cover most of Chapter 5-7. Homework. There will be weekly due homework sets. Homework is due every Tuesday at the beginning of the lecture. Exams. There will be one midterm exam and one final exam. The Midterm is on March 3rd. The Final is on May 5th, 1:00-3:00p.m. Grading scale. Homework: 40%.
Chapter 1. Preliminaries to Complex Analysis 1 1 Complex numbers and the complex plane 1 1.1 Basic properties 1 1.2 Convergence 5 1.3 Sets in the complex plane 5 2 Functions on the complex plane 8 2.1 Continuous functions 8 2.2 Holomorphic functions 8 2.3 Power series 14 3 Integration along curves 18 4Exercises 24 Chapter 2. Cauchy’s Theorem.
Mathematics 6321 Complex Analysis Spring, 2005 Current reading and homework assignments Due Monday, 2 May There will be a final exam on this date Reading. S-S, Chapter 8, Appendix A, 1-3. Lecture notes from 21 April; Lecture notes from.
Complex Analysis by Elias M. Stein and Rami Shakarchi. Other popular volumes on the subject are Complex Analysis by Lars Ahlfors. Complex Analysis by Ted Gamelin. Analytic Functions by Stanislaw Saks and Antoni Zygmund, which is available online. Our discussion of harmonic functions is strongly influenced by Chapter 2 of.
Course textbook: Complex Analysis by Elias M. Stein and Rami Shakarchi. Princeton University Press, 2003. Course syllabus: open in PDF; Course lecture notes. Complex Analysis Lecture Notes (PDF, version of March 22, 2020) Some supplementary material; Homework. Recommended HW for week 1: problems 1-7 in the lecture notes.
Chapter 2 Complex Analysis In this part of the course we will study some basic complex analysis. This is an extremely useful and beautiful part of mathematics and forms the basis of many techniques employed in many branches of mathematics and physics. We will extend the notions of derivatives and integrals, familiar from calculus.
Week: Reading: Homework: Solutions: 13: Nov 30 - Dec 2 Moduli Spaces and Modular Forms Serre, Ch. VII; Ahlfors, Ch. 7; Course Notes 5. HW: SOLN: 12: Nov 23.
Homework is due in class on Tuesday. Late homework is not accepted. Do not submit homework by email. Late homework is not accepted. Do not submit homework by email.
Several complex variables; S. G. Krantz, Function Theory of Several Complex Variables, 2nd ed., AMS, 2001. L. Hormander, An Introduction to Complex Analysis in Several Variables, Elsevier, 1973. Despite its title, Narasimhan and Nievergelt, Complex Analysis in One Variable, contains an introductory chapter on several complex variables.
Homework Assignments. Homework 1 due Friday, January 24 (Read Intro and Chapter 1) Homework 2 due Monday, February 3 (Start Chapter 2) Homework 3 due Wednesday, February 12 (Chapter 2) Homework 4 due Friday, February 21 (Start Chapter 3) Homework 5 due Friday, February 28 (Chapter 3) Homework 6 due Friday, March 27 (Chapter 3).
Final: The final is 1-2:30 PM on Friday, April 27. It will be replica of the complex analysis half of the analysis prelim. Grades: Your grade will be determined by your homework scores and the final. Roughly speaking if I think you have a good chance of passing the prelim you will get an A.
