132/3 - Complex Analysis for Applications - Spring 2012 - UCLA

• 04/02 - I.1-2: complex numbers and the polar representation.
• 04/04 - I.4-5: the square and square root functions and the exponential function.
• 04/06 - I.6-7: the logarithm function and power functions.
• 04/09 - I.7-8: phase factors, trig, and hyperbolic functions.
• 04/11 - II.1-2: sequences, convergence, limits, continuity, and analyticity.
• 04/13 - II.3: the Cauchy-Riemann equations, inverse mappings, the jacobian, harmonic functions.
• 04/16 - II.4-5: the Jacobian, inverse mappings, and harmonic functions.
• 04/18 - II.6: conformal mappings.
• 04/20 - II.7: fractional linear transformations.
• 04/23 - III.1: line integrals.
• 04/25 - III.1: line integrals.
• 04/27 - III.1: Green's theorem.
• 04/30 - III.2: independence of path.
• 05/02 - III.3-4: harmonic conjugates and the mean value property.
• 05/04 - III.5: the maximum principle. Midterm posted on-line [pdf].
• 05/07 - IV.1: complex line integrals. Midterm due [Solutions].
• 05/09 - IV.1-2: ML-inequality and the fundamental theorem of calculus.
• 05/11 - IV.2-3: proof of the fundamental theorem and Cauchy's theorem.
• 05/14 - IV.4: the Cauchy integral formula.
• 05/16 - IV.5-6: Liouville and Morera's theorems.
• 05/18 - V.2: sequences and series of functions.
• 05/21 - V.3-6: power series expansions of analytic functions.
• 05/23 - V.3-6: power series expansions of analytic functions.
• 05/25 - V.7: the zeros of an analytic function.
• 05/28 - No class, Memorial Day.
• 05/30 - VI.1: the Laurent decomposition.
• 06/01 - VI.2: isolated singularities.
• 06/04 - VII.1: the residue theorem.
• 06/06 - VII.2: integrals of rational functions.
• 06/08 - VII.3-4: integrals of trig functions and integrals over branch points. Final posted on-line [pdf].
• 06/14 - Final exam due. Slip it far under my door, MS 6617D.

• Week 2 (due 04/12) - To turn in: I.1: 8, 9. I.2: 1.b. I.4: 1.a, and I.6: 2.b. Strongly suggested: I.1: 1.b, 1.g, 1.c, 2, 11. I.2: 1.a, 1.c, 1.h, 4, 6, 8. I.4: 1.d, 2.a, 2.d, 3. I.5: 1, 3, 4. I.6: 1, 2.a. I.7: 1, 2, 5. I.8: 1-3. [pdf]
• Week 3 (due 04/19) - To turn in: II.1: 13. II.2: 2. II.3: 1.b. II.4: 2. II.5: 1.d. Strongly suggested: II.1: 1, 2, 11, 13, 15, 19. II.2: 1, 3, 6. II.3: 1.a, 1.c, 3, 4, 8. II.4: 1, 3, 7, 8. II.5: 1, 4, 5, 8. II.6: 1, 2. II.7: 1.a, 1.b, 6.
• Week 4 (due 04/27) - To turn in: II.6: 5. III.1: 6-7. III.2: 2. III.3: 1.b. Suggested: II.7: 11-12. III.1: 1-3, 8. III.2: 1. III.3: 1.
• Week 5 (due 05/04) - To turn in: III.2: 3, 7. III.3: 1.c, 4. III.4: 1. Suggested: III.2: 5, 6. III.3: 1, 2, 3. III.4: 2.
• Week 7 (due 05/18) - To turn in: IV.1: 5. IV.2: 4. IV.4: 1.c, 1.g. IV.5: 2. Suggested: IV.1: 1-4, 6-8. IV.2: 1-2, 5. IV.3: 4, 6 IV.4: 1, 2, 4. IV.5: 1, 3. IV.6: 1.
• Week 8 (due 05/25) - [hw6.pdf].
• Week 9 (due 06/01) - [hw7.pdf].
• Week 10 (due 06/08) - [hw8.pdf].

• The final raw score will be computed with the following weights: 25% homework, 20% midterm, 30% final, 25% final project.
• Both the midterm and the final will be take-home exams.
• The final project will consist of a 10 minute presentation to one of the instructors in private, together with a write-up, on a topic you will choose in consultation with us.
• A grade of 'F' will be assigned to any student who misses the final. Incompletes are reserved for those who have completed all of the work for the class, including the midterm, but who, for a legitimate, documented reason, miss the final.
• The math department sets suggested ratios for the number of A grades, B grades, and so forth. For this course, the suggestion is 30% As, 33% Bs. The remainder mostly receive Cs, except for those who are not prepared to move on.
• However, we will give a template for what the letter grades mean, and we will stick to giving final grade based on those templates.

• We encourage everyone to use the free discussion board piazza.com for discussion of the class. You may go to their website, and enroll in MATH 132/3. This is a site that allows everyone to ask and answer questions. It is my hope that you will help each other out on the site, but I would prefer you restrict the questions to questions about the content, instead of simply about the homework. I don't want to see all of the homework solutions posted there. If there are questions about policies, exams, etc, please post them on piazza as well. I will answer them there so that the answers will be public and useful to other students.
• We encourage you to post broader questions, questions about applications, interesting problems, questions about the culture of mathematics, and so forth.
• You may post anonymously, for reference.
• You may give us anonymous feedback by posting a private note on piazza.

• If you wish to request an accommodation due to a disability, please contact the Office for Students with Disabilities as soon as possible at A255 Murphy Hall, (310) 825-1501, (310) 206-6083 (telephone device for the deaf). Website: www.osd.ucla.edu.
• This class will use the myUCLA gradebook facility.
• Come to office hours!