Introduction to Complex Analysis (Summer 2017)

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Julia set

Professor: Richard Borcherds

Office hours: M Tu W Th 12:00-1:00  927 Evans Hall.

email: borcherds followed by at berkeley dot edu

Lectures: Hearst mining 310  M Tu W Th 10:00-12:00

Catalog Description: Mathematics 185

Analytic functions of a complex variable. Cauchy's integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mapping.

Textbook:

Complex Variables and Applications, by James Ward Brown, Ruel V. Churchill. We will  cover chapters 1-8.

There is no need to get the latest (9th) edition and the 8th edition is fine for the course and costs far less. (My copy is the 8th edition.) The 7th and earlier editions are also OK but the sections and homework exercises may be renumbered. You should be able to get second hand copies from Abebooks or Amazon or the ASUC store for far less than new copies.

Exams:

Almost all the questions in the midterms or finals will be similar to homework questions or problems discussed in class.

Each question on the midterms and final will be worth 3 points. The grading scheme is: 3 points for a completely correct and clear answer in simplified form, 2 points for an essentially correct answer with some minor errors, 1 point for a reasonable start on the question, 0 points for no significant progress. It is your responsibility to make your answers clear: if you get the question right but the grader does not notice, then this is your fault for not making your answer clear enough, and you will lose points for it. Students will never get extra partial credit by asking for it, as this is unfair to students who do not ask. Marks for exams will only be changed if there is a clear error on the part of the grader, such as adding up marks incorrectly or forgetting to mark a question.

 The lowest of your 3 exam scores will be dropped and your score for the exams will be based on your best two.  There will be no makeup midterms or finals.  

You may not use any electronic devices in the exams. You may bring one sheet of paper with writing on both sides to the exams. Apart from this one sheet, the exams are "closed book".

Homework:

Homework is due by the end of the Monday lecture the week after it is assigned, except for the last homework which is due on the last day of class (August 10). Late homework will not be accepted. Collaboration on homework is fine, but if you hand in similar homework to your collaborator you should clearly state so and say who you are working with, in order to avoid unfortunate misunderstandings.

About half the marks for homework will be based on the number of questions that you made a serious attempt on, and about half will be based on more detailed marking of a few questions. Your homework scores for the 2 lowest weeks will be dropped and your final homework score will be based on your  homeworks for the best 6 weeks.

For each lecture, you should read the sections of the textbook, and do the homework exercises listed below. The homework exercise numbers are given for the 8th edition and for the 9th edition and may need adjustment for other editions. 

Provisional Reading and Homework Schedule
# Date Reading 8ed Homework for 8th edition of textbook Reading 9ed Homework for 9th edition of textbook
1 M  6-19 1: 1- 6 2:4,11   3:1   4:1, 5    5:1a,2,15 1: 1- 7 2:4,11   3:1   5:1, 5    6:1a,2,15
2 Tu 6-20 1: 7-11 8:1,  5c, 9, 10    10:1a, 2, 7    11:1 1:8-12 9:1, 5c, 9, 10    11:1a, 2, 7   12:1
3 W 6-21 2:12-16 12:1, 2, 4    14:2, 3, 8 2:13-16 14: 1, 2, 4 , 6, 8, 9
4 Th 6-22 2:17-20 18:3, 5, 10   20:1, 2, 7 2:17-20 18: 3, 5, 10    20:2, 3,  7
5 M  6-26 2:21-24 23:4ac, 7, 10 2:21-25 24:4ab, 5, 8
6 Tu 6-27 2:25-28 25:1,4, 6   26:5, 7, 8, 11    28:2, 5 2:26-29 25:1, 4, 6  27: 1,  2, 3  6   29:2, 5
7 W 6-28 3:29-32 29:1, 8, 10, 11   31: 1, 2, 11.  32.2 3:30-34 30:1, 8, 10,11  33:1, 2, 12  34:1
8 Th 6-29 3:33-36 33: 1, 3, 9   34:2, 15   35.1  36.1 3:35-40 36:1, 3, 9  38:2, 15   39:1   40:1
9 M  7- 3 4:37-39 38: 2abc, 3, 5   39:1, 5, 6 4:41-43 42:2bcd,3, 5   43:1, 5, 6
Tu 7- 4 Holiday
10 W 7- 5 4:40-42 42: 1, 8  4:44-46 46:1, 10
11 Th 7- 6 Midterm 1 (covers chapters 1-3)
12 M  7-10 4:43-45 43: 1, 2, 4, 7   45:1, 2, 5 4:47-49 47:1, 2, 4, 7  49:1, 2, 5
13 Tu 7-11 4:46-48 4:50-52
14 W 7-12 4:49-51 49:1af, 4, 7, 8 4:53-56 53:1af,4, 7, 8   
15 Th 7-13 4:52-54 52:1, 2, 3, 8    54: 1,3, 7, 9 4:57-59 57:1, 2, 3, 8   59:1, 3, 6, 8
16 M  7-17 5:55-58 56.4, 6, 9 5:60-63 61:4, 6, 8   
17 Tu 7-18 5:59-61 59:1, 3,5, 6, 11b, 12a, 13 5:64-67 65:1, 3, 8, 9, 10, 11
18 W 7-19 5:62-64 62:1,3, 4, 8, 10 5:68-70 68:1,2, 4, 7, 9
19 Th 7-20 5:65-67 66:1, 5, 11    67:1, 3, 4, 5, 6, 7, 8 5:71-73 72:1, 5, 11   73:1, 4, 5, 6, 7, 8, 9
20 M  7-24 6:68-73 71:1, 2, 4, 5, 6    72:1, 2, 5  6:74-80 77:1, 2, 5, 6, 7   79:1, 2, 4
21 Tu 7-25 6: 74-77 74:1, 2, 3, 5, 6, 7  76:1, 2b, 3, 4, 5, 6 6:81-84 81:1, 2, 4, 6, 7, 8  83:1,3b,4,5,6,7
22 W 7-26 7:78-80 79: 1, 2, 3, 4, 5, 6, 7, 8, 9 7:85-87 86:1,  2, 3, 5, 6,  7, 8, 9 , 10
23 Th 7-27 Midterm 2 (covers chapters 4-5)
24 M  7-31 7:81-83 81: 1, 2, 3, 4, 5,  7, 8, 12 7:88-90 88:1, 2, 3, 4, 5, 6, 7, 12
25 Tu 8- 1 7:84-86 84: 1, 5 , 7 , 8    85: 1, 4, 7 7:91-93 91:1, 4, 5, 6    92:1, 4, 6
26 W 8- 2 7:87-89 87: 1, 2, 5, 6, 7, 9   89.1 7:94-96 94:1, 2, 5, 6, 7, 9   95:1 
27 Th 8- 3 8:90-92 90:4, 6   92:2, 4, 5 8:96-98 96:4, 6  98:2, 4, 5
28 M  8- 7 8:93-95 94:2, 4, 5, 7, 10.    95: 3 8:99-102 100:2, 4, 5, 7    102:3
29 Tu 8- 8 8:96-98 96:1,5    97.1, 2, 7    98:1 8:103-109 106:5, 9  108:1,  2, 7   109:1
30 W 8- 9 8:99-100 99:1,3  100:1, 3 8:110-111 110:1, 3   111:1, 3
31 Th 8-10 Final (covers chapters 6-8)


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