Math 313 - Complex Variables, Fall 2017

Time: Tue & Thur 2:00 - 3:15 p.m., DSH 223, Syllabus
Instructor Info: Anna Skripka, skripka [at] math [dot] unm [dot] edu
 
Prerequisite: Math 264 (required), other 300- or 400-level math courses (strongly recommended, will become an official prerequisite in Spring 2018)
Sample Math 313 goals (deviation is possible)
 
Textbook: Fundamentals of complex analysis with applications, by E.B. Saff and A.D. Snider, Prentice Hall, 3rd ed., 2003, ISBN 0139078746
Extra examples and exercises: Schaum's outlines. Complex variables, by M. Spiegel, S. Lipschutz, J. Schiller, D. Spellman, McGraw-Hill, 2nd ed., 2009, ISBN 0071615695
Supplementary textbook: Visual Complex Analysis, by T. Needham, Oxford University Press, 1999, ISBN 0198534469
 
Homework problems for grade along with solutions and grades are to be posted on UNM Learn.
 
Video lectures by one of the textbook authors.
 
Assignments will be graded only if they are submitted by the deadline. A student is allowed to submit homework by email in a SINGLE PDF file. To help the grader, please write your solutions neatly and clearly, provide all details and justifications, circle/box your answers to the questions, staple the sheets. Grades will depend on clarity of exposition, completeness of steps and justifications, correctness.
In addition to the specified topics, quizzes may also contain questions on old as well as prerequisite material.
 
Attendance: Students with excessive absences will be dropped from the course according to the university attendance rules. This also applies to students in the wait list.
 
Want a regrade? Check the solution key and state precisely in your claim which step of your solution seems to have been overlooked by the grader. This should be done within a week since the assignments were distributed in class.
 
Office hours in SMLC 212: Tue and Thur 11 a.m. - noon, and also by appointment
CAPS tutoring sessions: TBA
 
Handouts: Analytic and harmonic functions,   Complex integration
 
TENTATIVE Schedule (will be updated at the end of each week)
Week
Important Dates
Sections
Topics
Homework for practice
1
Aug 22, 24
1.1-1.3
(Schaum p. 9-32)
Complex numbers. Polar form.
section 1.1: #7,9,11,13-16,20,22-24; section 1.2: #4,7(except (f)), 9,10; section 1.3: #2,5,7,9,10,12,13
HW for grade is on UNM Learn
2
Aug 29, 31 (Q 1 & HW 1 on 1.1-1.3)
1.4, 1.5
home reading: 1.6
Complex exponential. Roots. Planar sets.
section 1.4: #1,2,4,5,7-11,16,17; section 1.5: #4-8; section 1.6: #2-8
HW for grade is on UNM Learn
3
Sep 5, 7 (Q 2 & HW 2 on 1.4, 1.5, 1.6)
Drop with no grade: Sep 8
2.1, 2.2
(Schaum p. 62-67)
Functions of complex variables. Limits and continuity.
section 2.1: #1-5,6(a,b),7-9,11,13; section 2.2: #7,11,19-21,25
4
Sep 12, 14 (Q 3 & HW 3 on 2.1, 2.2)
2.3, 2.4,
home reading: 3.1
(Schaum p. 85-96)
Analytic functions. Cauchy-Riemann equations. Polynomials and rational functions.
section 2.3: #4,7,11,13,15; section 2.4: #1,3,5,7,8,10,11,13 (apply 10,12), 15; section 3.1: #1,3(a,b),7,11,13 (using (21) is not required)
5
Sep 19, 21 (Q 4 on 2.3, 2.4, 3.1)
2.5, 3.2, 3.3
Harmonic functions. Exponential, trigonometric, and logarithmic functions.
section 2.5: #1-4,7,16,18; section 3.2: #1,2,4,5(a,b,c,d),7,9(a,b,c,d),10,11,15,17-20; section 3.3: #1-6,9-15
6
Sep 26, 28 (Exam 1 on 1.1-3.3; HW 4 on 2.3-2.5, 3.1-3.3)
3.4
Application: boundary value problems.
section 3.4: #1*-6 (*there is a typo in the book answer)
7
Oct 3, 5
3.5, 4.1-4.3
Complex powers & inverse trigonometric functions. Complex integration.
section 3.5: #1-9*,11 (*instead of deriving (11), may derive -i(z^2-1)^(-1/2)); section 4.1: #1-5,7,8,10,11; section 4.2: #3,5-14; section 4.3: #1,2,4,5,7
8
Oct 10 (HW 5 on 3.4, 3.5, 4.1-4.3)
4.4
Cauchy's integral theorem.
section 4.4: #1,3,9-13,15-17
9
Oct 17, 19 (Q 5 on 3.4, 3.5, 4.1-4.3)
4.5, 4.6,
home reading: 5.1
(Schaum p. 184-186)
Cauchy's integral formula. Bounds for analytic functions. Review of series.
section 4.5: #1,3,4,5,7,8,11,14; section 4.6: #4,5,6,8,10,11,13,14; section 5.1: # 1(a,b,c),2(b,c),7,11,14(b,c),21
10
Oct 24, 26 (Q 6 & HW 6 on 4.4-4.6, 5.1)
5.2, 5.3, 5.5
(Schaum p. 188-190)
Power, Taylor, and Laurent Series.
section 5.2: #5(a,b,c,d,g),7,8,13,14; section 5.3: #4,5(a,b,c),6; section 5.5: #1-6,9
11
Oct 31, Nov 2 (Exam 2 on 3.4-5.5; HW 7 on 5.2, 5.3, 5.5)
5.6
home reading: 5.7
Laurent Series. Classification of singularities.
section 5.6: #1(a,b,c,d,g),3,5; section 5.7: #1,3(b,c)
12
Nov 7, 9 (HW 8 on 5.6, 5.7)
Withdrawal deadline: Nov 10
6.7, 7.1, 7.2, 7.3
Argument principle and Rouche's theorem. Conformal mappings and their applications.
section 6.7: #1,3(see Theorem 3),6-9,13,18; section 7.1: #1; section 7.2: #3,5,10,11(a,c,d,e)
13
Nov 14, 16 (Q 7 on 5.6, 6.7, 7.1, 7.2; HW 9 on 6.7, 7.1, 7.2)
7.3, 7.4, 7.6
Möbius transformations and boundary value problems.
section 7.3: #2-9; section 7.4: #2,6,9; section 7.6: #1,2,3,6
14
Nov 21
6.1, 6.2
(Schaum p. 214-226)
Residue theorem and its applications. Trigonometric integrals.
section 6.1: #3,7; section 6.2: #1,2&3(see Example 2),4,5
15
Nov 28, 30 (Q 8 & HW 10 on 7.3, 7.4, 7.6, 6.1, 6.2)
6.3, 6.4, 6.5
Improper integrals. Indented contours.
section 6.3: #1,2,3(use Example 2 in 6.1),4-7; section 6.4: #4-9; section 6.5: #2-7
16
Dec 5 (HW 11 on 6.1-6.5), 7
6.6
Integrals involving multiple-valued functions. Review.
section 6.6: #1-4
17
Dec 12 (Tuesday), 10 a.m. - noon: Final Exam