Elementary Complex Analysis

2018 Fall, University of Nevada, Las Vegas

- do various calculations with complex numbers, complex functions (polynomials, rational functions, exponential and trigonometric functions) and muti-valued functions (argument, logrithm and squre root);
- define the limit of a complex function at a single point and apply properties of limits and determine whether a given complex function is continuous;
- define the derivative of a complex function;
- derive the Cauchy-Riemann equations for a complex differentiable function and identify whether a complex function is differentiable at a point;
- understand the basic integration and differentiation theory for functions of several variables;
- determine if a sequence of complex numbers is convergent;
- determine if an infinite series of complex numbers is convergent and describe the convergence properties of a complex power series and compute the radius of convergence;
- find Taylor and Laurent series for simple complex functions, determine the nature of the singularities and calculate residues;
- compute residues and apply the residue theorem to evaluate some integrals;
- translate real-life situations into mathematical problems and find their solutions.

- Test 1: Monday, Oct. 1.
- Test 2: Monday, Nov. 5.
- Final: Wednesday, Dec. 12, 10:10am-12:10pm.

- A: 92% -- 100%, A-: 90% -- 91.9%.
- B+: 87% -- 89.9%, B: 82% -- 86.9%, B-: 80% -- 81.9%
- C+: 77% -- 79.9%, C: 72% -- 76.9%, C-: 70% -- 71.9%
- D+: 67% -- 69.9%, D: 62% -- 66.9%, D-: 60% -- 61.9%
- F: 0% -- 59%

- Week 1:
- Monday, Aug. 27: §13.1.

Homework: §13.1: 8–13, 16–19. - Wednesday, Aug. 29: §13.2.

Homework: §13.2: 1, 2, 4, 8, 9, 10, 13, 15, 16, 21, 22, 25, 26, 28, 31. - Friday, Aug. 31: Quiz 1.

- Monday, Aug. 27: §13.1.
- Week 2:
- Monday, Sept. 3: (Labor Day Recess)
- Wednesday, Sept. 5: §13.3 and §13.4.

Homework: §13.3: 1-6, 10, 12, 18, 19, 20.

§13.4: 2-7. - Friday, Sept. 7: Quiz 2.

- Week 3:
- Monday, Sept. 10: §13.4 and §13.5.

Homework: §13.4: 10, 12, 16, 19, 22, 27.

§13.5: 2, 3, 10, 13, 15, 20. - Wednesday, Sept. 12: §13.6 and §13.7.

Homework: §13.6: 2, 4, 8, 10, 13, 18.

§13.7: 9, 10, 14, 16, 20, 24, 28. - Friday, Sept. 14: Quiz 3.

- Monday, Sept. 10: §13.4 and §13.5.
- Week 4:
- Monday, Sept. 17: §14.1.

Homework: §14.1: 1, 2, 3, 4, 6, 10, 11, 14, 16, 17, 19, 21, 22, 25, 26, 28, 29, 30, 35 - Wednesday, Sept. 19: §14.2.

Homework: §14.2: 9, 10, 12, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 27. - Friday, Sept. 21: Quiz 4.

- Monday, Sept. 17: §14.1.
- Week 5:
- Monday, Sept. 24: §14.3 and §14.4.

Homework: §14.3: 1-4, 5-8, 13, 14, 17, 19.

§14.4: 1-4, 8, 10, 19. - Wednesday, Sept. 26: Review for Midterm 1.
- Friday, Sept. 28: Quiz 5.

- Monday, Sept. 24: §14.3 and §14.4.
- Week 6:
- Monday, Oct. 1: (First midterm test)
- Wednesday, Oct. 3: §15.1:

Homework: §15.1: 1, 3, 4, 10, 16, 17, 18, 19, 25. - Friday, Oct. 5: Quiz 6.

- Week 7:
- Monday, Oct. 8: §15.2 and §15.3.

Homework: §15.2: 1, 5, 6, 7, 10, 16, 17, 18. - Wednesday, Oct. 10: §15.3.

Homework: §15.3: 5, 6, 7, 8, 9, 11, 13, 14, 15. - Friday, Oct. 12: Quiz 7.

- Monday, Oct. 8: §15.2 and §15.3.
- Week 8:
- Monday, Oct. 15: §15.4:

Homework: §15.4: 3, 4, 5, 7, 9, 10, 11, 13, 18, 19, 22, 24. - Wednesday, Oct. 17: §16.1.

Homework: §16.1: 1, 2, 3, 8, 11, 13, 14, 19, 20, 21, 22, 25. - Friday, Oct. 19: Quiz 8.

- Monday, Oct. 15: §15.4:
- Week 9:
- Monday, Oct. 22: §16.2.

Homework: §16.2: 1, 2, 3, 4, 6, 8, 10, 13, 14, 15, 18, 19, 22. - Wednesday, Oct. 24: §16.3.

Homework: §16.3: 3-12, 14-22. - Friday, Oct. 26: (Nevada day recess).

- Monday, Oct. 22: §16.2.
- Week 10:
- Monday, Oct. 29: §16.4.

Homework: §16.4: 1, 3, 5, 7, 10, 12, 14, 16, 19, 23, 24, 26. - Wednesday, Oct. 31: Review for Midterm 2.
- Friday, Nov. 2: Quiz 10.

- Monday, Oct. 29: §16.4.
- Week 11:
- Monday, Nov. 5: (Second midterm test)
- Wednesday, Nov. 7: §17.1.

Homework: §17.1: 11, 12, 15-20, 22-26, 29, 33. - Friday, Nov. 9: Quiz 11.

- Week 12:
- Monday, Nov. 12: (Veterans Day Recess)
- Wednesday, Nov. 14: §17.2 and §17.3.

Homework: §17.2: 7-10, 11-16. - Friday, Nov. 16: Quiz 12.

- Week 13:
- Monday, Nov. 19: §17.3.

Homework: §17.3: 8-12, 16-20, . - Wednesday, Nov. 21: §17.4 and §17.5.

Homework: §17.4: 3, 4, 5, 11, 12, 13, 20, 21, 22, 24, 25. - Friday, Nov. 23: (Thanksgiving Day).

- Monday, Nov. 19: §17.3.
- Week 14:
- Monday, Nov. 26: §18.1 and §18.2.

Homework: §18.1: 1, 5, 12.

§18.2: 4, 7, 8,. 9, 10, 15. - Wednesday, Nov. 28: §18.5 and §18.6.

Homework: §18.5: 5, 16. - Friday, Nov. 30: Quiz 14.

- Monday, Nov. 26: §18.1 and §18.2.
- Week 15:
- Monday, Dec. 3: Review I.
- Wednesday, Dec. 5: Review II.

An example of academic misconduct is plagiarism. Plagiarism is using the words or ideas of another, from the Internet or any source, without proper citation of the sources. See the Student Academic Misconduct Policy (approved December 9, 2005) located at:http://studentconduct.unlv.edu/misconduct/policy.html.