MATH 432-1001 Mathematics for Engineers and Scientists II
Elementary Complex Analysis
2018 Fall, University of Nevada, Las Vegas
Instructor: Dr. Le Chen
Email: le.chen@unlv.edu
Office: SEB, 3131
Office Hours: Mon, Tue, Wed, 9:00am--10:00am, or by appointment
Class Meeting Times: MW 11:30am-12:45pm in CHE 101
Discussion Classes: Friday, 11:30am-12:45pm at CBC C133, and 4:00pm-5:15pm at CBC C213.
Teaching Assistant: Min Chen (chenm1@unlv.nevada.edu)
Time period: Aug. 27, 2018 (first lecture) --- Dec. 5, 2018 (last lecture)
Topics to be discussed:
Complex numbers, complex functions, complex differentiation, analytic and harmonic functions, complex integrations, Taylor and Laurent seires, Cauchy's integral theorem and formula, calculus of residues, conformal mapping, linear fractional transformations, and some applications.
Learning outcomes:
Upon successful completion of this course, students should be able to
- 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.
Textbook:
Advanced Engineering Mathematics, by Erwin Kreyszig (Chapters 13-18)
Prerequisite: Math 431.
Note: The syllabus was created in Aug. 2018, and it is subject to change during the semester.
Homework: Homework will be assigned after each class meeting and due every Friday before discussion class. Only part of the problem set (randomly chosen) will be graded and you will receive some credits for completing all homework problems.
Quiz: Quiz will be given at the beginning of the discussion session on each Friday.
Attendence: You are expected to attend class regularly. You are responsible for all the materials presented and all the announcements made, if any, at each lecture. You will be asked to sign the attendence sheet on each class meeting.
Tests and Final: There will be 2 tests and a cumulative final exam. Failure to take an exam during the scheduled class time will result in a score of zero for that exam. There will be no make-up exam except for well-documented reasons such as a medical emergency. Scientific (non-programmable and non-graphing) calculators are allowed during exams.
- Test 1: Monday, Oct. 1.
- Test 2: Monday, Nov. 5.
- Final: Wednesday, Dec. 12, 10:10am-12:10pm.
Student ID: Each student will be assigned an ID number for this class. Please use this ID for submitting homework, quizzes, tests, and final exam.
Grading Policy:
There will be Homework (15%), Quiz (15%), two tests (20%+20%) and the final exam (30%).
- 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%
Tentative schedule and assignments of homework
- 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.
- 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.
- 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.
- 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.
- 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.
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.
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).
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.
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).
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.
Week 15:
- Monday, Dec. 3: Review I.
- Wednesday, Dec. 5: Review II.
Academic Misconduct:
Academic integrity is a legitimate concern for every member of the campus community; all share in upholding the fundamental values of honesty, trust, respect, fairness, responsibility and professionalism. By choosing to join the UNLV community, students accept the expectations of the Student Academic Misconduct Policy and are encouraged when faced with choices to always take the ethical path. Students enrolling in UNLV assume the obligation to conduct themselves in a manner compatible with UNLV's function as an educational institution.
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.
Copyright:
The University requires all members of the University Community to familiarize themselves with and to follow copyright and fair use requirements. You are individually and solely responsible for violations of copyright and fair use laws. The university will neither protect nor defend you nor assume any responsibility for employee or student violations of fair use laws. Violations of copyright laws could subject you to federal and state civil penalties and criminal liability, as well as disciplinary action under University policies. Additional information can be found at: http://www.unlv.edu/provost/copyright.
Disability Resource Center (DRC):
sability Resource Center (SSC-A 143, http://drc.unlv.edu/, 702-895-0866) provides resources for students with disabilities. If you feel that you have a disability, please make an appointment with a Disabilities Specialist at the DRC to discuss what options may be available to you. If you are registered with the UNLV Disability Resource Center, bring your Academic Accommodation Plan from the DRC to the instructor during office hours so that you may work together to develop strategies for implementing the accommodations to meet both your needs and the requirements of the course. Any information you provide is private and will be treated as such. To maintain the confidentiality of your request, please do not approach the instructor in front of others to discuss your accommodation needs.
Religious Holiday Policy:
ny student missing class quizzes, examinations, or any other class or lab work because of observance of religious holidays shall be given an opportunity during that semester to make up missed work. The make-up will apply to the religious holiday absence only. It shall be the responsibility of the student to notify the instructor no later than the end of the first two weeks of classes, January 26, 2018, of his or her intention to participate in religious holidays which do not fall on state holidays or periods of class recess. For additional information, please visit: http://catalog.unlv.edu/content.php?catoid=6&navoid=531.
Incomplete Grades:
The grade of I -- Incomplete -- can be granted when a student has satisfactorily completed three-fourths of course work for that semester/session but for reason(s) beyond the student's control, and acceptable to the instructor, cannot complete the last part of the course, and the instructor believes that the student can finish the course without repeating it. The incomplete work must be made up before the end of the following regular semester for undergraduate courses. Graduate students receiving "I" grades in 500-, 600-, or 700-level courses have up to one calendar year to complete the work, at the discretion of the instructor. If course requirements are not completed within the time indicated, a grade of F will be recorded and the GPA will be adjusted accordingly. Students who are fulfilling an Incomplete do not register for the course but make individual arrangements with the instructor who assigned the I grade.
Tutoring:
The Academic Success Center (ASC) provides tutoring and academic assistance for all UNLV students taking UNLV courses. Students are encouraged to stop by the ASC to learn more about subjects offered, tutoring times and other academic resources. The ASC is located across from the Student Services Complex (SSC). Students may learn more about tutoring services by calling 702-895-3177 or visiting the tutoring web site at: http://academicsuccess.unlv.edu/tutoring/.
UNLV Writing Center:
ne-on-one or small group assistance with writing is available free of
charge to UNLV students at the Writing Center, located in CDC-3-301. Although walk-in
consultations are sometimes available, students with appointments will receive priority assistance.
Appointments may be made in person or by calling 702-895-3908. The student's Rebel ID Card, a
copy of the assignment (if possible), and two copies of any writing to be reviewed are requested
for the consultation. More information can be found at: http://writingcenter.unlv.edu/.
Rebelmail:
By policy, faculty and staff should e-mail students' Rebelmail accounts only. Rebelmail is UNLV's official e-mail system for students. It is one of the primary ways students receive official university communication such as information about deadlines, major campus events, and announcements. All UNLV students receive a Rebelmail account after they have been admitted to the university. Students' e-mail prefixes are listed on class rosters. The suffix is always @unlv.nevada.edu.
Emailing within WebCampus is acceptable.
Final Examinations:
The University requires that final exams given at the end of a course occur at the time and on the day specified in the final exam schedule. See the schedule at: http://www.unlv.edu/registrar/calendars.
© 2018 Le Chen