University of Waterloo AMath 332-Outline-S21 University of Waterloo AMath 332-Outline-S21 PDF

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University of Waterloo pmath332-amath332Applied Complex Analysis Pmath 332 course outline. University of Waterloo pmath332-amath332Applied Complex Analysis Pmath 332 course outline....

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AMath/PMath 332 – Spring 2021 Course Outline Applied Complex Analysis ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Instructor:

Joe West; [email protected].

Prerequisites:

Math 237. Having taken AMath 231 is also helpful, but it isn’t necessary. And of course, since we're online, a reliable internet connection is required.

Textbook:

Fundamentals of Complex Analysis, Classic (or 3rd) Edition, by Saff & Snider. ISBN is 9780134689487. The "3rd edition" and "Classic Edition" have different ISBN’s but are otherwise identical. There will probably be several used copies of the 3rd edition available--in fact, I have the 3rd edition! The bookstore also has an electronic copy; see wstore.uwaterloo.ca. I recommend the hardcopy over the electronic copy.

Websites:

learn.uwaterloo.ca; we'll also use piazza.com (to be set up soon) for discussion.

Getting Help:

The main way to get help is using the piazza discussion forum. I will monitor it daily, except weekends. I also plan to hold some live office hours; details to come.

Assignments:

There will be a written assignment each week, except first week and test weeks. After submission each week, a subset of students will be selected to discuss their submission, sort of a "mini oral exam".

Tests:

There will be three tests; exact time(s) or time window to be announced: - Test 1: *Thursday, June 10th - Test 2: *Thursday, July 15th (*dates subject to change) - Final Exam: date TBA, held during the final exam period

Grading Scheme**: Assignments 20%, Post-Assignment Mini Oral Exams 15%, Tests 1 and 2 15% each, Final Exam 25%, Participation 10%. **NOTE: • The lowest nonzero assignment score will be dropped. Furthermore, you are expected to submit at least two questions on each assignment at least two days before the due date. Any entirely-missed assignments will count as zero. • The participation mark will consist of two parts. The "poll" portion reflects the extent to which you participated in surveys and polls, and will be easy to calculate. The exact portion of the 10% will depend on how many polls/surveys we end up having. The "non-poll" portion is more subjective. For many students, I will not know enough to make a reasonable estimate of it. You may have something to say on piazza, for example, but it might have already been said. For many, some or all of it will be zeroweighted, e.g. if the non-poll part ends up being worth 5%, your grade would simply become the rest divided by 0.95. • I may change the weight of certain course components if there is a compelling reason, such as lowerthan-expected TA-to-student ratio; you will be consulted and/or notified if this is the case. • A subset of students may be selected for a special final exam worth up to 50% (which might be written-with video proctoring a possibility--or a combination of written and oral, or purely oral), with the rest of the components taking up the remaining part of the grade. Plenty of notice will be given.

Course schedule: Lec #

Week

Dates

Topics

1-3

1

May 10 – 14

Introduction: the Basics of Complex Numbers

4-6

2

May 17th – 21st

Euler’s Formula, Application to Circuit Analysis, Planar Sets, Functions

7, 8

3

May 25th – 28th

9-11

4

31st – June 4th

12-14

5

June 7th - 11th

th

th

[Monday is a holiday.] Limits, Differentiability Harmonic Fun., Elementary Functions Elementary Functions ctd., Contours

Text Sections

Events

1.1-1.5

(Check assignments for exact due times)

3.6, 1.6, 1.7, 2.1

A1 due

2.2-2.5

A2 due

2.5, 3.1-3.3

A3 due

3.3, 3.5, 4.1

Test 1

4.2-4.4

A4 due

15-17

6

June 14th – 18th

Contour Integrals, Complex Analogue to FTC (Independence of Path), Cauchy's Integral Theorem

18-20

7

June 21st – 25th

Cauchy’s Integral Thm. ctd., Formula

4.4-4.6

A5 due

21, 22

8

June 28th - 30th

Sequences and Series, Taylor and Laurent Series ... [Thurs+Fri are holidays.]

5.1, 5.2

A6 due

23-25

9

July 5th – 9th

... ctd., Zeros and Singularities...

5.2, 5.5, 5.6

A7 due

26-28

10

July 12th – 16th

ctd., Residues, Residue Thm.

5.6 ctd., 6.1, 6.2

Test 2

29-31

11

th

July 19 – 23

12

July 26th – 30th

6.2-6.5 2.6, 3.4, 7.1-7.4, 7.6

A8 due

32-34

35

13

Aug. 3rd-5th

Application to Real-Valued Integrals Applications to Physics, Möbius Transforms Applications ctd. [Monday is a holiday, Tues.=Mon., Wed.=Thur., Thur=Fri. schedule]***

7.4, 7.6

A10 due

rd

A9 due

*** This means that Tuesday follows a "Monday" schedule, Wednesday follows a "Thursday" schedule, and Thursday follows a "Friday" schedule, not that we're really scheduled this term anyway. (Thanks again, covid. [That was sarcastic.])

See next page for the "fine print".

Grievance: A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70, Student Petitions and Grievances, Section 4, http://www.adm.uwaterloo.ca/ infosec/Policies/policy70.htm. When in doubt please be certain to contact the department's administrative assistant who will provide further assistance. Discipline: A student is expected to know what constitutes academic integrity to avoid committing academic offenses and to take responsibility for his/her actions. A student who is unsure whether an action constitutes an offense, or who needs help in learning how to avoid offenses (e.g., plagiarism, cheating) or about rules for group work/collaboration should seek guidance from the course professor, academic advisor, or the undergraduate associate dean. For information on categories of offenses and types of penalties, students should refer to Policy 71, Student Discipline, http://www.adm.uwaterloo.ca/infosec/Policies/polic y71.htm. For typical penalties check Guidelines for the Assessment of Penalties, http://www.adm.uwaterloo.ca/infosec/guidelines/pe naltyguidelines.htm. Appeals: A decision made or penalty imposed under Policy 70, Student Petitions and Grievances (other than a petition) or Policy 71, Student Discipline may be appealed if there is a ground. A student who believes he/she has a ground for an appeal should refer to Policy 72, Student Appeals, http://www.adm.uwaterloo.ca/infosec/Policies/polic y72.htm. Note for students with disabilities: AccessAbility Services (AAS), located in Needles Hall, Room 1132, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with AAS at the beginning of each academic term.

Intellectual Property: Students should be aware that this course contains the intellectual property of their instructor, TA, and/or the University of Waterloo. Intellectual property includes items such as: • • •

Lecture content, spoken and written (and any audio/video recording thereof); Lecture handouts, presentations, and other materials prepared for the course; and Questions or solution sets from various types of assessments (e.g., assignments, quizzes, tests, final exams)

Course materials and the intellectual property contained therein are used to enhance a student's educational experience. However, sharing this intellectual property without the intellectual property owner's permission is a violation of intellectual property rights. For this reason, it is necessary to ask the instructor, TA and/or the University of Waterloo for permission before uploading and sharing the intellectual property of others online. Permission from an instructor, TA or the University is also necessary before sharing the intellectual property of others from completed courses with students taking the same/similar courses in subsequent terms/years. In many cases, instructors might be happy to allow distribution of certain materials. However, doing so without expressed permission is considered a violation of intellectual property rights. Please alert the instructor if you become aware of intellectual property belonging to them (past or present) circulating, either through the student body or online. The intellectual property rights owner deserves to know (and may have already given their consent). See policy 73 -- Intellectual property rights (https://uwaterloo.ca/secretariat-generalcounsel/policies-procedures-guidelines/policy-73intellectual-property-rights)...