**MATH 300 **

Complex Analysis

Spring 2018

**COURSE PAGE
**

**FINAL EXAM INFORMATION (more information coming soon)**

**TIME**: APR 10 2018 08:30-11:00 AM

**PLACE**: MATH 100

**SEATING PLAN**: PLAN

**MATERIAL**: The final exam will roughly cover all topics/texbook chapters 1 to 5 excluding the following sections: 1.7; 2.6, 2.7; 3.4, 3.6; 4.4b, 4.7; 5.4, 5.7 5.8. We will also cover 6.1 and 6.3. See the Course Summary

In addition to your class materials (notes, quizes, midterms), the PAST FINAL EXAMS are an excellent source of practise problems and will give you a good idea of what to expect in terms of topics, depth and difficulty on our exam.

This is the course page for MATH 300 in
Term 2 of the 2018 session (January to April 2018). Your grade in the course will be determined by your grades in

weekly homework assignments (worth 10% of overall grade)
weekly in class quizes (worth 15% of overall grade)
1 midterm exam (worth 25% of overall grade)
1 final exam (worth 50% of overall grade)

All The basic information on these can be found below.

**INSTRUCTOR INFORMATION**

**Name**: Albert Chau

**email**: chau@math.ubc.ca

**Classes**: Tues/Thurs 2:00pm-3:30pm in MATX 1100

**Office hour**: Wed 11:00am-12:30pm

**TEXTBOOK AND COURSE PLAN**

Our primary reference for the course will be

Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics by Edward B. Saff (Author), Arthur David Snider (Author).

We will cover most of Chapters 1-6 and in particular, we will cover the following topics

**Complex Numbers**

** - complex arithmetic **

** - geometry of complex arithmetic**

** - conjugation **
**Analytic functions: differentiation**

** - complex differentiation**

** - the Cauchy Riemann equations**

** - the elementary analytic functions**
**Analytic functions: integration**

** - Cauchy's Theorem**

** - Cauchy's Formula**
**Taylor series**
**Laurant series; residue calculus**

Lecture Notes (2)

Lecture Notes (3)

Lecture Notes (4)

Lecture Notes (5)

Lecture Notes (6)

Lecture Notes (7)

Lecture Notes (8+9)

Lecture Notes (10: missing (basically beginnign Chapter 3 on polynomials and rational functions)

Lecture Notes (11)

Lecture Notes (12)

Lecture Notes (13)

Lecture Notes (14)

Lecture Notes (15-16)

Lecture Notes (17-18)

Lecture Notes (19-20)

Lecture Notes (21-22)

Lecture Notes (23)

Lecture Notes (24)

**WEEKLY QUIZES AND HOMEWORK ASSIGNENTS**

There will be 10 in class quizes. These will be short quizes to take place in class on the dates listed below. The information for each quiz below will be updated closer to the time of the quiz. Your seating for the quiz will be assigned (the quizes will be handed out with your names already on them according to the seating plan so please know where to sit on quiz days). You can find your assigned seats here: **SEATING PLAN **

**Quiz 1 (based on the content of HW#1)**: (Thurs Jan 11) solutions

**Quiz 2 (based on the content of HW#2)**: (Thurs Jan 18) solutions

**Quiz 3 (based on the content of HW#3)**: (Thurs Jan 25) solutions

**Quiz 4 (based on the content of HW#4) **: (Thurs Feb 1) solutions

**Quiz 5 (based on the content of HW#5)**: (Thurs Feb 8) solutions

**Quiz 6 (based on the content of lectures 13-14)**: (Thurs Mar 1) solutions

**Quiz 7** (based on the content of HW#6): (Thurs Mar 8) solutions

**Quiz 8**: (based on the content of HW#7)(Thurs Mar 15) solutions

**Quiz 9**: (based on the content of HW#8)(Thurs Mar 22) solutions

**Quiz 10**: (Thurs Mar 29)

There will also be weekly homework assignments which will be due on the same days that you have quizes. Information on these will be posted below

**HW 1**:section 1.1 #21, 22 section 1.2 #7d, 13, 14 section 1.3 #5c, 7g, 17. (due thurs Jan 11) solutions

**HW 2**:section 1.4 #18 b)d) section 1.5 #11, 19 section 2.1 #10, 13, 15(this one, #15, will not be graded). (due thurs Jan 18) solutions

**HW 3**:section 2.2 #9, 17 section 2.3 #2, 4(b), 7(e), 9(b), 11(e) solutions (due thurs Jan 25)

**HW 4**:section 2.4 #2, 3, 6, 13, 14 section 2.5 #3e, 13, 18, 21 solutions (due thurs Feb 1)

**HW 5**:section 2.7 #1, 4, 9, 10 section 3.1 #7, 9, 19 solutions (due thurs Feb 8 )

**HW 6**:section 4.2 #3 (b), #9, #12, #14 (c); section 4.3 #1 (f, g), #2, #7, solutions (due thurs Mar 8 )

**HW 7**: section 4.4 #3, 5, 9, 10, 11(in your explanation, you MUST cite the main Theorems used including section and Theorem numbers), 12, 13, 14, 16, 19((in your proof, you MUST cite the main Theorems used including section numbers and Theorem numbers) solutions (due thurs Mar 15)

**HW 8**: section 4.5 #3cd, 6, 8, 10, 11; 4.6 #4, 6, 9, 15, 18 solutions (due thurs Mar 22)

**HW 9**: section 5.2 #3a,c), 6, 11a,b), 13, 15 (some of these use Theorems 4, 5, 6 in the section, and these do not appear in Lecture 19-20), section 5.3 #2, 3f, 5d, 11 solutions (due thurs Mar 29)

3, 5, 9, 10, 11(in your explanation, you MUST cite the main Theorems used including section and Theorem numbers) 12, 13, 14, 16, 19((in your proof, you MUST cite the main Theorems used including section numbers and Theorem numbers)
**MIDTERM EXAM INFORMATION**

**SOLUTIONS TO THE MIDTERM**: solutions

**TIME**: During regular class time on Thurs Feb 15th (test will be one hour long)

**PLACE**: During regular class time

**TOPIC LIST**: Textbook sections: 1.1-1.6; 2.1-2.5; 3.1-3.3, 3.5 (complex powers).
Complex arithmetic. Mappings by complex functions, complex differentiability (limit definition, rules of differentiation, local model, using to show a specific function is differentiable or not), Cauchy-Riemann equations (using in examples to show a specific is differentiable or not. Using to show various properties of analytic functions), harmonic functions and conjugates. The basic analytic functions, namely the polynomials, rationals, exponential, logarithm, trig and complex powers: know the definitions of these functions (pay special attention where multivaluedness and branches of the argumnt function are concerned), know where they are analytic (again pay special attention when a choice of ``branch" has to be made), and know the formulas for their derivatives (the derivatives of these are in fact given by the same formulas as for real the corresponding real values functions)

Prepare by studying the lectures notes, and also the homeowrks and quizes. Past final exams also provide excellent review problems, but be careful and only look at those problems which are relevant to our midtrem topics (typically no more than the first two problems on the exam). The following are links to previous years course pages where you will find practise midterms. Look only at midterm 1 for each link below (midterm 2 in the links below consist mostly of problems which will not appear on our test).

practise midterms from 2017

practise midterms from 2015

practise midterms from 2015

practise midterms from 2015