# Spring 2022

### Time and Place

• Lectures: TR 12:40pm – 1:55pm Carver 298

### Assessment

#### Homework (25%)

• Late homework is not accepted.
• All homework problems are from the book.
• Odd numbered exercises have answers in the back, so you must show your work to get credit.
• Write neatly and use a stapler if you hand in multiple pages.
• There will be 8 – 10 problems per week.
• Each problem is graded on a scale from 0 to 5.
Due Date Assigned Homework
Thu 1/27 Read: Sections 1.1 and 1.2. Hand in: Exercises 1.1: 1(a,b,c,g), 3(a,b,c,g), 5(a,b,c,i) and 1.2: 3, 7, 15, 23, 25
Thu 2/3 Read: Sections 1.3 and 1.4. Hand in: Exercises 1.3: 1, 5, 7, 10, 15 and 1.4: 1, 2, 5, 16, 23
Thu 2/10 Read: Sections 1.4 and 1.5. Hand in: Exercises 1.4: 31, 35, 36, 37, 40 and 1.5: 5, 11, 13, 15, 18
Tue 2/15 Read: Chapter 1. Work on: Sample Problems 1
Thu 2/17 Read: Section 1.6. Hand in: Exercises 1.6: 1, 4, 6, 9, 12
Thu 2/24 (No homework this week)
Thu 3/2 Read: Sections 2.1 and 2.2. Hand in: Exercises 2.1: 1(abe), 10, 14, 20(bc), 23 and 2.2: 2, 3, 4, 5, 15
Thu 3/10 Read: Sections 2.2 and 2.3. Hand in: Exercises 2.2: 9, 10, 13, 18, 19 and 2.3: 1, 3, 4, 5, 7
Thu 3/24 Read: Section 2.4. Hand in: Exercises 2.4: 1, 2, 3, 6, 9, 10, 11, 13
Thu 3/31 Read: Section 2.5. Hand in: Exercises 2.5: 1, 2, 3, 5, 6, 7, 9, 12, 13, 15
Tue 4/5 Read: Chapter 2. Work on: Sample Problems 2
Thu 4/7 Read: Section 2.6. Hand in: Exercises 2.6: 1, 2, 3, 4, 5, 6, 9, 10
Thu 4/14 (No homework this week)
Thu 4/21 Read: Sections 3.1, 3.3. Hand in: Exercises 3.1: 12, 13, 18, 21; 3.3 2, 3, 4(abc), 5a, 7a
Thu 4/28 Read: Sections 3.5, 4.2. Hand in: Exercises 3.5: 1, 2, 3, 4, 5, 7; 4.2 13, 14
Thu 5/5 Work on: Practice Problems Optional: hand in solutions for up to 50 HW bonus points

#### Midterm 1 (25%)

• Takes place during the lecture on Thursday, February 17.
• Closed-book exam, no calculators, no formula sheet.
• 50 minute exam, 5 problems, lowest score dropped.
• This midterm covers Chapter 1.
• Sample Problems 1
• Solutions to Midterm 1

### Lecture Plan

Date Topic
1/18 Section 1.1 The Complex Numbers, Polar Representation
1/20 Section 1.2 Triangle Inequality, Roots of Complex Numbers
1/25 Section 1.3 Subsets of the Plane
1/27 Section 1.4 Limits and Continuity
2/1 Section 1.4 Infinite Series
2/3 Section 1.5 The Exponential, Logarithm, and Trigonometric Functions
2/8 Section 1.6 Curves and Line Integrals
2/10 Section 1.6 Green's Theorem
2/15 Catch-up and Review
2/17 Midterm 1: Chapter 1
2/22 Section 2.1 Analytic Functions, Cauchy-Riemann Equations
2/25 Section 2.2 Power Series
3/1 Section 2.2 (cont.)
3/3 Section 2.3 Cauchy's Theorem and Cauchy's Formula
3/8 Section 2.3 (cont.)
3/10 Section 2.4 Consequences of Cauchy's Formula
Spring Break
3/22 Section 2.5 Isolated Singularities
3/24 Section 2.5 (cont.)
3/29 Section 2.6 The Residue Theorem
3/31 Section 2.6 (cont.)
4/5 Catch-up and Review
4/7 Midterm 2: Chapter 2
4/12 Section 3.1 The Zeros of an Analytic Function
4/14 Section 3.3 Linear Fractional Transformations
4/19 Section 3.5 The Riemann Mapping Theorem
4/21 Section 4.2 (Electrostatics)
4/26 Section 4.2 (Flow of an Ideal Fluid)
4/28 The Gamma Function
5/3 Review/Extra
5/5 Problem Discussions
5/10 Final Exam

### General Class Policies

Class policies of the Department of Mathematics at ISU.

### Statement on Free Expression

Iowa State University supports and upholds the First Amendment protection of freedom of speech and the principle of academic freedom in order to foster a learning environment where open inquiry and the vigorous debate of a diversity of ideas are encouraged. Students will not be penalized for the content or viewpoints of their speech as long as student expression in a class context is germane to the subject matter of the class and conveyed in an appropriate manner.