James Cook's Complex Analysis Homepage
Course Materials for Fall 2026:
I have resources for Math 331 of Fall 2026 posted below, some of these are also in Canvas:

1. Fall 2026 Complex Analysis Course Planner
2. Lecture Notes (updated 2023, time permitting I may update these this term, I'll probably write some pdfs to supplement this document rather than modifiying it directly. There are lots of quotes in here it's nice to read, I do hope you'll read these)
3. Complex Analysis Lectures of Fall 2026 (this is the YouTube playlist for this course for the Fall 2026 term)
4. Missions for Fall 2026 semester: (aka homework)
   
   • Mission 1
   • Mission 2
   • Mission 3
   • Mission 4
   • Mission 5
   • Mission 6
   • Mission 7
   • Mission 8
   • Mission 9

Lectures for Fall 2026 semester: (aka course notes I'm writing to prepare for lecturing this term, please read the typed pdf in addition to these, the text of the course is best understood as the superposition of these documents and the typed document above, there are no documents posted here yet... 7-19-26)

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Lecture 6
• Lecture 7
• Lecture 8
• Lecture 9
• Lecture 10
• Lecture 11
• Lecture 12
• Lecture 13
• Lecture 14
• Lecture 15
• Lecture 16
• Lecture 17
• Lecture 18
• Lecture 19
• Lecture 20
• Lecture 21
• Lecture 22
• Lecture 23
• Lecture 24

Course Materials for Fall 2024:

Fall 2024 Complex Analysis Course Planner

Lecture Notes (updated 2023)

Complex Analysis Lectures of Fall 2024

Homeworks and Quizzes assigned in Fall 2024 semester:

• Mission 1
• Mission 2
• Mission 3
• Quiz 1
• Mission 4
• Mission 5
• Mission 6
• Quiz 2

Useful Materials and Links:

1. Complex Analysis Lectures of Fall 2015 this is the playlist for the rather standard course I taught in 2015 from Gamelin's text, enjoy.

In the Fall 2015 semester we used Gamelin's Complex Analysis as the required text. For the most part, his approach aligns closely with out aims, but, I have some examples to add in many sections. Also, I have added a fair number of historically significant quotes and pointers to rigorous treatments of various topics as found in Reinhold Remmert's Complex Function Theory. You should read Gamelin before my notes for most sections. Enjoy:


2. Guide to Gamelin's Complex Analysis (updated November 11, 2014)

I am fairly happy with these notes, however, some of the sections towards the end could use a few more proofs. If you would like the LaTeX source file for these notes feel free to ask me for the file. In Fall 2015 semester I think we'll cover Chapter IV on hyperbolic geometry and we may drop some of the material on infinite products depending on the interest of the class.


3. Wolfram Alpha, a good way to check your answers (and learn more math)
4. Infinite Series and the Residue Theorem by Noah A. Hughes (a student who worked with my brother at ASU)
5. Gamma Function some notes from Gamelin Chapter XIV Section 1.
6. Homeworks assigned in Fall 2015 semester:
   
   • Mission 1 (2015)
   • Mission 2 (2015)
   • Mission 3 (2015)
   • Mission 4 (2015)
   • Mission 5 (2015)
   • Mission 6 (2015)
   • Mission 7 (2015)
   • Mission 8 (2015)
7. Complex Analysis Lectures of Fall 2018 this is the playlist for our course on my You Tube channel, enjoy.
8. More Than Complex Analysis: (these are a work in progress)

Course Notes from Spring 2013:
I collect here the documents which comprise complex analysis of the Spring 2013 semester. We follow, roughly, Chapters 1-3 of Frietag and select topics of Chapter 4. However, it's more accurate to say we covered most of Churchill or Saff and Snider. Marsden, Gamelin, Alhfors, Albowitz and Fokas also contributed to our thinking. I hope to produce a more coherent set of notes with greater analytical depth when I next teach this course. If I teach the course in 2014 then I will likely use Gamelin for the text.

1. Complex numbers and basic properties. Pages 1-6.
2. Complex exponential notation and Euler's formula. Pages 7-10.
3. Complex exponential, roots of unity, logs. Pages 8-21.
4. Sequences, series, some proofs. Pages 21-28.
5. basic topological concepts, continuity. Pages 29-34.
6. limit laws, discontinuity. Pages 29-38.
7. complex differentiation by limits. Pages 39-45.
8. complex differentiation and its relation to real differentiability. Cauchy Riemann eqns. Pages 46-61.
9. harmonic functions, complex mappings as transformations. Pages 62-78.
10. contour integral, Cauchy's Integral Theorem, Cauchy-Goursat, other properties of the complex integration theory (see older notes for bounding theorem proof). Pages 79-105.
11. theory of power series, introductory remarks on analytic continuation and Laurent series. E65-E73.
12. discussion of meromorphic functions.
13. methods of contour integration (has E100 to E117).
14. methods of contour integration (this came with a handout)
15. analytic continuation, argument principle and Rouche's Theorem, Mobius transformation revealed, existence of Laurent expansion.
16. lecture by Dr. Ethan Smith on Analytic Number theory
17. final lecture on Mittag Leffler and Weierstrauss' Product theorem (did not get to full story of products in lecture)

Solutions to Homework of 2013 and 2014:

1. Mission 1 solution (2014)
2. Mission 2 solution (2014)
3. Mission 3 solution (2014)
4. Mission 4 solution (2014)
5. Mission 5 solution (2014)
6. Mission 6 solution (2014)
7. Mission 7 solution (2014)
8. Mission 8 solution (2014)
9. Mission 9 solution (2014)

1. Problem Set 1 solution (2013)
2. Problem Set 2 solution (2013)
3. Problem Set 3 solution (2013)
4. Problem Set 4 solution (2013)
5. Problem Set 5 solution (2013)
6. Problem Set 6 solution (2013)
7. Problem Set 7 solution (2013)

Tests and Solutions from 2013:

1. Test 1 solution (2013)
2. Test 2 solution (2013)
3. Test 3 takehome (no solution, just the problems)(2013)
4. Test 1 Solution, Spring 2010.
5. Test 3 Solution, Spring 2010.

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Last Modified: 7-19-2026