Online Complex Variables
with online videos
Dr. Bob's Online University
(Not an actual university)
Robert 'Dr. Bob' Gardner

This website includes links to class notes and supplements (in PDF) used in the teaching of East Tennessee State University's senior/graduate level class Complex Variables (MATH 4337/5337). Links are also available for video presentations of the notes. The videos have been used as of the teaching of online Complex Variables, starting in spring 2020. The material is based closely on James Ward Brown and Ruel V. Churchill's Complex Variables and Applications, 8th Edition, McGraw-Hill (2009):

Brown and Churchill's Complex Variables with Applications book, 8th edition


Robert "Dr. Bob" Gardner can be reached by e-mail at: gardnerr@etsu.edu. His office is in Gilbreath Hall, Room 308F on the ETSU campus.


The following notes and supplements are all in PDF. The following notes and supplements are all in PDF. The videos can be streamed from YouTube and should remain permanently available. (The videos previously on ETSU's Panopto host site have been, or may soon be, deleted.)

Chapter 2. Analytic Functions.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
2.26. Harmonic Functions
2.26 Notes
2.26 Supplement
2.26 Supplement Print File
2.26 Video, Part 1 (10:30)
2.26 Video, Part 2 (15:29)
2.27. Uniquely Determined Analytic Functions
2.27 Notes
2.27 Supplement
2.27 Supplement Print File
-
2.28. Reflection Principle
2.28 Notes
2.28 Supplement
2.28 Supplement Print File
2.28 Video (7:08)


Chapter 3. Elementary Functions.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
3.29. The Exponential Function
3.29 Notes
3.29 Supplement
3.29 Supplement Print File
3.29 Video (13:52)
3.30. The Logarithm Function
3.30 Notes
-
3.30 Video (12:53)
3.31. Branches and Derivatives of Logarithms
3.31 Notes
-
3.31 Video (12:16)
3.32. Some Identities Involving Logarithms
3.32 Notes
3.32 Supplement
3.32 Supplement Print File
3.32 Video (16:37)
3.33. Complex Exponents
3.33 Notes
3.33 Supplement
3.33 Supplement Print Final
3.33 Video (23:10)
3.34. Trigonometric Functions
3.34 Notes
3.34 Supplement
3.34 Supplement Print Final
3.34 Video (26:23)
3.35. Trigonometric Functions
3.35 Notes
-
-
3.36. Inverse Trigonometric and Hyperbolic Functions
3.35 Notes
-
-


Chapter 4. Integrals.

SECTION
NOTES
SUPPLEMENTS
VIDEOS ON YOUTUBE
4.37. Derivatives of Functions w(t)
4.37 Notes
-
4.37 Video (13:52)
4.38. Definite Integrals of Functions w(t)
4.38 Notes
-
4.38 Video (10:52)
4.39. Contours
4.39 Notes
-
4.39 Video (22:04)
4.40. Contour Integrals
4.40 Notes
-
4.40 Video (11:15)
4.41. Some Examples
4.41 Notes
-
4.41 Video (25:43)
4.42. Examples with Branch Cuts
4.42 Notes
-
4.42 Video (23:59)
4.43. Upper Bounds for Moduli of Contour Integrals
4.43 Notes
4.43 Supplement
4.43 Supplement Print File
4.43 Video, Part 1 (16:24)
4.43 Video, Part 2 (6:59)
4.44. Antiderivatives
4.44 Notes
-
4.44 Video (30:52)
4.45. Proof of the Theorem
4.45 Notes
-
-
4.46. Cauchy-Goursat Theorem
4.46 Notes
-
4.46 Video (22:48)
4.47. Proof of the Theorem
4.47 Notes
-
-
4.48. Simply Connected Domains
4.48 Notes
-
4.48 Video (13:53)
4.49. Multiply Connected Domains
4.49 Notes
4.49 Supplement
4.49 Supplement Print File
4.49 Video (27:51)
4.50. Cauchy Integral Formula
4.50 Notes
4.50 Supplement
4.50 Supplement Print File
4.50 Video (16:06)
4.51. An Extension of the Cauchy Integral Formula
4.51 Notes
4.51 Supplement
4.51 Supplement Print File
4.51 Video, Part 1 (8:52)
4.51 Video, Part 2 (8:53)
4.52. Some Consequences of the Extension
4.52 Notes
4.52 Supplement
4.52 Supplement Print File
4.52 Video (18:17)
4.53. Liouville's Theorem and the Fundamental Theorem of Algebra
4.53 Notes
4.53 Supplement
4.53 Supplement Print File
4.53 Video (31:09)
4.54. Maximum Modulus Principle
4.54 Notes
4.54 Supplement
4.54 Supplement Print File
4.54 Video (46:53)


Additional notes and supplements based on Brown and Churchill's Complex Variables and Applications, 8th Edition are available on the Complex Variables Class Notes webpage.

Return to Dr. Bob's webpage

Last updated: May 12, 2024.