Math 295: Complex analysis - Fall 2020

A1--A7: BMPS Sections 1.1, 1.2 and 1.3

A1, A2, A5, A6, A7: Baby Knopp Chapter II

A1, A2, A5, A6, A7: Bowman Chapter 2

A1, A5, A6, A7: Lec 1.2: Algebra and Geometry in the Complex Plane

A2, A3: Lec 1.3: Polar Representation of Complex Numbers

A4: Lec. 1.4: Roots of Complex Numbers

Before Monday/For warm up 2.1:

• BMPS Section 1.4
• Bowman Section 2.3, specifically tasks 32 and 33 (Objective A8)
  Bowman Section 7.1 (Objectives A9, A10)
• Baby Knopp Section 12 (Objective A8)
  Knopp Part I Section 4 (Objectives A9, A10)

Before Wednesday/For warm up 2.2:

• BMPS Section 1.4
• Bowman Section 4.1, 4.2
• Baby Knopp Section 23

Before Monday/For warm up 2.1:

• Multiplication of complex numbers in polar form, cis(phi) is short for cos(phi) + i sin(phi) (Objective A8)
• Contours and arc length by William Nesse, you can ignore the arc length for now (Objectives A9, A10)
  
• Sketching Subsets of the Complex Plane Part 1 and Part 2 by Peter Woolfe, in Part 2 the last example is complicated (Objective A9)
  

Before Wednesday/For warm up 2.2:

• Lec. 1.5: Topology in the Plane

Before Monday/For warm up 3.1:

• BMPS Sections 2.1 and 2.2
• Bowman Sections 4.3--4.5
  Bowman Sections 5.1, 5.2, 5.5
• Baby Knopp Sections 31--34, 36
  Knopp Part I Sections 5, 6

Before Wednesday/For warm up 3.2:

• BMPS Sections 2.3 and 2.4
• Bowman Section 5.3
• Knopp Part I Section 7

Before Monday/For warm up 3.1:

• Lec 2.2: Sequences and Limits of Complex Numbers
• Lec 3.1: The Complex Derivative
• Lec 4.2: Conformal Mappings

Before Wednesday/For warm up 3.2:

• Lec. 3.2: The Cauchy-Riemann Equations
• Lec 3.5: First properties of analytic functions

Before Monday/For warm up 4.1:

• BMPS Section 3.1
• Bowman Sections 3.1, 3.2 and 3.4
  Bowman Section 11.4
• Baby Knopp Chapter IV (Sections 16--18)

Before Wednesday/For warm up 4.2:

• BMPS Sections 3.2 and 3.3
• Bowman Sections 11.1, 11.3
• Baby Knopp Chapter III (Sections 14 and 15)
  Knopp Part I Section 2

Before Monday/For warm up 4.1:

• Lec. 4.3: Möbius Transformations, Part 1
• Lec. 4.4: Möbius Transformations, Part 2

Before Wednesday/For warm up 4.2:

• Stereographic Projection, by Maths For all
• Stereographic Projection, by Science Projects (he made his own model!)
• Stereographic projection of Riemann sphere (very cool very short video showing how circles on the sphere project to the complex plane)

Before Monday/For warm up 5.1:

• BMPS Section 3.4
• Bowman Sections 3.5, 3.6, 3.7, 3.8
• Baby Knopp Section 38

Before Wednesday/For warm up 5.2:

• BMPS Section 3.5
• Bowman Section 3.9
• Baby Knopp Sections 41, 45, 47

Before Monday/For warm up 5.1:

• The Complex Exponential Function by BriTheMathGuy
• Complex mappings by BriTheMathGuy (what z^2 does to a line)
• Lec. 3.3: The complex exponential function

Before Wednesday/For warm up 5.2:

• Lec 4.1: Inverse functions of analytic functions

• BMPS Sections 4.1 and 4.2
• Bowman Sections 7.3, 7.4, and 8.1
• Knopp Part I Sections 10, 11, 12, 13, 14

• Lec 5.1: Complex integration
• Lec 5.2: Complex Integration: examples and first facts
• Lec 5.3: The fundamental theorem of calculus for analytic functions

Before Monday/For warm up 7.1:

• BMPS Section 4.3
• Bowman Sections 8.2, 8.3 and 8.4
• Knopp Part I Sections 12, 13, 14

Before Wednesday/For warm up 7.2:

• BMPS Section 4.4
• Bowman Section 9.2
• Knopp Part I Section 15

Before Monday/For warm up 7.1:

• Lec 5.4: Cauchy's Theorem and Integral Formula (stop video at minute 13 when the Cauchy Integral Formula comes up)

Before Wednesday/For warm up 7.2:

• Lec 5.4: Cauchy's Theorem and Integral Formula (from minute 13 to the end of minute 23, stop when PBT announces an amazing consequence of the Cauchy Integral Formula)

Before Monday/For warm up 8.1:

• BMPS Sections 7.4 and 8.1
• Bowman Sections 6.2 (6.2.1, 6.2.2, 6.2.3 only), 6.3, 6.4, 6.5

Before Monday/For warm up 8.1:

• Lec 6.1: Infinite Series of Complex Numbers
• Lec 6.2: Power Series
• Lec 6.3: The Radius of Convergence of a Power Series

Before Monday/For warm up 9.1:

• BMPS Section 8.3
• Bowman Section 10.2

Before Monday/For warm up 9.1:

• Lec 7.1: Laurent Series
• Lec 7.3: The Residue Theorem (you can stop the video at the end of minute 12 when PBT introduces the Residue Theorem; don't mind her discussion of singularities, we will do this next week)

Before Monday/For warm up 10.1:

• BMPS Theorem 8.14 of Section 8.2
  BMPS Section 9.1
• Bowman Section 10.3

Before Wednesday/For warm up 10.2:

• BMPS Section 9.2
• Bowman Section 10.1

Before Monday/For warm up 10.1:

• Lec 7.2: Isolated Singularities of Analytic Functions

Before Wednesday/For warm up 10.2:

• Lec 7.3: The Residue Theorem (this time, the whole video!)
• Lec 7.4: Finding Residues
• Lec 7.5: Evaluating Integrals via the Residue Theorem