Introductory Complex Analysis with Bill Kinney

Course Description

Based on "Fundamentals of Complex Analysis, with Applications to Engineering and Science", by E.B. Saff and A.D. Snider (3rd Edition). "Visual Complex Analysis", by Tristan Needham, is also referred to a lot. Mathematica is often used, especially to visualize complex analytic (conformal) mappings.

Introductory Complex Analysis with Bill Kinney
Prof. Kinney in Lec 29: Uniform Convergence, Taylor Series Facts
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Video Lectures & Study Materials

# Lecture Play Lecture
1 Complex Arithmetic, Cardano's Formula Play Video
2 Geometric Interpretations of Complex Arithmetic, Triangle Inequality Play Video
3 Polar Form, Principal Value of Arg, Basic Mappings Play Video
4 Mappings, Linear Mappings, Squaring Map, Euler's Identity Play Video
5 Squaring Mapping, Euler's Identity & Trigonometry, 5th Roots Example Play Video
6 Exponential Map on Mathematica, Squaring Map, Intro to Topology Play Video
7 Exponential & Reciprocal Maps, Domains, Derivative Limit Calculations Play Video
8 Topological Definitions, Limits, Continuity, Linear Approximation Play Video
9 Facts to Recall, Animations, Continuity Proofs (z^2 and 1/z) Play Video
10 Open Disks are Open, Derivatives, Analyticity, Linear Approximations Play Video
11 Areas of Images, Differentiability, Analyticity, Cauchy-Riemann Eqs Play Video
12 Cauchy-Riemann Eqs (Rectangular & Polar), Intro Harmonic Functions Play Video
13 Preimages, Laplace's Equation, Harmonic and Analytic Functions Play Video
14 Preimages, Mathematica, Maximum Principle (Harmonic), Polynomials Play Video
15 Review Analytic Functions, Amplitwist Concept, Harmonic Functions Play Video
16 Taylor Polynomials, Complex Exponential, Trig & Hyperbolic Functions Play Video
17 Complex Logarithm, Functions as Sets, Multivalued Functions Play Video
18 Branches of Arg, Harmonic Functions over Washers, Wedges and Walls Play Video
19 Complex Powers, Inverse Trigonometric Functions, Branch Cuts Play Video
20 Invariance of Laplace's Eq, Real & Im Parts of Complex Integrals Play Video
21 Conformality, Riemann Mapping Theorem, Vector Fields, Integration Play Video
22 Complex Integrals, Cauchy-Goursat Theorem, Quick Exam 2 Review Play Video
23 Real Line Integrals and Applications, Complex Integration Play Video
24 Integration, Cauchy-Goursat Theorem, Cauchy Integral Formula Play Video
25 Cauchy Integral Formula, Applications, Liouville's Theorem Play Video
26 Sequences and Series of Functions, Maximum Modulus on Mathematica Play Video
27 Review Cauchy's Theorem, Cauchy Integral Formulas, and Corollaries Play Video
28 Taylor Series Computations, Graphs of Partial Sums, Ratio Test Play Video
29 Uniform Convergence, Taylor Series Facts Play Video
30 Laurent Series Calculations, Visualize Convergence on Mathematica Play Video
31 Laurent Series, Poles, Essential Singularities Play Video
32 More Laurent Series, Review Integrals & Cauchy Integral Formula Play Video
33 Integrating 1/(1+z^2), Mathematica programming, Residues Play Video
34 Series, Zeros, Isolated Singularities, Residues, Residue Theorem Play Video
35 Residue Theorem Examples, Principal Values of Improper Integrals Play Video

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