# Introduction to Applied Complex Variables

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### Video Lectures & Study Materials

# Lecture Play Lecture
1 Math 3160 introduction (21:47) Play Video
2 Basic Complex Algebra (24:31) Play Video
3 Moduli, conjugates, triangle inequality, and polar coordinates (21:36) Play Video
4 Products and quotients in exponential form (16:46) Play Video
5 Roots of complex numbers (26:09) Play Video
6 Functions of complex variables and mappings (27:36) Play Video
7 Regions in the complex plane (31:26) Play Video
8 Mappings by the exponential function (14:39) Play Video
9 Limits of complex functions (24:57) Play Video
10 Limits at infinity (30:51) Play Video
11 The derivative of a complex function (17:55) Play Video
12 Differentiation formulas for complex functions (7:15) Play Video
13 Cauchy-Riemann equations (28:44) Play Video
14 Analytic functions (16:05) Play Video
15 Harmonic functions and analytic functions (20:04) Play Video
16 The complex exponential and logarithm functions (23:54) Play Video
17 Complex log identites (14:09) Play Video
18 The information in analytic functions (16:20) Play Video
19 Applications to signal processing (57:26) Play Video
20 Applications of analytic functions to fluid flow (24:45) Play Video
21 Complex exponents (14:12) Play Video
22 Complex trigonometric functions (9:01) Play Video
23 Inverse trigonometric functions of a complex variable (16:44) Play Video
24 Derivatives and integrals of complex functions w(t) (19:05) Play Video
25 Contours and arc length in the complex plane (10:22) Play Video
26 Contour integrals of complex functions (31:19) Play Video
27 Closed circle integral of 1/z and branch cuts (20:37) Play Video
28 Moduli of complex integrals and integral bounds (20:05) Play Video
29 Complex antiderivatives and the fundamental theorem (26:53) Play Video
30 Proof of the antiderivative theorem for contour integrals (25:46) Play Video
31 Cauchy-Goursat theorem (26:49) Play Video
32 Simply and multiply connected domains (26:55) Play Video
33 Cauchy integral formula (29:16) Play Video
34 Cauchy Integral Results (23:15) Play Video
35 The fundamental theorem of algebra revisited (12:27) Play Video
36 Harmonic oscilators in the complex plane (optional) (19:05) Play Video
37 How Schrodinger's equation works (optional) (46:41) Play Video
38 Sequences and series involving complex variables (23:11) Play Video
39 Taylor series for functions of a complex variable (37:16) Play Video
40 Laurent series (29:56) Play Video
41 Examples of Laurent series computations (27:22) Play Video
42 Aspects of complex power series convergence (20:42) Play Video
43 Singularities and residues of complex functions (23:10) Play Video
44 The residue theorem (17:37) Play Video
45 Residues at infinity (27:37) Play Video
46 Taxonomy of singularities of complex functions (17:19) Play Video
47 Aspects of zeros and poles of analytic functions (19:10) Play Video
48 Zeros and poles of rational functions (6:44) Play Video
49 Applications of residues to improper real integration (28:07) Play Video
50 Fourier type integrals using residues (21:02) Play Video