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Complex Analysis
Complex Analysis
42 lessons across 14 topics
1. Complex Numbers and the Complex Plane
1
Algebra Of Complex Numbers
2
Modulus And Argument
3
Polar Form And Roots
2. Functions of a Complex Variable
4
Analyticity
5
Differentiability
6
Limits And Continuity
3. Cauchy-Riemann Equations
7
Derivation And Interpretation
8
Examples And Counterexamples
9
Harmonic Functions
4. Elementary Analytic Functions
10
Branch Issues
11
Exponential And Logarithm
12
Trigonometric And Hyperbolic Functions
5. Contours and Complex Integration
13
Antiderivatives
14
Estimation
15
Paths And Contour Integrals
6. Cauchy’s Theorem
16
Consequences Of Path Independence
17
Morera-type Intuition If Included
18
Simply Connected Domains
7. Cauchy Integral Formula
19
Derivatives Of Analytic Functions
20
Fundamental Theorem Of Algebra
21
Liouville’s Theorem
8. Midterm 1 and Taylor Series
22
Analytic Continuation Intuition
23
Midterm 1
24
Power Series Representations
9. Laurent Series
25
Annuli
26
Expansion Methods
27
Principal Parts
10. Singularities
28
Essential Singularities
29
Poles
30
Removable Singularities
11. Residues
31
Applications To Contour Integrals
32
Residue Computation
33
Residue Theorem
12. Applications of Residues
34
Argument Principle Overview, If Included
35
Improper Real Integrals
36
Trigonometric Integrals
13. Conformal Mapping
37
Linear Fractional Transformations
38
Local Angle Preservation
39
Mapping Regions
14. Final Review
40
Key Themes In Final Review
41
Review And Synthesis
42
The Structure And Power Of Analytic Functions
