Complex Analysis for Engineers
( 25 Modules )

Module #1
Introduction to Complex Analysis
Overview of complex analysis, importance in engineering, and brief history

Module #2
Complex Numbers and Functions
Definition, algebra, and geometry of complex numbers; functions of complex variables

Module #3
Polar Form and De Moivres Theorem
Polar representation of complex numbers, De Moivres theorem, and applications

Module #4
Analytic Functions
Cauchy-Riemann equations, harmonic functions, and the Laplace equation

Module #5
Cauchys Integral Theorem
Statement and proof of Cauchys integral theorem, and its consequences

Module #6
Cauchys Integral Formula
Derivation and applications of Cauchys integral formula

Module #7
Taylor and Laurent Series
Taylor series, Laurent series, and their applications in engineering

Module #8
Residue Theory
Residues, residue theorem, and its applications in engineering

Module #9
Application to Electric Circuits
Analysis of electric circuits using complex analysis

Module #10
Application to Control Systems
Stability analysis of control systems using complex analysis

Module #11
Conformal Mapping
Introduction to conformal mapping, Riemann surfaces, and applications

Module #12
Mobius Transformations
Properties and applications of Mobius transformations

Module #13
Boundary Value Problems
Solution of boundary value problems using complex analysis

Module #14
Schwarz-Christoffel Transformations
Introduction to Schwarz-Christoffel transformations and their applications

Module #15
Riemann Surfaces
Introduction to Riemann surfaces, charts, and atlases

Module #16
Application to Signal Processing
Applications of complex analysis in signal processing

Module #17
Application to Image Processing
Applications of complex analysis in image processing

Module #18
Application to Electromagnetics
Applications of complex analysis in electromagnetics

Module #19
Numerical Methods in Complex Analysis
Introduction to numerical methods for complex analysis

Module #20
Computer-Aided Complex Analysis
Use of software packages for complex analysis, such as MATLAB or Python

Module #21
Case Studies in Complex Analysis
Real-world applications and case studies in complex analysis

Module #22
Group Projects and Presentations
Students work in groups to apply complex analysis to real-world problems

Module #23
Review and Practice Problems
Review of key concepts and practice problems for the final exam

Module #24
Final Exam
Comprehensive final exam covering all modules

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Complex Analysis for Engineers career

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