What you will learn In Introduction to Complex Analysis Course
Understand the foundational concepts of complex numbers and the complex plane.
Learn about complex functions and their properties.
Explore the concept of analyticity and the Cauchy-Riemann equations.
Study complex integration and Cauchy’s integral theorem.
Delve into series expansions, including Taylor and Laurent series.
Examine singularities and residues.
Apply complex analysis to solve real-world problems in physics and engineering.
Program Overview
Introduction to Complex Numbers
⏳ 4 hours
- Learn about the history and algebra of complex numbers, their geometric representation in the complex plane, and polar coordinates.
Complex Functions and Iteration
⏳ 3 hours
- Explore complex functions, sequences, limits, and the basics of complex dynamics, including Julia sets and the Mandelbrot set.
Analytic Functions
⏳ 4 hours
- Study complex differentiation, the Cauchy-Riemann equations, and analytic functions.
Conformal Mappings
⏳ 4 hours
- Learn about conformal mappings, including the complex logarithm, complex roots, Möbius transformations, and the Riemann mapping theorem.
Complex Integration
⏳ 4 hours
- Understand complex path integrals, Cauchy’s integral theorem, and applications like the Fundamental Theorem of Algebra.
Power Series
⏳ 4 hours
- Study power series representations of analytic functions, including convergence and the Riemann zeta function.
Laurent Series and the Residue Theorem
⏳ 4 hours
- Learn about Laurent series, isolated singularities, and the residue theorem.
Applications of Complex Analysis
⏳ 4 hours
- Apply complex analysis to solve real-world problems, especially in physics and engineering.
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Job Outlook
Enhances mathematical proficiency for careers in data science, engineering, and computational modeling.
Provides a solid foundation for advanced studies in mathematical theory and analysis.
Completing this course can bolster qualifications for roles requiring strong analytical and problem-solving skills.
Specification: Introduction to Complex Analysis
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