Complex Analysis Courses and Certifications

Introduction to complex analysis

4 ratings at OpenLearn

This free course, Introduction to complex analysis, is an extract from the third level Open University course M337 Complex Analysis, which develops the theory of functions of a complex variable, ...

• OpenLearn
• 12 hours
• On-Demand
• Free Certificate

Steve Brunton

Engineering Math - Crash Course in Complex Analysis

Master complex analysis fundamentals from arithmetic to residues, exploring Euler's formula, analytic functions, and Cauchy integrals for differential equations modeling.

• YouTube
• 6 hours 28 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Overview & Motivation, Complex Arithmetic, Euler's Formula & Polar Coordinates

Introduction to complex numbers, their arithmetic operations, Euler's formula, and polar coordinates. Covers solutions to differential equations and lays foundation for further complex analysis topics.

• YouTube
• 29 minutes
• On-Demand
• Free Video

ICTP Mathematics

Complex Analysis

Master complex analysis fundamentals through comprehensive lectures covering essential theorems, functions, and applications in this ICTP diploma program.

• YouTube
• 1 day 4 hours 21 minutes
• On-Demand
• Free Video

Complex Analysis: Multivalued Functions and Integration - Lecture 4

Delve into holomorphic functions, multivalued functions, and contour integration theory through advanced complex analysis concepts and their real-world counterparts.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Examples of Complex Integrals

Explore practical applications of complex integration theorems through challenging examples, enhancing your understanding of advanced mathematical concepts.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Complex Residues

Explore the residue theorem and learn to compute complex contour integrals around singular points, culminating in the integral of f(z)=1/z.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Integrals in the Complex Plane

Explore contour integration in complex analysis, covering theorems, continuous deformation, and integration around singularities for a deeper understanding of complex functions.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Analytic Functions Solve Laplace's Equation

Explore how analytic complex functions' real and imaginary parts solve Laplace's equation, introducing harmonic functions in this in-depth mathematical analysis.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Analytic Functions and Cauchy-Riemann Conditions

Explore analytic complex functions and learn to test for analyticity using Cauchy-Riemann conditions in this comprehensive mathematical exploration.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Roots of Unity and Rational Powers of Z

Explore complex logarithms and exponentials to compute fractional powers of complex numbers, including nth roots of unity and special cases like the square root of i.

• YouTube
• 35 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Functions of a Complex Variable, f(z)

Explore complex functions including monomials, exponentials, and trigonometric functions. Learn about Taylor series and important identities in complex analysis.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Bromwich Integrals and the Inverse Laplace Transform

Explore Bromwich integrals and inverse Laplace transforms in complex analysis, culminating this series with practical computation techniques.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 8

Explore advanced concepts in complex analysis within o-minimal expansions of real closed fields, focusing on theoretical foundations and applications in mathematical logic.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 7

Explore advanced concepts in complex analysis within o-minimal expansions of real closed fields, focusing on theoretical foundations and applications in mathematical logic.

• YouTube
• 1 hour 42 minutes
• On-Demand
• Free Video