Complex Analysis Courses and Certifications

Beijing Jiaotong University

Complex Variables and Integral Transforms

Let's take you into the magic world of complex numbers and complex functions. Join us, enjoy your study!

• XuetangX
• On-Demand
• Free Online Course

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

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

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

Explore complex analysis in o-minimal expansions, covering analytic functions, differentiability, and definability. Gain insights into advanced mathematical concepts and their applications.

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

Fields Institute

Complex Analysis in O Minimal Expansions of Real Closed Fields Lecture

Explore advanced topics in complex analysis within o-minimal expansions, including singularity removal, differentiable functions, and power series in real closed fields.

• YouTube
• 1 hour 48 minutes
• On-Demand
• Free Video

Fields Institute

Complex Analysis in O-minimal Expansions of Real Closed Fields - Lecture 2

Explore complex analysis in o-minimal expansions of real closed fields, covering topics from linearly ordered fields to finite extensions and K-linear matrices.

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

Fields Institute

Complex Rotation Numbers

Explore complex rotation numbers, their theory, dynamics, and applications in tame geometry and analysis. Delve into bubbles, self-similarity, and normalization concepts.

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

Fields Institute

Carathéodory Balls and Proper Holomorphic Maps on Multiply-Connected Planar Domains

Explore Carathéodory balls and proper holomorphic maps on multiply-connected planar domains, focusing on circular domains, proper maps, and related mathematical concepts.

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

Fields Institute

Mini-course on Blaschke Products and Inner Functions - Part 1

Explore Blaschke products and inner functions in complex analysis, covering definitions, singular inner functions, and dynamical properties in this advanced mathematics lecture.

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

Fields Institute

Mini-course on de Branges-Rovnyak Spaces - Part 1

Explore de Branges-Rovnyak spaces, covering history, multipliers, and types of spaces. Learn about Bronzerovnik and range spaces, general lemmas, and boundary behavior.

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

Fields Institute

Mini-course on Bergman Spaces - Part 1

Explore Bergman Spaces in mathematics, covering key concepts, theorems, and applications in analytic function theory. Gain insights from expert Stefan Richter.

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

Fields Institute

Hardy Spaces: Uniqueness and Harmonic Representation Theorems - Part 6

Explore uniqueness, harmonic representation, and representation theorems in Hardy spaces, advancing understanding of analytic function spaces and their applications.

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

Fields Institute

Mini-course on Hardy Spaces - Part 3

Explore Hardy spaces with a focus on rotation, generalization, and approximate identities. Delve into uniform boundedness, Poisson PR constructions, and harmonic functions.

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

International Centre for Theoretical Sciences

From Local to Global Holomorphic Peak Functions - Lecture 1

Explore holomorphic peak functions in complex analysis, from local to global perspectives. Gain insights into Cauchy-Riemann equations, L2-theory, and applications in higher-dimensional complex manifolds.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video