Complex Analysis Courses and Certifications

Introduction to Complex Analysis

1092 ratings at Coursera

Explore complex functions, differentiation, integration, and power series. Delve into conformal mappings, Laurent series, and the Residue Theorem. Gain insights into complex dynamics and the Riemann hypothesis.

• Coursera
• 1 day 5 hours 18 minutes
• On-Demand
• Paid Course

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

Centre de recherches mathématiques - CRM

Holomorphic Movements in Complex Analysis - Lecture 1

Explorez les mouvements holomorphes et leur application aux ensembles de Julia. Découvrez le lambda-lemma et son impact sur les systèmes dynamiques complexes.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

Steve Brunton

Integration in the Complex Plane - Cauchy-Goursat Integral Theorem

Explore integration in the complex plane and the Cauchy-Goursat Integral Theorem, essential concepts in engineering mathematics for advanced problem-solving techniques.

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

Insights into Mathematics

Bernhard Riemann and the Complex Sphere - Geometric Thinking in Mathematics

Explore Riemann's geometrical thinking on the complex sphere, from abstract discussions on mathematical space to practical applications in complex analysis and higher-dimensional geometry.

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

Tom Rocks Maths

Helmholtz Principle and Vortex Motion

Explore Helmholtz' Principle and vortex motion in 2D potential flow. Learn about complex potentials, velocity fields, and the Method of Images to understand fluid dynamics and vortex trajectories.

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

Michael Penn

Complex Numbers and the Special Properties of Factorials in Mathematics

Explore the fascinating relationship between complex numbers and factorial functions in this mathematical deep dive with Professor Penn.

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

Michael Penn

The Complex Derivative: Understanding Its Unique Properties

Explore the peculiarities of complex derivatives, unraveling their unique properties and counterintuitive behavior in mathematical analysis.

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

IIT Delhi;  NPTEL

Ideal fluid flows using complex analysis

Learn to model and solve ideal fluid flow problems using complex analysis, focusing on flow superposition, complex potentials, and conformal transformations for engineering applications.

• Swayam
• 4 weeks
• On-Demand
• Free Online Course

Fields Institute

Hardy Spaces Mini-Course and Workshop - Part 1

Explore Hardy Spaces with expert Javad Mashreghi in this focused workshop, covering key concepts and applications in analytic function theory.

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

Tom Rocks Maths

Building the Multiverse Library

Explore complex mathematics behind the Multiverse Library, focusing on branch cuts and multifunctions. Learn about holomorphic branches of complex logarithms and square root functions in this engaging mathematical journey.

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

ICTP Mathematics

New Complex Analytic Methods in the Theory of Minimal Surfaces - Franc Forstnerič

Explore recent developments in minimal surface theory using complex analytic methods, covering global theory, Calabi-Yau problem, and complex Gauss map applications.

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

Wolfram

Everything to Know About Mellin-Barnes Integrals - Part 1

Explore Mellin-Barnes Integrals with Oleg Marichev: convert special functions, evaluate integrals, and understand existence conditions in this comprehensive mathematical deep dive.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

New Perspectives on Borel Summation - Lecture 4

Explore Airy-Lucas functions through Borel summation, focusing on thimble integrals and hypergeometric Laplace transforms. Gain insights into Stokes phenomenon reflections in the Borel plane.

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

Institut des Hautes Etudes Scientifiques (IHES)

New Perspectives on Borel Summation - Lecture 1

Explore new perspectives on Borel summation, focusing on linear ODEs and integrals over Lefschetz thimbles, to understand when divergent series solutions produce holomorphic solutions.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video