Complex Analysis Courses and Certifications

Michael Penn

The Natural Log of Imaginary Numbers

A focused mathematical exploration of the natural logarithm of imaginary numbers.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Steve Brunton

Roots of Unity, Branch Cuts, Analytic Functions, and the Cauchy-Riemann Conditions

Explores roots of unity, multivalued complex functions and branch cuts, and the Cauchy-Riemann conditions for analytic functions.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Steve Brunton

Complex Numbers and Functions

Explore complex numbers and functions as foundational tools for partial differential equations, including Euler’s formula, Taylor series, and multivalued logarithms.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Steve Brunton

Integration in the Complex Plane - Cauchy-Goursat Integral Theorem

Explores integration in the complex plane through the Cauchy-Goursat Integral Theorem.

• YouTube
• 50 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Math Sorcerer

Complex Variables Unveiled - Changing Your Perspective on Math

Explore complex analysis through an insightful book review and learn to derive the inverse of complex numbers using ordered pairs, revolutionizing your mathematical perspective.

• YouTube
• 14 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Michael Penn

A Complex Approach to Finding Classic Mathematical Series Sums

Explore an innovative mathematical solution using complex analysis to solve a classic summation problem, demonstrating advanced problem-solving techniques.

• YouTube
• 13 minutes
• Self-Paced
• Free Video

Michael Penn

Important Concepts in Complex Function Theory

Explore fundamental concepts of complex functions through clear explanations and practical examples of key mathematical principles.

• YouTube
• 14 minutes
• Self-Paced
• Free Video

Steve Brunton

Cauchy Integral Formula

A lecture on the Cauchy integral formula within an engineering mathematics sequence.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Michael Penn

Gamma Reflection via Double and Contour Integration

A derivation of the gamma function’s reflection formula using double integrals and contour integration.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Tom Rocks Maths

Building the Multiverse Library

Branch cuts give complex functions such as the logarithm and square root single-valued branches, illustrated through the Multiverse Library.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

Contour Integrals - Concepts and Examples

Explore contour integrals, including regular arcs, piecewise regular arcs, and simple closed contours. Learn through practical examples to enhance understanding.

• YouTube
• 18 minutes
• Self-Paced
• Free Video

Steve Brunton

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

Introduces complex numbers through Euler’s formula, basic arithmetic, and polar coordinates, motivated by oscillatory solutions of differential equations.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Regression Analysis: Simplify Complex Data Relationships

608 ratings at Coursera

Model variable relationships in Python: build simple and multiple linear regressions, run Chi-squared and one- and two-way ANOVA tests, and construct binomial logistic regression models.

• Coursera
• 6 weeks, 5 hours a week
• Self-Paced
• Paid Course