Complex Analysis Courses and Certifications

International Centre for Theoretical Sciences

The Monge-Ampère Equations and the Bergman Kernel - Lecture 1

Explore complex analysis in higher dimensions, focusing on Cauchy-Riemann equations, L2 theory, and applications to geometry. Learn about Bergman kernels and extension theorems in this advanced mathematics lecture.

• YouTube
• 1 hour 4 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

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

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

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

Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 4

Explore advanced concepts in complex analysis within o-minimal expansions of real closed fields, building on previous lectures in this graduate-level series.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 3

Explore advanced concepts in complex analysis within o-minimal expansions of real closed fields, building on previous lectures in this graduate-level series.

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

Fields Institute

Complex Analysis in O-Minimal Expansions of Real Closed Fields - Lecture 1

Explore complex analysis in o-minimal expansions of real closed fields, delving into advanced mathematical concepts and their applications in this graduate-level lecture.

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