MATH-201: Analysis III

Lectures in this course (109)

Explores the Residues Theorem and the classification of holomorphic functions.

Covers the concept of line integrals and their application in vector fields.

Explores applications of the residues theorem in various scenarios, with a focus on Laurent series development.

Covers the theory and examples of conformal applications, focusing on the concept of conformal mappings and Moebius transformations.

Explores conformal transformations, including holomorphic functions and Moebius transformations.

Covers the Cauchy-Riemann conditions and potential functions in complex analysis.

Covers variational methods in mechanics, focusing on the Ritz-Galerkin method.

Covers vector calculus concepts like gradient, divergence, and curl with applications in physics and engineering.

Explores the Cauchy integral formula in complex analysis and its applications in evaluating complex integrals.

Explores Taylor series in complex analysis, emphasizing the behavior around singular points.

Explores regular curves and their bijectivity properties in mathematical analysis.

Explores the applications of Green's Theorem in 2D, emphasizing the importance of regular domains for successful integration.

Explores the theory of domains in complex analysis, emphasizing regular and oriented domains.

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

Covers the concept of parametric surfaces and the importance of orientation.

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Covers the heat equation for diffusion and conservation of thermal energy.

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