MATH-201: Analysis III

Lectures in this course (104)

Covers the fundamental concepts of vector analysis, including the gradient, divergence, and curl operators.

Covers a recap of Analysis 1 and 2, emphasizing normed space R^n, subsets, and continuous functions.

Covers the analysis of incompressible fluid flow and numerical solutions in fluid dynamics.

Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.

Discusses the uniqueness of implicit functions solutions and surfaces described by equations.

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

Explores regular curves and their bijectivity properties in mathematical analysis.

Covers the basics of implicit differentiation, focusing on techniques and applications.

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

Covers the Cauchy-Schwarz inequality and the Lagrange identity in R^n with related mathematical expressions and proofs.

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

Explores regular curves, examples like segments and functions, and curvilinear integrals along regular curves.

Explores deriving fields from a potential, curvilinear integrals, and necessary conditions for domains.

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

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