Course

MATH-201: Analysis III

Lectures in this course (104)

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

Covers the parameterization of curves, tangent and normal vectors, simple closed curves, exterior normal, regular curves, and domains in R^2.

Covers the Green and Gauss theorems, focusing on their applications in vector calculus.

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

Covers the Green-Riemann formulas and their applications in evaluating integrals and solving differential equations.

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

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.

Covers the Euler equations for fluid dynamics and the conservation laws applied.

Explores Green's theorem, vector field curl, Ampère's law, and magnetic field modeling.

Covers the concept of surface integrals for scalar fields, focusing on regular, orientable surfaces in 3D space.

Explains the surface integral for vector fields and demonstrates its calculation process through examples.

Explores holomorphic functions, Cauchy-Riemann conditions, and principal argument values in complex analysis.

Covers the Stokes theorem, extending the Green theorem to surfaces in R3 and explaining its application.

Covers derivatives, continuity, properties, and applications of derivative rules.

Explores the Cauchy Theorem and its applications in complex analysis.

Explores the Gauss theorem in R^n+1, covering regular domains, vector fields, surface integrals, and volume calculations.

Covers the Cauchy theorem, complex functions, and contour integrals.

Explores Fresnel integrals through curvilinear integrals in R^2, focusing on cos(x²-y) and sin(x) functions.

Explores simply connected domains in complex analysis, including holomorphic functions, Cauchy's integral formula, and Taylor series.