Analysis

Related lectures (25)

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Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.