Convex Functions: Analytical Definition and Geometric Interpretation

Related lectures (25)

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Explores properties and applications of complex numbers, including De Moivre's theorem and finding complex roots.

Explores norm equivalence in complex functions, covering homogeneity and triangular inequality.

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.

Explores the comparison of convergence of improper integrals and the importance of analyzing functions for convergence.

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.

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

Discusses Laurent series and the residue theorem in complex analysis, providing examples and applications for evaluating complex integrals.

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