Real Analytical Functions

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Related lectures (24)

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Analyzing Analytic Functions

Covers the analysis of analytic functions and the Runge phenomenon in function approximation.

Complex Analysis: Derivatives and Integrals

Provides an overview of complex analysis, focusing on derivatives, integrals, and the Cauchy theorem.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Hadamard Factorisation

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Analytical Real Functions

Explores analytical real functions, focusing on series expansion and properties of u(x) in different neighborhoods.

Riemann Zeta Function

Covers the definition and properties of the Riemann Zeta function, including convergence and singularities.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in complex analysis, including integral calculations and Laurent series.

Cauchy-Hadamard Theorem

Explores the Cauchy-Hadamard theorem on convergence radius of power series and real analytical solutions.

Real Analysis: Summary

Covers real numbers, sequences, series, functions, limits, derivatives, Taylor series, integrals, and more.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series and the residue theorem in complex analysis, focusing on singularities and their applications in evaluating complex integrals.