MATH-201: Analysis III

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Lectures in this course (104)

Complex Analysis: Cauchy Integral Formula

Explores the Cauchy integral formula in complex analysis and its applications in evaluating complex integrals.

Complex Analysis: Taylor Series

Explores Taylor series in complex analysis, emphasizing the behavior around singular points.

Residue Calculation and Singularities Classification

Covers the calculation of residues and the classification of singularities in complex functions.

Residual Theorem: Cauchy

Covers the residual theorem from Cauchy, focusing on simple closed curves and holomorphic functions.

Residues Method: Generalized Integrals

Covers the calculation of generalized integrals using the residues method and provides examples for better understanding.

Trigonometric Integrals: Residues Method

Covers the calculation of integrals using the residues method and discusses singularities, poles, and examples.

Fourier Transform: Residue Method

Covers the calculation of Fourier transforms using the residue method and applications in various scenarios.

Mellin Transform: Residue Method

Covers the calculation of Mellin transforms using the residue method and provides examples of its application.

Generalized Integral and Main Value

Covers the concept of the generalized integral and main value, including singularities, principal value at infinity, and residues.

Principal Value of an Integral: Examples

Covers examples of principal value of an integral with sin functions and singularities.

Analytic Continuation and Uniqueness of Holomorphic Functions

Covers the concept of analytic continuation and the uniqueness of holomorphic functions, including the extension of holomorphic functions and the properties of entire and meromorphic functions.

Analytical Extension of Gamma Function

Covers the analytical extension of the Gamma function to real and complex numbers, discussing properties and convergence.

Riemann Zeta Function

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

Analytic Continuation of Zeta Function

Explores the analytic continuation of the zeta function and its relation to holomorphic functions and natural numbers.

Riemann Integral: Construction and Properties

Explores the construction and properties of the Riemann integral, including integral properties and mean value theorem.

Riemann Integral: Techniques and Fundamentals

Explores Riemann integrability, the fundamental theorem of integral calculus, and various integration techniques.

Generalized Integrals: Simplified Concepts

Explains generalized integrals with simplified concepts, convergence criteria, and variable changes in integration.

Riemann Integral: Convergence and Limit Process

Explores Riemann integral, convergence, and limit processes, emphasizing continuity and monotonic convergence.

Multiple Integrals: Extension and Properties

Explores the extension and properties of multiple integrals for continuous functions on rectangles.

Double Integral Techniques: Change of Variable

Covers techniques for double integrals, focusing on the concept of change of variable.

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