Analytic function

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Related lectures (30)

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Analytical Trajectories: Key Ingredients

Explores analytical trajectories, emphasizing critical points, inequalities, and analyticity.

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 Real Functions

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

Non-analytic Smooth Functions

Explores non-analytic smooth functions, their properties, and applications in differential geometry and partitioning unity.

Analytical Functions: Integration Techniques

Explores integration techniques and variable transformations for calculating integrals.

Real Functions: Continuity Theorem

Covers the Continuity Theorem for functions dependent on a parameter, proving the continuity of a function g.

Real Functions: Composition and Limits

Explores real functions, composition, and limits, including algebraic operations and sequence characterization.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Analyzing Critical Points in Finite Solutions

Explores critical points in finite solutions, emphasizing isolated points and their significance.