Advanced Analysis II: Polar Coordinates

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Related lectures (28)

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Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Continuity and Limits

Covers continuity, limits, and different approaches to approaching points in various coordinate systems.

Limits of Functions: Calculus Methods

Explores the concept of limits of functions of several variables and methods for calculation, including criteria based on convergent sequences and the 'two gendarmes' theorem.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Derivability and Composition

Covers derivability conditions, function composition, Jacobian matrix, and chain derivation.

Gradient and Taylor Formula

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Transforms of the Place

Explores the intuition behind transforms of the place and addresses audience questions on integral calculations and function choices.

Entropy and the Second Law of Thermodynamics

Covers entropy, its definition, and its implications in thermodynamics.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Limits of Functions in Several Variables

Explores limits of functions in several real variables, including the two gendarmes theorem and the minimum and maximum theorem on compact sets.