Lectures related to Coordinate Transformations: Polar and Spherical Coordinates

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

Coordinate Systems: Applications and Transformations

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

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.

Geometric Examples: Triangles and Functions

Explores geometric examples of triangles and functions, demonstrating the variation of x and y within defined ranges.

Transforms of the Place

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

Integration and Transformations

Covers the calculation of definite integrals and different coordinate systems.

Continuity and Limits

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

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Advanced Analysis II: Integrals and Functions

Covers advanced topics in analysis, focusing on integrals, functions, and their properties.

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

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.

Center of Gravity and Variable Change

Discusses center of gravity, variable change, spherical coordinates, and bijectivity in mathematical analysis.

Analysis I Exam Solutions

Provides solutions to an Analysis I exam, covering various topics.

Change of Variables in Multiple Integrals

Explores changing variables in multiple integrals, with a focus on polar transformations and their applications in calculating areas.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Derivability and Composition

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

Definite Integrals: Properties and Interpretation

Covers the calculation of minimum points and the concept of definite integrals.