Coordinate Transformations: Polar and Spherical Coordinates

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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.