Advanced Analysis II: Level Sets and Limits

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Introduction to Analysis: Understanding Real Numbers and Proofs

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Cinématique: Polar Coordinates Part 1

Covers the basics of polar coordinates and their application in kinematics.

Directional Derivatives

Explores directional derivatives, their calculation, examples, and cases of lack of continuity.

Coordinate Systems: Polar, Cylindrical, and Spherical

Explains polar, cylindrical, and spherical coordinates in physics, emphasizing their advantages in simplifying motion analysis.

Analysis IV: Convolution and Hilbert Structure

Explores convolution, uniform continuity, Hilbert structure, and Lebesgue measure in analysis.

Coordinate Systems: Transformations and Applications

Covers the transformation and application of coordinate systems, focusing on cylindrical coordinates and Jacobian matrix.

Taylor Polynomial: Order 2

Explores Taylor polynomials of order 2 and their applications in differential calculus and polar coordinates.

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.

Laplacian Operator in Cartesian and Polar Coordinates

Explores the Laplacian operator in Cartesian and polar coordinates, showcasing its application through examples.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.