Advanced Analysis II: Tangent Plan and Differentiability

Related lectures (27)

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Covers the terminology related to the graph of a function and intervals.

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Explores definitions and examples of real functions of a real variable.

Explores real functions of two real variables, illustrating domains, images, and graphs.

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Explores differentiability in functions and geometric interpretation of tangent planes.

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

Covers differentiability, derivatives, continuity, and matrices in functions from R^n to R^m.

Covers the concept of the exponential family and discusses forward and backward maps, expensive computations, parameters, functions, and convexity.

Explains the relationship between two functions through restriction and prolongation, emphasizing the importance of defining a function by its graph.