Lectures related to Advanced Analysis II: Tangent Plan and Differentiability

Covers the analysis of functions, composition, and mathematical induction.

Explores finding the equation of the tangent line to a function's graph at a point.

Covers the properties and operations of convex functions.

Covers the graphical definition of functions, focusing on level sets and domains.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Covers the definitions and basic properties of real functions, including domain, image set, notation, and graph.

Covers the concept of affine transformations in functions, including shifting and compressing functions.

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.