Lectures related to Limits of Functions in R^n

Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.

Introduces partial derivatives in functions of several variables and their properties.

Recurrence Method: Generalization and Differential Calculus

Explores the fundamental principle of the recurrence method and differential calculus of functions of several variables.

Implicit Function Theorem: Tangent Planes and Derivatives

Discusses the Implicit Function Theorem and its application to tangent planes and derivatives.

Functions with Multiple Variables

Covers functions with values in R^m, discussing limits, partial derivatives, and differentiability.

Differential Functions: Derivability and Gradient

Explores differentiability in functions and the role of gradients in directional derivatives.

Introduction to Topology

Covers fundamental concepts of space, topology, groups, and homology theory.

Continuity and Differentiability of Functions

Covers continuity, differentiability, and applications in calculus with an emphasis on fundamental concepts.

Graph Alignment: Wasserstein-based

Discusses challenges in comparing non-Euclidean data, proposing a Laplacian-based solution for graph alignment and exploring optimal transport for graph distance computation.

Optimization: Local Extrema

Explains how to find local extrema of functions using derivatives and critical points.

Comparing Functions MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores using Bernoulli de l'Hospital's theorem to compare functions' asymptotic behavior.

Linear Differential Equations: Homogeneous Case

Explores linear ordinary differential equations, focusing on homogeneous cases and unique solutions.

Partial Derivatives: Derivability Log in to Mediaspace to watch this video

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Partial Derivatives and Functions Log in to Mediaspace to watch this video

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Derivatives and Tangent Planes Log in to Mediaspace to watch this video

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.

Derivatives and Continuity in Multivariable Functions Log in to Mediaspace to watch this video

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

Limits and Derivatives in Multivariable Functions Log in to Mediaspace to watch this video

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.

Partial Derivatives: Definitions and Applications Log in to Mediaspace to watch this video

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Partial Derivatives and Functions Log in to Mediaspace to watch this video

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Partial Derivatives: Examples Log in to Mediaspace to watch this video

Explains the concept of partial derivatives through various examples involving functions of two variables.