Objective function, Differentiability, The second order

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Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Partial Differentiation

Explores simple examples of partial differentiation, demonstrating how to calculate partial derivatives and gradients in various scenarios.

Second Order Approximations: The Hessian Matrix

Explores second order approximations for twice differentiable functions using the Hessian matrix.

Differential Functions: Derivability and Gradient

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

Partial Derivatives: Matrices and Local Extrema

Covers hessian matrices, positive definite matrices, and local extrema of functions.

Normal and Tangential Acceleration MOOC: Newton's mechanics

Explores vector acceleration, decomposing it into tangential and normal components related to changes in scalar velocity and the trajectory's curvature.

Partial Derivatives and Derivability Theorems

Introduces partial derivatives, directional derivatives, and differentiability of functions with examples and the Schwartz theorem.

Functions with Values in R^m

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

Partial Derivatives: Introduction

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

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Partial Derivatives and Gradient

Explores partial derivatives, gradient, directional derivatives, and differentiability in determining slopes.

Limits of Functions in R^n

Explores limits of functions in R^n and the importance of understanding derivatives in multiple dimensions.

Derivatives and Continuity

Explores properties of functions with continuous partial derivatives in open subsets of Rn.

Methods of Demonstrations: Recurrence and Differential Calculus

Covers methods of demonstrations and differential calculus of functions of several variables.

Hyperbolic Geometry

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Functions with Multiple Variables

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

Second Fundamental Tensor Log in to Mediaspace to watch this video

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Curvature and Osculating Circle Log in to Mediaspace to watch this video

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

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

Covers partial derivatives, gradient, and second partial derivatives with their applications.

Partial Derivatives and Matrix Hessians Log in to Mediaspace to watch this video

Covers partial derivatives, Hessian matrices, and their importance for functions with multiple variables.

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