Lectures related to Implicit Functions

Explores the geometric interpretation of derivatives and properties of derivable functions.

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

Explores conditions for non-differentiability in multivariable calculus and the implications of the differentiability theorem.

Directional Derivatives and Tangent Planes

Explores directional derivatives, tangent planes, and function differentiability in multivariable calculus.

Tangent Planes and Implicit Functions

Explores tangent planes, implicit functions, and directional derivatives in relation to graphs of functions.

Derivatives and Continuity in Multivariable Functions

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

Functions: Multivariable Functions and Exact Differentials

Explores functions as a function of time and space, differentiation of multivariable functions, exact differentials, and gradients.

Tangent to Graph of a Function

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

Implicit Functions

Covers directional derivatives, implicit functions, and the concept of the maximum.

Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

Partial Derivatives: Definitions and Interpretations

Explores partial derivatives, their interpretations, and geometric applications in multivariable functions.

Hessian Matrix

Covers the concept of the Hessian matrix and its role in optimization problems.

Differentiability and Tangent Planes

Explores differentiability in functions and tangent planes to surfaces.

Partial Derivatives: Understanding and Applications

Explores the computation and significance of partial derivatives in determining rates of change.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Advanced Analysis II: Hessians and Directional Derivatives

Explores Hessians, directional derivatives, and function continuity in advanced analysis.

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Tangent Planes and Derivatives

Explores directional derivatives, tangent planes, and normal vectors in surfaces.

Analyse II: Directional Derivative

Covers the concept and calculation of directional derivatives in multivariable calculus.

Partial Derivatives

Covers the concept of partial derivatives and properties of saddle points.