Lectures related to Tangent Planes and Implicit Functions

Analyse II: Directional Derivative

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

Tangent to Graph of a Function

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

Derivatives and Continuity in Multivariable Functions

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

Mathematical Analysis: Functions and Composition

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

Differentiable Functions and Lagrange Multipliers

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

Tangent Planes and Derivatives

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

Partial Derivatives: Understanding Tangents

Explores partial derivatives and their role in determining tangents to graphs.

Differentiability and Tangent Planes

Explores differentiability in functions and tangent planes to surfaces.

Geometric Interpretation of Derivatives

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

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Functions with Values in R^m

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

Directional Derivatives and Tangent Planes

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

Exact Differential Equations

Revisits exact differential equations, discussing implicit function theorem and factors integrants.

Linear Transformations: Matrices and Kernels

Covers linear transformations, matrices, kernels, and properties of invertible matrices.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Functions: Definitions and Notations

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

Derivative: Application Examples

Explores examples of using derivatives to find tangent lines and points on graphs.

Graph Sketching: Motion Analysis

Explores motion graph analysis, focusing on function study and derivative interpretation.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Implicit Functions

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