Lectures related to Differential and Tangent Plan

Tangent to Graph of a Function

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

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Differentiable Functions and Lagrange Multipliers

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

Functions and Coordinate Changes

Explores bijective functions, coordinate transformations, and graphical representations in two dimensions.

Supporting hyperplanes

Covers supporting hyperplanes for approximating functions' graphs in different dimensions using hyperplanes and linear approximations.

Chain Rules

Explores the extension of the chain rule to higher dimensions and compositions of functions.

Differentiability and Tangent Planes in Multivariable Functions

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

Derivatives and Continuity in Multivariable Functions

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

Tangent Plane to Implicit Function

Explores the tangent plane to implicit functions, emphasizing equations and graphical representations.

Functions with Values in R^m

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

Local Inversion Theorem

Explores the Local Inversion Theorem and extremum points in functions.

Derivatives and Tangent Planes

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

Algebraic Operations on Derivatives

Explores algebraic operations for derivatives, including addition, multiplication, and composition of functions on an interval.

Supporting Hyperplanes

Explores supporting hyperplanes for approximating function graphs in higher dimensions through normal vectors and linear approximations.

Differentiable Functions: Definitions and Properties

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

Linear Approximation and Derivative Parametric

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

Differentiable Functions: Definitions and Interpretation

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Directional Derivatives and Tangent Planes

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

Implicit Function Theorem

Covers the Implicit Function Theorem for functions of two variables and explores graphical representations and tangent lines.

Differential Equations: Introduction and Theoretical Results

Covers differential equations, including examples and unique solutions.