Lectures related to Derivability and Limits in Analysis I

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

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

Differentiability of Functions of Several Variables

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

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Linear Approximation and Derivative Parametric

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

Differentiable Functions and Lagrange Multipliers

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

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 Approximations: Logarithmic Functions

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Optimality Conditions: Unconstrained

Covers Fermat's theorem, necessary optimality conditions, convexity, and eigenvalue curvature in optimization.

Differentiability and Derivatives

Revisits the definition of differentiability and the existence of derivatives for functions in open intervals.

Derivability and Continuity

Explores derivability, continuity, and composite functions with illustrative examples.

Derivatives and Continuity in Multivariable Functions

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

Differentiable Functions: Definitions and Properties

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

Differentiability and Tangent Lines

Explores differentiability, tangent lines, and graph interpretation.

Computing Derivatives: Derivatives and Algebraic Operations

Covers the computation of derivatives and the properties of differentiable functions.

Derivatives: Definition and Examples

Covers the definition of derivatives and provides examples of differentiable functions.

Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Functions and Coordinate Changes

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

Differentiable Functions: Definitions and Interpretation

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