Lectures related to Recursive Expression: Derivative of R

Differential Calculus: Definition and Derivability

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

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Tangent to Graph of a Function

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

Derivatives: Definition and Properties

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

Parametric Curves - Introduction

Introduces parametric curves and discusses tangent vectors and symmetry properties.

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Linear Approximation and Derivative Parametric

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

Derivative of a Product of Functions

Explores the derivative of a product of functions and discusses algebraic products and scalar products of functions.

Derivability and Continuity

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

Theorems of Continuity and Derivative Number

Explores the theorems of continuity and derivative numbers, including strict monotonicity and the Newton ratio.

General Physics: Mechanics SV

Covers the basics of General Physics, focusing on Mechanics SV and key mathematical concepts.

Exact Linearization: Earth Dynamics and Stabilization

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

Jacobian Matrix: Derivative of Composite Functions

Explains the Jacobian matrix and derivative of composite functions with examples.

Derivative Chain Rule

Covers the derivative of the composition of two functions and the chain rule theorem.

Differentiable Functions in R²

Explores differentiable functions in R², including vector fields and coordinate transformations.

Differential Calculus: Differentials, Linear Approximations, Parametric Functions

Covers differentials, linear approximations, and parametric function derivatives with examples and applications.

Partial Derivatives and Functions

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Partial Derivatives: Definitions and Applications

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Rolle's Theorem: Applications and Examples

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

Connections: motivation and definition

Explores the definition of connections for smooth vector fields on manifolds.