Lectures related to Chain Rules

Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

Functions with Multiple Variables

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

Taylor Series: Derivatives and Integrals

Explores Taylor series expansions for derivatives and integrals, including practical applications.

Derivatives and Continuity

Covers continuous differentiability, the Bernoulli-l'Hôpital rule, and finding extrema using derivatives.

Tangent to Graph of a Function

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

Functions and Coordinate Changes

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

Algebraic Operations on Derivatives

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

Differentiability and Composition

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.

The Increment Theorem: Understanding Derivatives

Explores the increment theorem and derivatives in calculus, focusing on polygonal valleys and curve traces.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Derivatives and Approximations: Logarithmic Functions

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

How to Succeed in Exams

Offers strategies for exam success through revisiting notes and taking mock tests.

Differential Calculus: Definition and Derivability

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

Directional Derivatives and Tangent Planes

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

Derivatives and Continuity in Multivariable Functions

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

Analysis Reminder: Open Sets and Denseness

Reviews open sets, denseness, real numbers, convergence, curves, continuity, and derivatives in analysis.

Differentiability Analysis

Explores differentiability, partial derivatives, Schwarz's theorem, and function continuity in mathematical analysis.

Differentiability: Theorem and Mean Value Theorem

Explores differentiability, gradients, and the Mean Value Theorem for functions.

Derivative Chain Rule

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

Differentiability: Theorem and Mean Value Theorem

Explores differentiability, gradients, and the Mean Value Theorem in open sets.