Lectures related to Differentiability and Limits

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

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

Covers limits and continuity in multivariable functions, including examples and techniques for showing the existence of limits.

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

Explores Taylor series expansion, derivatives, uniqueness, and applications in function approximation.

Covers the concept of limits and continuity in real analysis.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

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

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

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

Covers the conditions for finding absolute extrema in multivariable functions.

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

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Explores generalized finite increments, derivatives, reciprocals, and Bernoulli-L'Hospital rule.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

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

Explores reciprocal trigonometric functions, hyperbolic functions, and area theorems.

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Covers the rules of derivatives, O-notation, and extrema in the context of theorem 6.5 and examples.