Lectures related to Derivatives and Hyperbolic Functions

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Mathematical Methods for Materials Science: Integrals, Exact Differentials

Explores limits, derivation rules, integrals, and exact differentials for practical applications.

Derivability and Composition of Functions

Explores derivability and function composition with examples.

Differentiability and Partial Derivatives

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

Derivatives and Extrema: Theory and Applications

Explores derivatives, extrema, and their practical applications in function analysis.

Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Derivability and Chain Rule

Covers the demonstration of the chain rule and the theorem of Rolle.

Optimization Techniques: Local and Global Extrema

Discusses optimization techniques, focusing on local and global extrema in functions.

Derivatives and Continuity

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

Differentiability and Composition

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

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Derivatives and Continuity in Mathematics

Covers derivatives, continuity, Rolle's Theorem, function examples, and extrema.

Partial Derivatives: Taylor Formula

Explores partial derivatives, Taylor formula, examples, and extrema of functions.

Derivative Chain Rule

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

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.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Derivatives: Chain Rule and Composed Functions

Covers derivatives, chain rule, and composed functions with examples and applications.