Lectures related to Derivative and Function Variation

Explores the conditions for a function to be continuous and differentiable.

Covers the rules of derivation and how to calculate derivatives.

Covers the concepts of increasing and decreasing functions and the relationship between the derivative and monotonicity.

Explores Rolle's Theorem and its corollaries, including applications and proofs.

Explores the immediate consequences of f' = 0 and monotonicity on intervals.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

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

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

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