Single Variable Calculus

Introduces the concepts of differentials and antiderivatives, fundamental operations in integral calculus, and explores their applications in solving mathematical problems.

Delves into the Mean Value Theorem, a cornerstone of differential calculus, and its implications for understanding function behavior and proving inequalities.

Explores Newton's method for approximating roots of real-valued functions and discusses various applications of differential calculus in problem-solving.

Focuses on related rates problems, demonstrating how to apply implicit differentiation to find the rate of change of one quantity in terms of the rate of change of another.

Covers the application of derivatives to solve optimization problems, specifically focusing on finding maximum and minimum values of functions.

Continues the discussion on approximations and introduces techniques for sketching curves using calculus, including identifying critical points and concavity.

Introduces linear and quadratic approximations, demonstrating how to use derivatives to estimate function values near a given point.

Covers exponential and logarithmic functions, logarithmic differentiation, and introduces hyperbolic functions, essential tools in single variable calculus.

Explains implicit differentiation and the concept of inverse functions, demonstrating techniques for finding derivatives of implicitly defined relationships.

Covers the chain rule for differentiation and the computation of higher-order derivatives, fundamental concepts in calculus.

Continues the discussion on hyperbolic functions and provides a review session for the first exam in single variable calculus.

Professor David Jerison introduces the fundamental rules of differentiation, covering the product rule, quotient rule, and derivatives of trigonometric functions in single variable calculus.

Professor David Jerison presents foundational concepts in single variable calculus, exploring limits, continuity, and the evaluation of limits involving trigonometric functions.

An introductory lecture from MIT's Single Variable Calculus course, establishing the fundamental concepts of derivatives, slope, velocity, and instantaneous rates of change.