Calculus I

Calculus I (NYU Open Education). Instructor: Professor Matthew Leingang. In this course, we will study the foundations of calculus, the study of functions and their rates of change. We want you to learn how to model situations in order to solve problems. If you have already taken calculus before, we want you to gain an even deeper understanding of this fascinating subject.

The derivative measures the instantaneous rate of change of a function. The definite integral measures the total accumulation of a function over an interval. These two ideas form the basis for nearly all mathematical formulas in science. The rules by which we can compute the derivative (respectively, the integral) of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way.

Functions and their Representations

Lecture 01 - Functions and their Representations
Lecture 02 - A Catalogue of Essential Functions
Lecture 03 - Limit
Lecture 04 - Calculating Limits
Lecture 05 - Continuity
Lecture 06 - Limits Involving Infinity
Lecture 07 - The Derivative
Lecture 08 - Basic Differentiation Rules
Lecture 09 - The Product, Quotient, and Chain Rules
Lecture 10 - Implicit Differentiation
Lecture 11 - Linear Approximations and Differentials
Lecture 12 - Exponential Functions
Lecture 13 - Derivatives of Logarithmic and Exponential Functions
Lecture 14 - Exponential Growth and Decay
Lecture 15 - Inverse Trigonometric Functions
Lecture 16 - Indeterminate Forms and L'Hospital's Rule
Lecture 17 - Maximum and Minimum Values
Lecture 18 - The Mean Value Theorem
Lecture 19 - Derivatives and the Shapes of Curves
Lecture 20 - Curve Sketching
Lecture 21 - Optimization
Lecture 22 - Antiderivatives
Lecture 23 - Areas and Distances, the Definite Integral
Lecture 24 - Evaluating Definite Integrals
Lecture 25 - The Fundamental Theorem of Calculus
Lecture 26 - Integration by Substitution