# InfoCoBuild

## 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