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