Single Variable Calculus (MIT 18.01) - Video lectures 2007
David Jerison

@article{,
title= {Single Variable Calculus (MIT 18.01) - Video lectures 2007},
journal= {},
author= {David Jerison},
year= {2007},
url= {http://ocw.mit.edu/18-01F06},
abstract= {Calculus is a foundational course at MIT; it plays an important role in the understanding of science, engineering, economics, and computer science, among other disciplines. This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

**Main course URL:** http://ocw.mit.edu/18-01F06

---

**Related materials**:
* [Single Variable Calculus (MIT 18.01) - Worked examples 2010](https://academictorrents.com/details/6ed053c563f13e01a3526bd8b359810a9ea6a9ca)

---

**Table of contents:**

* Unit 1: Differentiation
  * Lecture 01: Derivatives, Slope, Velocity, Rate of Change.
  * Lecture 02: Limits, continuity. Trigonometric Limits.
  * Lecture 03: Derivatives of Products, Quotients, Sine, Cosine.
  * Lecture 04: Chain rule. Higher derivatives.
  * Lecture 05: Implicit differentiation, inverses.
  * Lecture 06: Exponential and Log. Logarithmic Differentiation; Hyperbolic Functions.
  * Lecture 07: Continuation and Review


* Unit 2: Applications of Differentiation
  * Lecture 09: Linear and Quadratic Approximations
  * Lecture 10: Curve Sketching
  * Lecture 11: Max-min problems
  * Lecture 12: Related Rates
  * Lecture 13: Newton's Method and other Applications
  * Lecture 14: Mean Value Theorem; Inequalities
  * Lecture 15: Differentials, Antiderivatives
  * Lecture 16: Differential Equations, Separation of Variables


* Unit 3: The Definite Integral and its Applications
  * Lecture 18: Definite Integrals
  * Lecture 19: First Fundamental Theorem of Calculus
  * Lecture 20: Second Fundamental Theorem
  * Lecture 21: Applications to Logarithms and Geometry
  * Lecture 22: Volumes by Disks and Shells
  * Lecture 23: Work, Average Value, Probability
  * Lecture 24: Numerical Integration
  * Lecture 25: Exam 3 Review


* Unit 4: Techniques of Integration
  * Lecture 27: Trigonometric Integrals and Substitution
  * Lecture 28: Integration by Inverse Substitution; Completing the Square Use
  * Lecture 29: Partial Fractions
  * Lecture 30: Integration by Parts, Reduction Formulae
  * Lecture 31: Parametric Equations, Arclength, Surface Area
  * Lecture 32: Polar Coordinates; Area in Polar Coordinates
  * Lecture 33: Exam 4 Review


* Unit 5: Exploring the Infinite
  * Lecture 35: Indeterminate Forms - L'Hôspital's Rule
  * Lecture 36: Improper Integrals
  * Lecture 37: Infinite Series and Convergence Tests
  * Lecture 38: Taylor's Series
  * Lecture 39: Final Review

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