Single Variable Calculus (MIT 18.01) - Worked examples 2010
Christine Breiner and David Jordan and Joel Lewis

@article{,
title= {Single Variable Calculus (MIT 18.01) - Worked examples 2010},
journal= {},
author= {Christine Breiner and David Jordan and Joel Lewis},
year= {},
url= {http://ocw.mit.edu/18-01SCF10},
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/18-01SCF10

---

**Related materials:** 
* [Single Variable Calculus (MIT 18.01) - Video lectures 2007](https://academictorrents.com/details/c38ec459fd87f1672e917634addba301ad26b248)

---

**Table of contents:**

* Unit 1: Differentiation
  * Lecture 01: Derivatives, Slope, Velocity, Rate of Change.
    * Recitation 00: Introduction to Recitations
    * Recitation 01: Definition of Derivative
    * Recitation 02: Graphing a Derivative Function
  * Lecture 02: Limits, continuity. Trigonometric Limits.
    * Recitation 03: Smoothing a Piecewise Function
  * Lecture 03: Derivatives of Products, Quotients, Sine, Cosine.
    * Recitation 04: Constant Multiple Rule
    * Recitation 05: Tangent to Graph of Polynomial
    * Recitation 06: Derivatives of Sine and Cosine
  * Lecture 04: Chain rule. Higher derivatives.
    * Recitation 07: Product Rule
    * Recitation 08: Quotient Rule
    * Recitation 09: Chain Rule
  * Lecture 05: Implicit differentiation, inverses.
    * Recitation 10: Implicit Differentiation
    * Recitation 11: Graphing the Arctan Function
    * Recitation 12: Derivative of the Arccos Function
  * Lecture 06: Exponential and Log. Logarithmic Differentiation; Hyperbolic Functions.
  * Lecture 07: Continuation and Review
    * Recitation 13: Log and Exponent Derivatives
    * Recitation 14: Rules of Logs
    * Recitation 15: Hyperbolic Trig Functions


* Unit 2: Applications of Differentiation
  * Lecture 09: Linear and Quadratic Approximations
  * Lecture 10: Curve Sketching
    * Recitation 16: Implicit Differentiation and Linear Approximation
    * Recitation 17: Quadratic Approximation of an Exponential Function
    * Recitation 18: Quadratic Approximation of a Product
  * Lecture 11: Max-min problems
    * Recitation 19: Sketching a Curve
  * Lecture 12: Related Rates
    * Recitation 20: Closest Point to the Origin
    * Recitation 21: Minimum Triangle Area
    * Recitation 22: Maximum Surface Area
  * Lecture 13: Newton's Method and other Applications
    * Recitation 23: Inflating a Balloon
    * Recitation 24: Sliding Ladder
  * Lecture 14: Mean Value Theorem; Inequalities
    * Recitation 25: Using Newton's Method
    * Recitation 26: Comparing Functions Using the MVT
    * Recitation 27: Increasing or Decreasing
    * Recitation 28: Derivative With a Discontinuity
  * Lecture 15: Differentials, Antiderivatives
    * Recitation 29: Computing Differentials
    * Recitation 30: Linear Approximation with Differentials
    * Recitation 31: Computing Antiderivatives
    * Recitation 32: Antidifferentiation by Substitution
  * Lecture 16: Differential Equations, Separation of Variables
    * Recitation 33: xy'=(x²+x)(y²+1)
    * Recitation 34: y"=6x


* Unit 3: The Definite Integral and its Applications
  * Lecture 18: Definite Integrals
    * Recitation 35: Summation Notation Practice
    * Recitation 36: Riemann Sum
    * Recitation 37: Computing the Volume of a Paraboloid
    * Recitation 37a: Diffusion of a Chemical
  * Lecture 19: First Fundamental Theorem of Calculus
    * Recitation 38: Definite Integrals of tan(x)
    * Recitation 39: Definite Integral by Substitution
  * Lecture 20: Second Fundamental Theorem
    * Recitation 40: Applying the Second Fundamental Theorem
    * Recitation 40a: Second Fundamental Theorem and Chain Rule 
    * Recitation 41: Second Fundamental Theorem and Quadratic Approximation
  * Lecture 21: Applications to Logarithms and Geometry
    * Recitation 42: Area Between the Graphs of Sine and Cosine
    * Recitation 43: Area Between y=x³ and y=3x-2
  * Lecture 22: Volumes by Disks and Shells
    * Recitation 44: Volume of a Paraboloid via Disks
    * Recitation 45: Volume of Revolution via Shells
  * Lecture 23: Work, Average Value, Probability
    * Recitation 46: Average Velocity
  * Lecture 24: Numerical Integration
    * Recitation 47: Average x-Coordinate in a Region
    * Recitation 48: Explanation of Simpson's Rule
    * Recitation 49: Using the Trapezoid and Simpson's Rules
  * Lecture 25: Exam 3 Review


* Unit 4: Techniques of Integration
  * Lecture 27: Trigonometric Integrals and Substitution
    * Recitation 50: Trig Integral Practice
    * Recitation 51: Trig Integrals and a Volume of Revolution
  * Lecture 28: Integration by Inverse Substitution; Completing the Square Use
    * Recitation 52: Integral of tan⁴θ
    * Recitation 53: Hyperbolic Trig Substitution
    * Recitation 54: Integration by Completing the Square
  * Lecture 29: Partial Fractions
  * Lecture 30: Integration by Parts, Reduction Formulae
    * Recitation 55: Partial Fractions Decomposition
    * Recitation 56: Finding u and v' When Integrating by Parts
    * Recitation 57: Integrating sinⁿ(x) Using Reduction
  * Lecture 31: Parametric Equations, Arclength, Surface Area
    * Recitation 58: Arc Length of y=x^(3/2)
    * Recitation 59: Surface Area of a Torus
    * Recitation 60: Parametric Arc Length
  * Lecture 32: Polar Coordinates; Area in Polar Coordinates
    * Recitation 61: Converting From Polar to Rectangular Coordinates
  * Lecture 33: Exam 4 Review
    * Recitation 62: Graph of r=1+cos(θ/2)
    * Recitation 63: Integration Practice I
    * Recitation 64: Integration Practice II
    * Recitation 65: Integration Practice III
    * Recitation 66: Integration Practice IV


* Unit 5: Exploring the Infinite
  * Lecture 35: Indeterminate Forms - L'Hôspital's Rule
    * Recitation 67: L'Hospital Practice
  * Lecture 36: Improper Integrals
    * Recitation 68: Failure of L'Hospital's Rule
    * Recitation 69: Indeterminate Forms
    * Recitation 69a: A Solid With Finite Volume and Infinite Cross Section
    * Recitation 70: Improper Integral
    * Recitation 71: Integral of xⁿe⁽⁻ˣ⁾
  * Lecture 37: Infinite Series and Convergence Tests
    * Recitation 72: Limit of a Series
    * Recitation 73: Comparison Tests
    * Recitation 74: Ratio Test for Convergence
    * Recitation 75: Integral Test for Convergence
    * Recitation 76: Using the Integral Test for Estimation
  * Lecture 38: Taylor's Series
    * Recitation 77: Radius of Convergence
    * Recitation 78: Power Series Practice
    * Recitation 79: Finding Taylor's Series
    * Recitation 80: Taylor's Series of a Polynomial
  * Lecture 39: Final Review
    * Recitation 81: Taylor's Series for sec(x)
    * Recitation 82: Integration of Taylor's Series
    * Recitation 83: Series Calculation Using a Riemann Sum

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