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Browse materialsMIT 18.01SC · Fall 2010 · OCW Scholar

Single Variable Calculus

Subjects: Calculus · Mathematics

Art: Anonymous painter,15th century, Westerner and Arab practicing geometry 15th century manuscript, 15th… · Public domain

Instructor
Prof. David Jerison
Term
Fall 2010
Level
Undergraduate
What's inside
364 videos · 12 problem sets · 14 exams · 1 solution · 841 other files · 112 web pages
Materials open
Videos here · files on MIT OCW
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About this course

Source: MIT OpenCourseWare 18.01SC Single Variable Calculus, Fall 2010, Prof. David Jerison — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own units, each a lecture sequence in MIT's listing order; no single course-wide order across units is claimed. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 22, 2026. The “How to start this course” route below is taken from MIT's own pages for this course, as fetched on September 25, 2026. How RedLectern is built.

Study route

How to start this course

Words in quotation marks are MIT’s own, from its pages for this course, linked under each part. The headings, labels and links are RedLectern’s.

Before you start

Can I start this?

MIT’s prerequisites, in MIT’s words. Tick each one you meet; nothing here is graded or saved.

From MIT: Syllabus ↗

What you'll learn

  • “Use both the limit definition and rules of differentiation to differentiate functions.”
  • “Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.”
  • “Apply differentiation to solve applied max/min problems.”
  • “Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.”
  • “Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions and integration by parts.”
  • “Determine the convergence/divergence of an infinite series and find the Taylor series expansion of a function near a point.”

The full list is on MIT’s syllabus ↗

From MIT: Syllabus ↗

Time

  • “MIT expects its students to spend about 150 hours on this course.”
  • “you can probably expect to spend an hour or more working through each individual session.”

From MIT: Syllabus ↗

What you need

  • “No textbook is required for this OCW Scholar course.”
    “For best results, we recommend viewing this course with Firefox, Safari or Chrome.”

Books

  • The free book on our Start page for this course is a companion book, not a text this course assigns.
  • “If you have access to a single variable calculus text it will probably serve as a useful companion to this course, although you might have to deal with slight differences in terminology and notation.”

From MIT: Syllabus ↗

If this isn't the right fit

Highlights of Calculus (RES.18-005, Spring 2010)

  • “Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important.”
  • “The intended audience is high school students, college students, or anyone who might need help understanding the subject.”

From MIT: RES.18-005 course home ↗

Your first sessions

  • “Because each session builds on knowledge from previous sessions, it is important you progress through the sessions in order.”
  • “As you begin each part of a unit, review the problem set at its end so that you may work toward solving those problems as you learn new material.”

From MIT: Syllabus ↗

  1. Session 1: Introduction to Derivatives

    This session on MIT’s site ↗

  2. Session 2: Examples of Derivatives

    This session on MIT’s site ↗

  3. Session 3: Derivative as Rate of Change

    This session on MIT’s site ↗

  4. Problem Set 1

    This session on MIT’s site ↗

Learn one topic

92 concept pages, one per MIT session: the clips, notes and practice for that topic. MIT solutions for 88 of 92 topics.

All 92 topics
  1. Introduction to Derivatives MIT solutions
  2. Examples of Derivatives MIT solutions
  3. Derivative as Rate of Change MIT solutions
  4. Limits and Continuity MIT solutions
  5. Discontinuity MIT solutions
  6. Calculating Derivatives MIT solutions
  7. Derivatives of Sine and Cosine MIT solutions
  8. Limits of Sine and Cosine MIT solutions
  9. Product Rule MIT solutions
  10. Quotient Rule MIT solutions
  11. Chain Rule MIT solutions
  12. Higher Derivatives MIT solutions
  13. Implicit Differentiation MIT solutions
  14. Examples of Implicit Differentiation MIT solutions
  15. Implicit Differentiation and Inverse Functions MIT solutions
  16. The Derivative of a^x MIT solutions
  17. The Exponential Function, its Derivative, and its Inverse MIT solutions
  18. Derivatives of other Exponential Functions MIT solutions
  19. An Interesting Limit Involving e MIT solutions
  20. Hyperbolic Trig Functions MIT solutions
  21. Linear Approximation MIT solutions
  22. Examples of Linear Approximation MIT solutions
  23. Introduction to Quadratic Approximation MIT solutions
  24. Using Quadratic Approximations MIT solutions
  25. Sketching Graphs I - Polynomials and Rational Functions MIT solutions
  26. Sketching Graphs II - General Strategies MIT solutions
  27. Optimization Problems MIT solutions
  28. Related Rates MIT solutions
  29. Ring on a String MIT solutions
  30. Newton's Method MIT solutions
  31. Introduction to the Mean Value Theorem MIT solutions
  32. Using the Mean Value Theorem MIT solutions
  33. Differentials MIT solutions
  34. Antiderivatives MIT solutions
  35. Integration by Substitution MIT solutions
  36. Introduction to Differential Equations MIT solutions
  37. Separation of Variables MIT solutions
  38. Definite Integrals MIT solutions
  39. Adding Areas of Rectangles MIT solutions
  40. Some Easy Integrals MIT solutions
  41. Riemann Sums MIT solutions
  42. Introduction of the Fundamental Theorem of Calculus MIT solutions
  43. The Fundamental Theorem of Calculus MIT solutions
  44. Applications of the Fundamental Theorem of Calculus MIT solutions
  45. Combining the Fundamental Theorem and the Mean Value Theorem MIT solutions
  46. The Second Fundamental Theorem of Calculus MIT solutions
  47. Proving the Fundamental Theorem of Calculus MIT solutions
  48. New Functions From Old MIT solutions
  49. The Second Fundamental Theorem and ln(x) MIT solutions
  50. Creating New Functions Using the Second Fundamental Theorem MIT solutions
  51. Geometric Interpretation of Definite Integrals MIT solutions
  52. How to Calculate Volumes MIT solutions
  53. Volume of a Sphere, Revolving About x-axis MIT solutions
  54. Volume of a Parabaloid, Revolving About y-axis MIT solutions
  55. Integrals and Averages MIT solutions
  56. Integrals and Weighted Averages MIT solutions
  57. Integrals and Probability MIT solutions
  58. Numerical Integration MIT solutions
  59. Numerical Integration, Continued MIT solutions
  60. Bell Curve, Conclusion MIT solutions
  61. Integral of sin^n(x) cos^m(x), Odd Exponents MIT solutions
  62. Integral of sin^n(x) cos^m(x), Even Exponents MIT solutions
  63. Preview of Trig Substitution and Polar Coordinates MIT solutions
  64. Integrals Involving secant, cosecant and cotangent MIT solutions
  65. Trig Substitution MIT solutions
  66. Completing the Square MIT solutions
  67. Integration by Partial Fractions MIT solutions
  68. Advanced Partial Fractions MIT solutions
  69. Integration by Parts MIT solutions
  70. Volume of a Wine Glass MIT solutions
  71. Computing the Length of a Curve MIT solutions
  72. Surface Area MIT solutions
  73. Parametric Curves MIT solutions
  74. Examples Using Parametrized Curves MIT solutions
  75. Polar Coordinates MIT solutions
  76. Polar Coordinates, Continued MIT solutions
  77. Polar Coordinates and Graphing MIT solutions
  78. L'Hospital's Rule MIT solutions
  79. Examples of L'Hospital's Rule MIT solutions
  80. L'Hospital's Rule and Rates of Growth
  81. Advanced Examples of L'Hospital's Rule MIT solutions
  82. Improper Integrals MIT solutions
  83. Integral Comparison MIT solutions
  84. Indefinite Integrals and Singularities
  85. Infinite Series MIT solutions
  86. Series Comparison MIT solutions
  87. Stacking Blocks
  88. Power Series MIT solutions
  89. Taylor's Series MIT solutions
  90. Taylor's Series, Continued
  91. Operations on Power Series MIT solutions
  92. Single Variable Calculus: Conclusion MIT solutions

Before you start

How this course was organized

What's here, and what isn't

  • This course has 360 videos, each embedded on its own MIT page, across 97 sections. They're shown in MIT's listing order within each section. A verified course-wide order is not claimed for this course.

Not included here

5 items from the source could not be safely included:

  • MIT's page format for this item wasn't recognized clearly enough to place it safely. (5 items)

Units

Each unit is offered as its own lecture sequence; there is no single course-wide order across units.

  1. 1. Differentiation81 activities · lecture sequence, in MIT's listing order
  2. 2. Applications of Differentiation70 activities · lecture sequence, in MIT's listing order
  3. 3. The Definite Integral and its Applications75 activities · lecture sequence, in MIT's listing order
  4. 4. Techniques of Integration67 activities · lecture sequence, in MIT's listing order
  5. 5. Exploring the Infinite67 activities · lecture sequence, in MIT's listing order

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Syllabus

1. Differentiation

47 files in this section

Part A: Definition and Basic Rules

Session 1: Introduction to Derivatives
Session 2: Examples of Derivatives
Session 3: Derivative as Rate of Change
Session 4: Limits and Continuity
Session 5: Discontinuity
Session 7: Derivatives of Sine and Cosine
Session 8: Limits of Sine and Cosine
Session 9: Product Rule
Session 10: Quotient Rule
Session 11: Chain Rule
Session 12: Higher Derivatives
Problem Set 1

Part B: Implicit Differentiation and Inverse Functions

Session 13: Implicit Differentiation
Session 14: Examples of Implicit Differentiation
Session 15: Implicit Differentiation and Inverse Functions
Session 16: The Derivative of aˣ
Session 17: The Exponential Function, its Derivative, and its Inverse
Session 19: An Interesting Limit Involving e
Session 20: Hyperbolic Trig Functions
Problem Set 2

Exam 1

Session 22: Materials for Exam 1

2. Applications of Differentiation

41 items in this section

Part A: Approximation and Curve Sketching

Session 23: Linear Approximation
Session 24: Examples of Linear Approximation
Session 25: Introduction to Quadratic Approximation
Session 26: Using Quadratic Approximations
Session 28: Sketching Graphs II - General Strategies
Problem Set 3

Part B: Optimization, Related Rates and Newton's Method

Session 30: Optimization Problems II
Session 31: Related Rates
Session 33: Newton's Method
Problem Set 4

Part C: Mean Value Theorem, Antiderivatives and Differential Equa

Session 34: Introduction to the Mean Value Theorem
Session 35: Using the Mean Value Theorem
Session 36: Differentials
Session 37: Antiderivatives
Session 38: Integration by Substitution
Session 39: Introduction to Differential Equations
Session 40: Separation of Variables
Problem Set 5

Exam 2

Session 42: Materials for Exam 2

3. The Definite Integral and its Applications

46 files in this section

Part A: Definition of the Definite Integral and First Fundamental

Session 43: Definite Integrals
Session 44: Adding Areas of Rectangles
Session 45: Some Easy Integrals
Session 46: Riemann Sums
Session 47: Introduction of the Fundamental Theorem of Calculus
Session 48: The Fundamental Theorem of Calculus
Session 49: Applications of the Fundamental Theorem of Calculus
Session 50: Combining the Fundamental Theorem and the Mean Value Theorem
Problem Set 6

Part B: Second Fundamental Theorem, Areas, Volumes

Session 54: The Second Fundamental Theorem and ln(x)
Session 55: Creating New Functions Using the Second Fundamental Theorem
Session 56: Geometric Interpretation of Definite Integrals
Session 57: How to Calculate Volumes
Session 58: Volume of a Sphere, Revolving About x-axis
Session 59: Volume of a Parabaloid, Revolving About y-axis
Problem Set 7

Part C: Average Value, Probability and Numerical Integration

Session 60: Integrals and Averages
Session 61: Integrals and Weighted Averages
Session 63: Numerical Integration
Session 64: Numerical Integration, Continued
Problem Set 8

Exam 3

Session 67: Materials for Exam 3

4. Techniques of Integration

38 items in this section

Part A: Trigonometric Powers, Trigonometric Substitution and Com

Session 68: Integral of sinⁿ(x) cos^m(x), Odd Exponents
Session 69: Integral of sinⁿ(x) cos^m(x), Even Exponents
Session 70: Preview of Trig Substitution and Polar Coordinates
Session 71: Integrals Involving secant, cosecant and cotangent
Session 72: Trig Substitution
Session 73: Completing the Square
Problem Set 9

Part B: Partial Fractions, Integration by Parts, Arc Length, and

Session 74: Integration by Partial Fractions
Session 75: Advanced Partial Fractions
Session 76: Integration by Parts
Session 78: Computing the Length of a Curve
Session 79: Surface Area
Problem Set 10

Part C: Parametric Equations and Polar Coordinates

Session 80: Parametric Curves
Session 81: Examples Using Parametrized Curves
Session 84: Polar Coordinates and Graphing
Problem Set 11

Exam 4

Session 86: Materials for Exam 4

5. Exploring the Infinite

22 files in this section

Part A: L'Hospital's Rule and Improper Integrals

Session 87: L'Hospital's Rule
Session 88: Examples of L'Hospital's Rule
Session 90: Advanced Examples of L'Hospital's Rule
Session 91: Improper Integrals
Session 92: Integral Comparison

Part B: Taylor Series

Session 94: Infinite Series
Session 95: Series Comparison
Session 97: Power Series
Session 98: Taylor's Series
Session 100: Operations on Power Series
Session 101: Conclusion

Final Exam

Other materials from this course

287 files
364 video transcripts
111 images

MIT OpenCourseWare, Prof. David Jerison, 18.01SC Single Variable Calculus, Fall 2010.

License: CC BY-NC-SA 4.0 · Edition: Fall 2010 · Open the original course on OCW ↗

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