Single Variable Calculus (MIT 18.01): Limits, Derivatives, Integrals and Series
A university-level calculus course of 35 lecture recordings covering limits, differentiation, applications of derivatives, integration techniques, and applications of integrals. It finishes with L'Hôpital's rule, improper integrals, infinite series and Taylor series. Suits motivated beginners with solid algebra and trigonometry, and students who want a rigorous, lecture-style first course in calculus.
Lessons by MIT OpenCourseWare on YouTubeCurated by YodaHut. These lessons are hosted on YouTube and produced by their original creators, who are not affiliated with YodaHut. You still earn YodaCoins, keep your streak and track progress here.
What You'll Learn
- Compute limits and test continuity, including trigonometric limits
- Differentiate polynomials, products, quotients, trig, exponential, logarithmic and inverse functions using the chain rule and implicit differentiation
- Solve optimization, related-rates and curve-sketching problems, and approximate with linearization and Newton's method
- Evaluate definite integrals using both fundamental theorems of calculus
- Apply integration techniques: substitution, trigonometric integrals, partial fractions and integration by parts
- Use integrals for volumes, work, average value, arclength and polar-coordinate area, and test infinite series and Taylor series for convergence
Prerequisites
- Algebra and functions, including graphing
- Trigonometry basics (sine, cosine, identities)
- Some comfort with a lecture-style, proof-flavoured presentation
Course Curriculum
- 1Derivatives, Slope, Velocity and Rate of Change51:33
- 2Limits, Continuity and Trigonometric Limits52:47
- 3Derivatives of Products, Quotients, Sine and Cosine49:55
- 4Chain Rule and Higher Derivatives46:03
- 5Implicit Differentiation and Inverse Functions49:01
- 6Exponentials, Logarithms and Logarithmic Differentiation47:57
- 7Hyperbolic Functions and Exam 1 Review50:53
- 8Linear and Quadratic Approximations46:48
- 9Approximations and Curve Sketching51:44
- 10Max-Min Problems49:42
- 11Related Rates49:56
- 12Newton's Method and Other Applications53:23
- 13Mean Value Theorem and Inequalities49:42
- 14Differentials and Antiderivatives48:53
- 15Differential Equations and Separation of Variables45:25
- 16Definite Integrals47:14
- 17First Fundamental Theorem of Calculus48:15
- 18Second Fundamental Theorem of Calculus49:30
- 19Applications to Logarithms and Geometry50:17
- 20Volumes by Disks and Shells49:58
- 21Work, Average Value and Probability48:36
- 22Numerical Integration50:30
- 23Exam 3 Review49:19
- 24Trigonometric Integrals and Substitution46:45
- 25Inverse Substitution and Completing the Square48:29
- 26Partial Fractions48:38
- 27Integration by Parts and Reduction Formulae51:24
- 28Parametric Equations, Arclength and Surface Area45:25
- 29Polar Coordinates and Area in Polar Coordinates49:23
- 30Exam 4 Review49:07
- 31Indeterminate Forms and L'Hôpital's Rule48:43
- 32Improper Integrals49:27
- 33Infinite Series and Convergence Tests50:12
- 34Taylor Series47:31
- 35Final Review39:14
About the Instructor
MIT OpenCourseWare
YouTube creator
The lessons in this course were produced by MIT OpenCourseWare and are published on YouTube. YodaHut selected and sequenced them into this course; we did not make them, and MIT OpenCourseWare is not affiliated with YodaHut.
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- 35 lessons
- 28h 32m of video
- Earns YodaCoins & streaks
- Timestamped notes
- Free — hosted on YouTube
No certificate is issued for Library courses.