18.01
Calculus
Differentiation and integration of functions of one variable, with applications. Informal treatment of limits and continuity. Differentiation: definition, rules, application to graphing, rates, approximations, and extremum problems. Indefinite integration; separable first-order differential equations. Definite integral; fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Polar coordinates. L'Hopital's rule. Improper integrals. Infinite series: geometric, p-harmonic, simple comparison tests, power series for some elementary functions.
Fall 2020 · Calculus I: Single Variable Calculus
Master the calculus of derivatives, integrals, coordinate systems, and infinite series. In this three-part series you will learn the mathematical notation, physical meaning, and geometric interpretation of a variety of calculus concepts. Along with the fundamental computational skills required to solve these problems, you will also gain insight into real-world applications of these mathematical ideas. - {{% resource_link "9201f1e9-a249-49d1-abf0-5f1c23af6038" "Part 1: Differentiation" %}} - {{% resource_link "b8fbb007-fed4-4c6c-adde-d1dc5d0ca6c2" "Part 2: Integration" %}} - {{% resource_link "e19bc5ac-1801-441f-9c39-71b8cd23b80b" "Part 3: Coordinate Systems & Infinite Series" %}} This series of courses is part of the {{% resource_link "0a5e1358-db40-41d0-b509-68a12a61b63c" "Open Learning Library" %}}, which is free to use. You have the option to sign up and enroll in the courses if you want to track your progress, or you can view and use all the materials without enrolling.
Fall 2006 · Single Variable Calculus
Topics
- Recitation: graphing
- Derivatives, slope, velocity, rate of change
- Derivatives of products, quotients, sine, cosine
- Implicit differentiation, inverses
- Linear and quadratic approximations
- Curve sketching
- Max-min problems
- Related rates
- Newton’s method and other applications
- Differentials, antiderivatives
- Differential equations, separation of variables
- Definite integrals
- First fundamental theorem of calculus
- Second fundamental theorem
- Applications to logarithms and geometry
- Volumes by disks, shells
- Work, average value, probability
- Numerical integration
- Trigonometric integrals and substitution
- Integration by inverse substitution; completing the square
- Partial fractions
- Integration by parts, reduction formulae
- Parametric equations, arclength, surface area
- Indeterminate forms - L’Hôspital’s rule
- Improper integrals
- Infinite series and convergence tests
- Taylor’s series
- Final review
Readings
- “Text” refers to the course textbook: Simmons, George F. Calculus with Analytic Geometry . 2nd ed. New York, NY: McGraw-Hill, October 1, 1996. ISBN: 9780070576421.
- SES #: 0 · TOPICS: Recitation: graphing · READINGS: Notes G, sections 1-4.
- SES #: 1 · TOPICS: Derivatives, slope, velocity, rate of change · READINGS: Text 2.1-2.4.
- SES #: 3 · TOPICS: Derivatives of products, quotients, sine, cosine · READINGS: Text 3.1, 3.2, and 3.4.
- SES #: 9 · TOPICS: Linear and quadratic approximations · READINGS: Notes A
- SES #: 10 · TOPICS: Curve sketching · READINGS: Text 4.1 and 4.2.
- SES #: 11 · TOPICS: Max-min problems · READINGS: Text 4.3 and 4.4.
- SES #: 12 · TOPICS: Related rates · READINGS: Text 4.5.
- SES #: 13 · TOPICS: Newton’s method and other applications · READINGS: Text 4.6. (Text 4.7 is optional)
- SES #: 15 · TOPICS: Differentials, antiderivatives · READINGS: Text 5.2 and 5.3.
- SES #: 16 · TOPICS: Differential equations, separation of variables · READINGS: Text 5.4 and 8.5.
- SES #: 19 · TOPICS: First fundamental theorem of calculus · READINGS: Text 6.6, 6.7 to top p. 215 (skip the proof pp. 207-8, which will be discussed in Ses #20.)
- SES #: 21 · TOPICS: Applications to logarithms and geometry · READINGS: Text 7.1, 7.2, and 7.3.
- SES #: 22 · TOPICS: Volumes by disks, shells · READINGS: Text 7.4.
- SES #: 24 · TOPICS: Numerical integration · READINGS: Text 10.9.
- SES #: 26 · TOPICS: Trigonometric integrals and substitution · READINGS: Text 10.2 and 10.3.
- SES #: 28 · TOPICS: Integration by inverse substitution; completing the square · READINGS: Text 10.4.
- SES #: 30 · TOPICS: Integration by parts, reduction formulae · READINGS: Text 10.7.
- SES #: 31 · TOPICS: Parametric equations, arclength, surface area · READINGS: Text 17.1, 7.5, and 7.6.
- SES #: 34 · TOPICS: Indeterminate forms - L’Hôspital’s rule · READINGS: Text 12.2 and 12.3. (examples 1-3, remark 1)
- SES #: 36 · TOPICS: Infinite series and convergence tests · READINGS: Text pp. 439-442 (top), pp. 451-3 (skip proof in example 3), and pp. 455-457 (top).
- SES #: 37 · TOPICS: Taylor’s series · READINGS: Text 14.4 through p. 498 (bottom); skip everything involving the remainder term R n (x), 14.3-p. 490 (top) and examples 1-5.
- Simmons, George F. Calculus with Analytic Geometry . 2nd ed. New York, NY: McGraw-Hill, October 1, 1996. ISBN: 9780070576421.
Fall 2005 · Single Variable Calculus
Topics
- Slope and Derivative
- Differentiation Formulas: Products and Quotients
- Chain Rule and Implicit Differentiation
- The Derivatives of Exponential and Logarithm Functions
- The Derivatives of Trigonometric Functions
- Approximations
- Curve Sketching
- Max-Min Problems
- Related Rates
- Inequalities, Zeros, and Newton’s Method
- Differentials and Indefinite Integrals
- Definite Integrals
- The Fundamental Theorem of Calculus
- Properties of Definite Integrals
- Differential Equations and Separation of Variables
- Numerical Integration and Review of Unit 3
- Areas between Curves, Volumes of Revolutions, and Slicing
- Volumes by Shells and Average Values
- Parametric Equations and Arc Length
- Surface Area and Polar Coordinate Graphs
- Area and Arc Length in Polar Coordinates
- Inverse Trigonometric Functions and Hyperbolic Functions
- Integration by Inverse Substitution
- Integration by Partial Fractions
- Integration by Parts
- Indeterminate Forms and L’Hospital’s Rule
- Improper Integrals
- Infinite Series
- Power Series
- Final Review
Readings
- Simmons, George F. Calculus with Analytic Geometry . 2nd ed. New York, NY: McGraw-Hill, October 1, 1995. ISBN: 0070576424.
- For each date, there is required reading from sections in the textbook and sections in the course reader. You are to read the material before the lecture.
- Readings in the textbook are listed by section numbers (e.g., § 2.1-2.4 means read sections 2.1 through 2.4.)
- ses #: 1 · TOPICS: Velocity and Rates of Change · readings: § 2.1-2.4.
- ses #: 2 · TOPICS: Slope and Derivative Limits and Continuity · readings: Notes C.
- ses #: 3 · TOPICS: Differentiation Formulas: Products and Quotients · readings: § 3.1-3.2.
- ses #: 4 · TOPICS: Chain Rule and Implicit Differentiation · readings: § 3.3, 3.5-3.6, and 8.1-8.2.
- ses #: 5 · TOPICS: The Derivatives of Exponential and Logarithm Functions · readings: § 8.3-8.4.
- ses #: 6 · TOPICS: The Derivatives of Trigonometric Functions · readings: § 9.1-9.2, and 9.4.
- ses #: 8 · TOPICS: Approximations Mean Value Theorem · readings: Notes A, MVT.
- ses #: 9 · TOPICS: Curve Sketching · readings: § 4.1-4.2.
- ses #: 10 · TOPICS: Max-Min Problems · readings: § 4.3-4.4.
- ses #: 11 · TOPICS: Related Rates · readings: § 4.5.
- ses #: 12 · TOPICS: Inequalities, Zeros, and Newton’s Method · readings: § 4.6 and 2.6, pp. 76-77.
- ses #: 13 · TOPICS: Differentials and Indefinite Integrals · readings: § 5.1-5.3.
- ses #: 14 · TOPICS: Definite Integrals · readings: § 6.1-6.4.
- ses #: 15 · TOPICS: The Fundamental Theorem of Calculus · readings: § 6.5-6.6.
- ses #: 16 · TOPICS: Properties of Definite Integrals · readings: Notes PI, Notes FT, and § 6.7.
- ses #: 17 · TOPICS: Differential Equations and Separation of Variables · readings: § 5.4 and 8.5.
- ses #: 18 · TOPICS: Numerical Integration and Review of Unit 3 · readings: § 10.9.
- ses #: 19 · TOPICS: Areas between Curves, Volumes of Revolutions, and Slicing · readings: § 7.1-7.3.
- ses #: 20 · TOPICS: Volumes by Shells and Average Values · readings: Notes AV, § 7.4.
- ses #: 21 · TOPICS: Parametric Equations and Arc Length · readings: § 17.1 and 7.5.
- ses #: 22 · TOPICS: Surface Area and Polar Coordinate Graphs · readings: § 7.6 and 16.1-16.3.
- ses #: 23 · TOPICS: Area and Arc Length in Polar Coordinates · readings: § 16.4-16.5.
- ses #: 24 · TOPICS: Inverse Trigonometric Functions and Hyperbolic Functions · readings: Notes G.7-G.9, § 9.5 and 9.7.
- ses #: 25 · TOPICS: Integration by Inverse Substitution · readings: § 10.4-10.5.
- ses #: 26 · TOPICS: Integration by Partial Fractions · readings: Notes F, § 10.6.
- ses #: 27 · TOPICS: Integration by Parts · readings: § 10.7-10.8.
- ses #: 28 · TOPICS: Indeterminate Forms and L’Hospital’s Rule · readings: § 12.1-12.3.
- ses #: 29 · TOPICS: Improper Integrals · readings: Notes INT, § 12.4.
- ses #: 30 · TOPICS: Infinite Series · readings: § 13.1-13.3.
- ses #: 31 · TOPICS: Power Series · readings: § 14.1 and 14.4.
Prerequisites & course information
Prereq: None U (Fall, Spring) 5-0-7 units. CALC I Credit cannot also be received for 18.01A , 18.01L , CC.1801 , ES.1801 , ES.181A
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2020
- MIT OpenCourseWare ↗Fall 2006
- MIT OCW calendar ↗
- MIT OCW readings ↗
- MIT OCW syllabus ↗
- MIT OpenCourseWare ↗Fall 2005
- MIT OCW syllabus ↗
- MIT OCW readings ↗
- MIT OCW calendar ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.