Single Variable Calculus

by MIT Open Courseware in Mathematics & Statistics

Enroll
This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Lecture 1

Derivatives, slope, velocity, rate of change

Discussion Board
Lecture 2

Limits, continuity Trigonometric limits

Discussion Board
Lecture 3

Derivatives of products, quotients, sine, cosine

Discussion Board
Lecture 4

Chain rule Higher derivatives

Discussion Board
Lecture 5

Implicit differentiation, inverses

Discussion Board
Lecture 6

Exponential and log Logarithmic differentiation; hyperbolic functions

Discussion Board
Lecture 7

Hyperbolic functions (cont.) and exam 1 review

Discussion Board
Lecture 8

Linear and quadratic approximations

Discussion Board
Lecture 9

Approximations (cont.); curve sketching

Discussion Board
Lecture 10

Max-min problems

Discussion Board
Lecture 11

Related rates

Discussion Board
Lecture 12

Newton's method and other applications

Discussion Board
Lecture 13

Mean value theorem; Inequalities

Discussion Board
Lecture 14

Differentials, antiderivatives

Discussion Board
Lecture 15

Differential equations, separation of variables

Discussion Board
Lecture 16

Definite integrals

Discussion Board
Lecture 17

First fundamental theorem of calculus

Discussion Board
Lecture 18

Second fundamental theorem

Discussion Board
Lecture 19

Applications to logarithms and geometry

Discussion Board
Lecture 20

Single Variable Calculus

Discussion Board
Lecture 21

Work, average value, probability

Discussion Board
Lecture 22

Numerical integration

Discussion Board
Lecture 23

Exam 3 review

Discussion Board
Lecture 24

Trigonometric integrals and substitution

Discussion Board
Lecture 25

Integration by inverse substitution; completing the square

Discussion Board
Lecture 26

Partial fractions

Discussion Board
Lecture 27

Integration by parts, reduction formulae

Discussion Board
Lecture 28

Parametric equations, arclength, surface area

Discussion Board
Lecture 29

Polar coordinates; area in polar coordinates

Discussion Board
Lecture 30

Exam 4 review

Discussion Board
Lecture 31

Indeterminate forms - L'Hospital's rule

Discussion Board
Lecture 32

Improper integrals

Discussion Board
Lecture 33

Infinite series and convergence tests

Discussion Board
Lecture 34

Taylor's series

Discussion Board
Lecture 35

Final review

Discussion Board
Back
Related Courses
Related Content
License
Citation
  • Jerison, David. 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu. License: Creative Commons BY-NC-SA
Instructors
  • Prof. David Jerison
Additional Notes
  • schooX is not affiliated or endorsed by Massachusetts Institute of Technology. Please consider donating to MIT by clicking on the donation button below.
External Links