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MIT OpenCourseWare

Single Variable Calculus

This is an introductory calculus course covering differentiation and integration of functions of one variable, with applications: differentiation, application of differentiation, definite integral and its applications, techniques of integration, and a brief discussion of infinite series. (from ocw.mit.edu )

Instructor

Professor David Jerison,

Mathematics

2009

Lecture 01 - Derivatives, Slope, Velocity, Rate of Change

Lecture 02 - Limits, Continuity

Lecture 03 - Derivatives

Lecture 04 - Chain Rule

Lecture 05 - Implicit Differentiation

Lecture 06 - Exponential and Log

Lecture 07 - Hyperbolic Functions

Lecture 09 - Linear and Quadratic Approximations

Lecture 10 - Curve Sketching

Lecture 11 - Max-min Problems

Lecture 12 - Related Rates

Lecture 13 - Newton's Method and Other Applications

Lecture 14 - Mean Value Theorem

Lecture 15 - Differentials, Antiderivatives

Lecture 16 - Differential Equations

Lecture 18 - Definite Integrals

Lecture 19 - First Fundamental Theorem

Lecture 20 - Second Fundamental Theorem

Lecture 21 - Applications to Logarithms and Geometry

Lecture 22 - Volumes by Disks and Shells

Lecture 23 - Work, Average Value, Probability

Lecture 24 - Numerical Integration

Lecture 25 - Exam 3 Review

Lecture 27 - Trigonometric Integrals and Substitution

Lecture 28 - Integration by Inverse Substitution

Lecture 29 - Partial Fractions

Lecture 30 - Integration by Parts

Lecture 31 - Parametric Equations

Lecture 32 - Polar Coordinates

Lecture 33 - Exam 4 Review

Lecture 35 - Indeterminate Forms

Lecture 36 - Improper Integrals

Lecture 37 - Infinite Series

Lecture 38 - Taylor's Series

Lecture 39 - Final Review