18.01 Single Variable Calculus (Fall 2006, MIT OCW) | Mathematics

18.01 Single Variable Calculus

18.01 Single Variable Calculus (Fall 2006, MIT OCW). This consists of 39 video lectures given by Professor David Jerison, on 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)

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 08 - No Class; Exam

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 17 - No Class; Exam

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 26 - No Class; Exam

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 34 - No Class; Exam

Lecture 35 - Indeterminate Forms

Lecture 36 - Improper Integrals

Lecture 37 - Infinite Series

Lecture 38 - Taylor's Series

Lecture 39 - Final Review

References

18.01 Single Variable Calculus
Instructors: Prof. David Jerison. Lecture Notes. Exams and Solutions. Subtitles/Transcript. Assignments (no Solutions). This covers differentiation and integration of functions of one variable, with applications.