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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)

Image: 18.01 Single Variable Calculus


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.