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source: MIT OpenCourseWare Last updated on 2014年7月1日

MIT Calculus Revisited: Single Variable Calculus

Resource Description: Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.

About the Instructor: Herbert Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the Mathematics As A Second Language website, providing arithmetic and algebra materials to elementary and middle school teachers. You can read more about Prof. Gross on his website.

Acknowledgements: Funding for this resource was provided by the Gabriella and Paul Rosenbaum Foundation.

View the complete course at: http://ocw.mit.edu/RES-18-006F10

License: Creative Commons BY-NC-SA

More information at http://ocw.mit.edu/terms

More courses at http://ocw.mit.edu

Preface | MIT Calculus Revisited: Single Variable Calculus 32:06

Unit I Sets, Functions, and Limits: Lec 1 Analytic Geometry 37:42

Unit I: Lec 2 Functions 39:43

Unit I: Lec 3 Inverse Functions 40:39Unit I: Lec 4 Derivatives and Limits 45:00

Unit I: Lec 5 A More Rigorous Approach to Limits 46:13

Unit I: Lec 6 Mathematical Induction 29:24

Unit II Differentiation: Lec 1 Derivatives of Some Simple Functions 28:17

Unit II: Lec 2 Approximations and Infinitesimals 34:36

Unit II: Lec 3 Composite Functions and the Chain Rule 39:16

Unit II: Lec 4 Differentiation of Inverse Functions 28:55

Unit II: Lec 5 Implicit Differentiation 39:58

Unit II: Lec 6 Continuity 22:49

Unit II: Lec 7 Curve Plotting 31:49

Unit II: Lec 8 Maxima and Minima 34:53

Unit II: Lec 9 Rolle's Theorem and its Consequences 30:28

Unit II: Lec 10 Inverse Differentiation 42:59

Unit II: Lec 11 The Definite Indefinite Integral 29:16

Unit III The Circular Function: Lec 1 Circular Functions 36:01

Unit III: Lec 2 Inverse Circular Functions 26:09

Unit IV The Definite Integral: Lec 1 The Definite Integral 36:37

Unit IV: Lec 2 Marriage of Differential and Integral Calculus 30:31

Unit IV: Lec 3 Three-Dimensional Area 42:06

Unit IV: Lec 4 One-Dimensional Area 36:45

Unit V Transcendental Functions: Lec 1 Logarithms without Exponents 34:46

Unit V: Lec 2 Inverse Logarithms 21:37

Unit V: Lec 3 What a Difference a Sign Makes 27:43

Unit V: Lec 4 Inverse Hyperbolic Functions 29:55

Unit VI More Integration Techniques: Lec 1 Some Basic Recipes 30:29

Unit VI: Lec 2 Partial Functions 32:29

Unit VI: Lec 3 Integration by Parts 27:01

Unit VI: Lec 4 Improper Integrals 29:39

Unit VII Infinite Series: Lec 1 Many Versus Infinite 26:31

Unit VII: Lec 2 Positive Series 34:50

Unit VII: Lec 3 Absolute Convergence 21:09

Unit VII: Lec 4 Polynomial Approximations 32:42

Unit VII: Lec 5 Uniform Convergence 28:57

Unit VII: Lec 6 Uniform Convergence of Power Series 27:04