Single Variable Calculus by Herbert Gross

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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 40:39
Unit 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