Calculus

Science & Math

Michael Spivak

Mathematics

W.A.Benjamin

The Hitchhiker's Guide to Calculus begins with a rapid view of lines and slope. Spivak then takes up non-linear functions and trigonometric functions. He places the magnifying glass on curves in the next chapter and effortlessly leads the reader to the idea of derivative. In the next chapterhe tackles speed and velocity, followed by the derivative of sine. Maxima and minima are next. Rolle's theorem and the MVT form the core of Chapter 11, """"Watching Experts at Play."""" The Hitchhiker's Guide to Calculus closes with a chapter on the integral, the fundamental theorem, and applications of the integral.

The Hitchhiker's Guide to Calculus

American Mathematical Society

Spivak's 5 volume set is a classic and overall the best and most thorough treatment of differential geometry

A Comprehensive Introduction to Differential Geometry. Volume Four

Publish or Perish

A Comprehensive Introduction to Differential Geometry, Volume Five

Publish or Perish, Inc.

From the Preface: The purpose of this book, or possibly series of books, is indicated precisely by the title Physics for Mathematicians. It is only necessary for me to explain what I mean by a mathematician, and what I mean by physics. By a mathematician I mean some one who has been trained in modern mathematics and been inculcated with its general outlook. ... And by physics I mean -- well, physics, what physicists mean by physics, i.e., the actual study of physical objects ... (rather than the study of symplectic structures on cotangent bundles, for example). In addition to presenting the advanced physics, which mathematicians find so easy, I also want to explore the workings of elementary physics ... which I have always found so hard to fathom. As these remarks probably reveal, basically I have written this work in order to learn the subject myself, in a form that I find comprehensible. And readers familiar with some of my previous books probably realize that this has pretty much been the reason for those works also. ... Perhaps this travelogue of an innocent abroad in a very different field will also turn out to be a book that mathematicians will like.

Physics for Mathematicians, Mechanics I

A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 4, 3rd Edition

A Comprehensive Introduction to Differential Geometry, Vol. 5, 3rd Edition

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Books by Michael Spivak