Tuesday, October 1, 2019

Calculus: Analytic Geometry and Calculus, with Vectors

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To a considerable extent, this book is a book about mathematics as well as a mathematics textbook that teaches formulas and procedures. The historical and philosophical aspects of our subject are not neglected. The text, problems, and remarks frequently give students quite unusual opportunities and incentives to think and to become genuine authorities on developments of ideas, terminologies, notations, and theories. The book strives to produce thoughtful articulate and perhaps even somewhat sophisticated students who will find that their course in calculus gives them admirable preparation for intellectual pursuits. It is frequently said that calculus textbooks contain so little of the spirit and content of modern mathematics that they do not enable students to decide whether they have the interests and the aptitudes required for life-long careers in pure mathematics or in another science in which mathematics plays a major role. Hopefully, this book does.

The first third of the book contains all or nearly all of the information about analytic geometry, vectors, and calculus that students normally need in their introductory full-year college and university courses in physics. One distinguishing feature of the book is the early introduction and continued use of vectors in three-dimensional space. These vectors simplify, clarify, and modernize our mathematics and, at the same time, make our course more interesting to teachers and vastly more interesting and immediately useful to students. Modern meaningful definitions and terminologies of the calculus are used, but we retain and explain the standard notations so students can be prepared to live in the parts of the world outside their own calculus classrooms.

CHAPTER 1: Analytic geometry in two dimensions
CHAPTER 2: Vectors and geometry in three dimensions
CHAPTER 3: Functions, limits, derivatives
CHAPTER 4: Integrals
CHAPTER 5: Functions, graphs, and numbers
CHAPTER 6: Cones and conics
CHAPTER 7: Curves, lengths, and curvatures
CHAPTER 8: Trigonometric functions
CHAPTER 9: Exponential and logarithmic functions
CHAPTER 10: Polar, cylindrical, and spherical coordinates
CHAPTER 11: Partial derivatives
CHAPTER 12: Series
CHAPTER 13: Iterated and multiple integrals
APPENDIX 1: Proofs of basic theorems on limits

Author Details
"Ralph Palmer Agnew" Professor of Mathematics Department of Mathematics Cornell University

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