Corral's Vector Calculus - GitHub Pages
VECTORCALCULUSMichael Corraland Anton Petrunin-5x
Corral’s Vector CalculusMichael Corral and Anton Petrunin
About the author:Michael Corral is an Adjunct Faculty member of the Department of Mathematics atSchoolcraft College. He received a B.A. in Mathematics from the University of Californiaat Berkeley, and received an M.A. in Mathematics and an M.S. in Industrial & OperationsEngineering from the University of Michigan.This text was typeset in LATEX 2ε with the KOMA-Script bundle, using the GNU Emacs texteditor on a Fedora Linux system. The graphics were created using MetaPost, PGF, andGnuplot.Copyright 2016 Anton Petrunin.Permission is granted to copy, distribute and/or modify this document under the terms of theGNU Free Documentation License, Version 1.2 or any later version published by the FreeSoftware Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-CoverTexts. A copy of the license is included in the section entitled “GNU Free DocumentationLicense”.
PrefaceThis book covers calculus in two and three variables. It is suitable for a one-semester course,normally known as “Vector Calculus”, “Multivariable Calculus”, or simply “Calculus III”.The prerequisites are the standard courses in single-variable calculus (also known as Calculus I and II).The exercises are divided into three categories: A, B and C. The A exercises are mostlyof a routine computational nature, the B exercises are slightly more involved, and the Cexercises usually require some effort or insight to solve. A crude way of describing A, B andC would be “Easy”, “Moderate” and “Challenging”, respectively. However, many of the Bexercises are easy and not all the C exercises are difficult.Answers and hints to most odd-numbered and some even-numbered exercises are providedin Appendix A.There are a few exercises that require the student to write a computer program, for example, the Monte Carlo method for approximating multiple integrals, in Section 4.4. Thecode samples in the text are in the Java programming language, hopefully with enoughcomments so that the reader can figure out what is being done even without knowing Java.Those exercises do not mandate the use of Java, so students are free to implement the solutions using the language of their choice. While it would have been simple to use a scriptinglanguage like Python, and perhaps even easier with a functional programming language(such as Haskell or Scheme), Java was chosen due to its ubiquity, relatively clear syntax,and easy availability for multiple platforms.This book is released under the GNU Free Documentation License (GFDL), which allowsothers to not only copy and distribute the book but also to modify it. For more details, seethe included copy of the GFDL. So that there is no ambiguity on this matter, anyone canmake as many copies of this book as desired and distribute it as desired, without needing apermission.This book can be downloaded at https://github.com/anton-petrunin/calc3book; the older,original version by Michael Corral, can be also obtained from http://www.mecmath.net.iii
ContentsPrefaceiii1 Vectors in Euclidean Space11.11.21.31.41.51.61.7Introduction . . . . . . . .Vector Algebra . . . . . .Dot Product . . . . . . . .Cross Product . . . . . . .Lines and Planes . . . . .Elementary surfaces . . .Curvilinear Coordinates .2 Curves191521334351562.1 Vector-Valued Functions . . .
This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as “Vector Calculus”, “Multivariable Calculus”, or simply “Calculus III”. The prerequisites are the standard courses in single-variable
Vector Calculus. By Michaei Corral, www. mecmath.net, 2008. 1 1.00. vi-f2l3 pp., soft-cover (free electronic download available). Vector Calculus is a traditional treatment of the topics covered in a third-semester calculus course, often called "Multivari-ate Calculus" or just "Cale III." While the treatment may be traditional, the
For Corrals organized prior to 1973 Los Angeles Corral, Los Angeles, California L. R. Spitzzeri, Sheriff For Corrals organized 1973 and later San Dimas Corral, San Dimas, California Dave Harbin, Sheriff Overseas Corrals Linz Corral, Linz, Austria Hans Jorg Ratzenboeck, Sheriff Corral Holds Westerner Day
Why Vector processors Basic Vector Architecture Vector Execution time Vector load - store units and Vector memory systems Vector length - VLR Vector stride Enhancing Vector performance Measuring Vector performance SSE Instruction set and Applications A case study - Intel Larrabee vector processor
Vector Calculus 16.1 Vector Fields This chapter is concerned with applying calculus in the context of vector fields. A two-dimensional vector field is a function f that maps each point (x,y) in R2 to a two-dimensional vector hu,vi, and similarly a three-dimensional vector field maps (x,y,z) to hu,v,wi.
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11/14/19 Multivariate Calculus:Vector CalculusHavens 0.Prelude This is an ongoing notes project to capture the essence of the subject of vector calculus by providing a variety of examples and visualizations, but also to present the main ideas of vector calculus in conceptual a framework that is adequate for the needs of mathematics, physics, and
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