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Math 234 2008 Lecture Notes

# Math 234 2008 Lecture Notes - CALCULUS III Three...

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CALCULUS III Three Dimensional Space Paul Dawkins

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Calculus III © 2007 Paul Dawkins i http://tutorial.math.lamar.edu/terms.aspx Table of Contents Preface ........................................................................................... Error! Bookmark not defined. Three Dimensional Space .............................................................. Error! Bookmark not defined. Introduction .......................................................................................... Error! Bookmark not defined. The 3-D Coordinate System .................................................................. Error! Bookmark not defined. Equations of Lines ................................................................................ Error! Bookmark not defined. Equations of Planes ............................................................................... Error! Bookmark not defined. Quadric Surfaces ................................................................................... Error! Bookmark not defined. Functions of Several Variables .............................................................. Error! Bookmark not defined. Vector Functions ................................................................................... Error! Bookmark not defined. Calculus with Vector Functions ............................................................. Error! Bookmark not defined. Tangent, Normal and Binormal Vectors ................................................. Error! Bookmark not defined. Arc Length with Vector Functions ......................................................... Error! Bookmark not defined. Curvature .............................................................................................. Error! Bookmark not defined. Velocity and Acceleration ..................................................................... Error! Bookmark not defined. Cylindrical Coordinates ......................................................................... Error! Bookmark not defined. Spherical Coordinates ............................................................................ Error! Bookmark not defined.
Calculus III © 2007 Paul Dawkins ii http://tutorial.math.lamar.edu/terms.aspx Preface Here are my online notes for my Calculus III course that I teach here at Lamar University. Despite the fact that these are my “class notes” they should be accessible to anyone wanting to learn Calculus III or needing a refresher in some of the topics from the class. These notes do assume that the reader has a good working knowledge of Calculus I topics including limits, derivatives and integration. It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric equations, vectors, and knowledge of three dimensional space. Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. 1. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn calculus I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. You will need to find one of your fellow class mates to see if there is something in these notes that wasn’t covered in class. 2. In general I try to work problems in class that are different from my notes. However, with Calculus III many of the problems are difficult to make up on the spur of the moment and so in this class my class work will follow these notes fairly close as far as worked problems go. With that being said I will, on occasion, work problems off the top of my head when I can to provide more examples than just those in my notes. Also, I often don’t have time in class to work all of the problems in the notes and so you will find that some sections contain problems that weren’t worked in class due to time restrictions.

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