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Author Soon, Frederick H. author Student's Guide to Calculus by J. Marsden and A. Weinstein [electronic resource] : Volume III / by Frederick H. Soon New York, NY : Springer New York, 1986 http://dx.doi.org/10.1007/978-1-4612-4970-2 XIV, 294 p. online resource

SUMMARY

This Student Guide is exceptional, maybe even unique, among such guides in that its author, Fred Soon, was actually a student user of the textbook during one of the years we were writing and debugging the book. (He was one of the best students that year, by the way. ) Because of his background, Fred has taken, in the Guide, the point of view of an experienced student tutor helping you to learn calculus. \ĩle we do not always think Fred's jokes are as funny as he does, we appreciate his enthusiasm and his desire to enter into communication with his readers; since we nearly always agree with the matheยญ matical judgements he has made in explaining the material, we believe that this Guide can serve you as a valuable supplement to our text. To get maximum benefit from this Guide, you should begin by spending a few moments to acquaint yourself with its structure. Once you get started in the course, take advantage of the many opportunities which the text and Student Guide together provide for learning calculus in the only way that any matheยญ matical subject can truly be mastered - through attempting to solve problems on your own. As you read the text, try doing each example and exercise yourยญ self before reading the solution; do the same with the quiz problems provided by Fred

CONTENT

13 -- Vectors -- 13.1 Vectors in the Plane -- 13.2 Vectors in Space -- 13.3 Lines and Distance -- 13.4 The Dot Product -- 13.5 The Cross Product -- 13.6 Matrices and Determinants -- 13.R Review Exercises for Chapter 13 -- 14 -- Curves and Surfaces -- 14.1 The Conic Sections -- 14.2 Translation and Rotstion of Axes -- 14.3 Functions, Graphs, and Level Surfaces -- 14.4 Quadric Surfaces -- 14.5 Cylindrical and Spherical Coordinates -- 14.6 Curves in Space -- 14.7 The Geometry and Physics of Space Curves -- 14.S Supplement to Chapter 14: Rotations and the Sunshine Formula -- 14.R Review Exercises for Chapter 14 -- 15 -- Partial Differentiation -- 15.1 Introduction to Partial Derivatives -- 15.2 Linear Approximation and Tangent Planes -- 15.3 The Chain Rule -- 15.4 Matrix Multiplication and the Chain Rule -- 15.R Review Exercises for Chapter 15 -- Comprehensive Test For Chapters 13 โ{128}{147} 15 -- 16 -- Gradients, Maxima, and Minima -- 16.1 Gradients and Directional Derivatives -- 16.2 Gradients, Level Surfaces, and Implicit Differentiation -- 16.3 Maxima and Minima -- 16.4 Constrained Extrema and Lagrange Multipliers -- l6.R Review Exercises for Chapter 16 -- 17 -- Multiple Integration -- 17.1 The Double Integral and Iterated Integral -- 17.2 The Double Integral Over General Regions -- 17.3 Applications of the Double Integral -- 17.4 Triple Integrals -- 17.5 Integrals in Polar, Cylindrical, and Spherical Coordinates -- 17.6 Applications of Triple Integrals -- l7.R Review Exercises for Chapter 17 -- 18 -- Vector Analysis -- 18.1 Line Integrals 839 -- 18.2 Path Independence -- 18.3 Exact Differentials -- 18.4 Green's Theorem -- 18.5 Circulation and Stokes' Theorem -- 18.6 Flux and the Divergence Theorem -- l8.R Review Exercises for Chapter 18 -- Comprehensive Test for Chapters 13 โ{128}{147} 18

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