![]() The Digital and eTextbook ISBNs for Vector Calculus are 9780321830869. Openlibraryedition OL656648M Openlibrarywork OL2622349W Page-progression lr Pagenumberconfidence 94.82 Pages 554 Pdfmoduleversion 0.0. Vector Calculus 4th Edition is written by Susan J. ![]() Professor Colley is a member of several professional and honorary societies, including the American Mathematical Society, the Mathematical Association of America, Phi Beta Kappa, and Sigma Xi. Publication date 1998 Topics Vector analysis Publisher Upper Saddle River, N.J. She has lectured internationally on her research and has taught a wide range of subjects in undergraduate mathematics. Professor Colley has published papers on algebraic geometry and commutative algebra, as well as articles on other mathematical subjects. Her research focuses on enumerative problems in algebraic geometry, particularly concerning multiple-point singularities and higher-order contact of plane curves. degrees in mathematics from the Massachusetts Institute of Technology prior to joining the faculty at Oberlin in 1983. Susan Colley is the Andrew and Pauline Delaney Professor of Mathematics at Oberlin College and currently Chair of the Department, having also previously served as Chair. Colley includes not only basic and advanced exercises, but also mid-level exercises that form a necessary bridge between the two. This text is distinguished from others by its readable narrative, numerous figures, thoughtfully selected examples, and carefully crafted exercise sets. It is ideal for students with a solid background in single-variable calculus who are capable of thinking in more general terms about the topics in the course. Sign up or login using form at top of the page to download this file.Vector Calculus, Fourth Edition, uses the language and notation of vectors and matrices to teach multivariable calculus.To the Student: Some Preliminary Notation Vectors Vectors in Two and Three Dimensions More About Vectors The Dot Product The Cross Product Equations for Planes Distance Problems Some n-dimensional Geometry New Coordinate Systems True/False Exercises for Chapter 1 Miscellaneous Exercises for Chapter 1 Differentiation in Several Variables Functions of Several Variables Graphing Surfaces Limits The Derivative Properties Higher-order Partial Derivatives The Chain Rule Directional Derivatives and the Gradient Newton’s Method (optional) True/False Exercises for Chapter 2 Miscellaneous Exercises for Chapter 2 Vector-Valued Functions Parametrized Curves and Kepler’s Laws Arclength and Differential Geometry Vector Fields: An Introduction Gradient, Divergence, Curl, and the Del Operator True/False Exercises for Chapter 3 Miscellaneous Exercises for Chapter 3 Maxima and Minima in Several Variables Differentials and Taylor’s Theorem Extrema of Functions Lagrange Multipliers Some Applications of Extrema True/False Exercises for Chapter 4 Miscellaneous Exercises for Chapter 4 Multiple Integration Introduction: Areas and Volumes Double Integrals Changing the Order of Integration Triple Integrals Change of Variables Applications of Integration Numerical Approximations of Multiple Integrals (optional) True/False Exercises for Chapter 5 Miscellaneous Exercises for Chapter 5 Line Integrals Scalar and Vector Line Integrals Green’s Theorem Conservative Vector Fields True/False Exercises for Chapter 6 Miscellaneous Exercises for Chapter 6 Surface Integrals and Vector Analysis Parametrized Surfaces Surface Integrals Stokes’s and Gauss’s Theorems Further Vector Analysis Maxwell’s Equations True/False Exercises for Chapter 7 Miscellaneous Exercises for Chapter 7 Vector Analysis in Higher Dimensions An Introduction to Differential Forms Manifolds and Integrals of k-forms The Generalized Stokes’s Theorem True/False Exercises for Chapter 8 Miscellaneous Exercises for Chapter 8 Suggestions for Further Reading Answers to Selected Exercises Index Although the mathematical background assumed is not exceptional, the reader will still be challenged in places. ![]() In particular, the necessary matrix arithmetic and algebra (not linear algebra) are developed as needed. ![]() The only technical prerequisite for this text, which is intended for a sophomore-level course in multivariable calculus, is a standard course in the calculus of functions of one variable. Moreover, it is an exciting and beautiful subject in its own right, a true adventure in many dimensions. Vector calculus is the essential mathematical tool for such analysis. The sociologist or psychologist who studies group behavior, the economist who endeavors to understand the vagaries of a nation’s employment cycles, the physicist who observes the trajectory of a particle or planet, or indeed anyone who seeks to understand geometry in two, three, or more dimensions recognizes the need to analyze changing quantities that depend on more than a single variable. Physical and natural phenomena depend on a complex array of factors.
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