Vector Calculus

Description

Vector Calculus, Fourth Edition, uses the language and notation of vectors and matrices to teach multivariable calculus. 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. This text is distinguished from others by its readable narrative, numerous figures, thoughtfully selected examples, and carefully crafted exercise sets. Colley includes not only basic and advanced exercises, but also mid-level exercises that form a necessary bridge between the two.

Table of Contents

• Introduction of basic linear algebra concepts throughout the text enables multivariable topics to be introduced in more general terms and illuminates the connection between concepts in single- and multivariable calculus.
• More than 600 diagrams and figures connect analytic work to geometry and assist with visualization.
• An appropriate level of mathematical rigor collects most of the technical derivations at the ends of sections. Many proofs are available for reference, but positioned so as not to disrupt the flow of main ideas.
• Large numbers of fully worked examples are integrated throughout to motivate students and to explicate the main ideas and techniques.
• More than 1,400 exercises are carefully crafted to meet student needs: from practice with the basics, to applications, to mid-level exercises, to more challenging conceptual questions. Also included are optional CAS exercises for instructors who incorporate this technology into the course.
• Chapter-ending exercises have been carefully crafted to help students synthesize material from multiple sections in the chapter.
• True/false exercises appear at the end of each chapter (approximately 230 total).
• Well-chosen advanced topics (such as those in Chapter 8 on Vector Analysis in Higher Dimensions), allow instructors to take the discussion to a higher level—beyond the level of other vector calculus texts.

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. She received S.B. and Ph.D. degrees in mathematics from the Massachusetts Institute of Technology prior to joining the faculty at Oberlin in 1983. Her research focuses on enumerative problems in algebraic geometry, particularly concerning multiple-point singularities and higher-order contact of plane curves. Professor Colley has published papers on algebraic geometry and commutative algebra, as well as articles on other mathematical subjects. She has lectured internationally on her research and has taught a wide range of subjects in undergraduate mathematics. 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.

For undergraduate courses in Multivariable Calculus.

Vector Calculus, Fourth Edition, uses the language and notation of vectors and matrices to teach multivariable calculus. 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. This text is distinguished from others by its readable narrative, numerous figures, thoughtfully selected examples, and carefully crafted exercise sets. Colley includes not only basic and advanced exercises, but also mid-level exercises that form a necessary bridge between the two. Instructors will appreciate the mathematical precision, level of rigor, and full selection of topics.

• 210 additional exercises at all levels provide practice for students and increased assignment flexibility for instructors.
• New, optional sections:
• Section 2.7 now collects the material on Newton’s method for approximating solutions to systems of n equations in n unknowns. This new section is optional.
• Section 5.7 covers numerical methods for approximating multiple integrals
• Content updates
• Section 2.2 contains new proofs of limit properties
• Section 2.5 contains new proofs of the general multivariable chain rule.
• Section 4.1 contains new proofs of both single-variable and multivariable versions of Taylor’s theorem.
• Refinements and clarifications throughout the text including many new and revised examples and explanations
• PowerPoint^® slides and Mathematica^® files are now available, showing key concepts and illustrations from the text.