Multivariable And Vector Calculus
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| Author | : Stanley J. Miklavcic |
| Publisher | : Springer Nature |
| Total Pages | : 319 |
| Release | : 2020-02-17 |
| Genre | : Mathematics |
| ISBN | : 3030334597 |
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
| Author | : Sarhan M. Musa |
| Publisher | : Mercury Learning and Information |
| Total Pages | : 491 |
| Release | : 2023-02-08 |
| Genre | : Mathematics |
| ISBN | : 1683929179 |
This book is designed primarily for undergraduates in mathematics, engineering, and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. Furthermore, it can be used to impower the mathematical knowledge for Artificial Intelligence (AI) concepts. It also provides numerous computer illustrations and tutorials using MATLAB® and Maple®, that bridge the gap between analysis and computation. Partial solutions and instructor ancillaries available for use as a textbook. FEATURES Includes numerous computer illustrations and tutorials using MATLAB®and Maple® Covers the major topics of vector geometry, differentiation, and integration in several variables Instructors’ ancillaries available upon adoption
| Author | : Theodore Shifrin |
| Publisher | : John Wiley & Sons |
| Total Pages | : 514 |
| Release | : 2004-01-26 |
| Genre | : Mathematics |
| ISBN | : 047152638X |
Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs. * Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts. * Numerous exercises of varying levels of difficulty, both computational and more proof-oriented. * Exercises are arranged in order of increasing difficulty.
| Author | : Joseph D. Fehribach |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 196 |
| Release | : 2024-07-22 |
| Genre | : Mathematics |
| ISBN | : 3111393488 |
This book covers multivariable and vector calculus. It can be used as a textbook for a one-semester course or self-study. It includes worked-through exercises, with answers provided for many of the basic computational ones and hints for the more complex ones.. This second edition features new exercises, new sections on twist and binormal vectors for curves in space, linear approximations, and the Laplace and Poisson equations.
| Author | : Hartley Rogers |
| Publisher | : |
| Total Pages | : 824 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : |
This text is for the third semester or fourth and fifth quarters of calculus; i.e., for multivariable or vector calculus courses. This text presents a conceptual underpinning for multivariable calculus that is as natural and intuitively simple as possible. More than its competitors, this book focuses on modeling physical phenomena, especially from physics and engineering, and on developing geometric intuition.
| Author | : Caspar R. Curjel |
| Publisher | : McGraw-Hill Science, Engineering & Mathematics |
| Total Pages | : 0 |
| Release | : 1990 |
| Genre | : Análisis vectorial |
| ISBN | : 9780070149496 |
Designed to supplement any traditional calculus text, this book of exercises covers topics from multivariable calculus that most books cover lightly. It enables students to go beyond routine technique exercises and to solidify their base for further study. While the primary audience is students in their third semester of calculus, this text could augment an intermediate/advanced text.
| Author | : Michael Spivak |
| Publisher | : Westview Press |
| Total Pages | : 164 |
| Release | : 1965 |
| Genre | : Science |
| ISBN | : 9780805390216 |
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
| Author | : James J. Callahan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 542 |
| Release | : 2010-09-09 |
| Genre | : Mathematics |
| ISBN | : 144197332X |
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.
| Author | : Serge Lang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 624 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210682 |
This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.
| Author | : Lynn Harold Loomis |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 595 |
| Release | : 2014-02-26 |
| Genre | : Mathematics |
| ISBN | : 9814583952 |
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
