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An Illustrative Guide to Multivariable and Vector Calculus

Author: Stanley J. Miklavcic

Publisher: Springer Nature

Published: 2020-02-17

Total Pages: 319

ISBN-13: 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.

Student’s Guide to Basic Multivariable Calculus

Author: Karen Pao

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 180

ISBN-13: 1475743009

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For use with Basic Multivariable Calculus

Vector Analysis Versus Vector Calculus

Author: Antonio Galbis

Publisher: Springer Science & Business Media

Published: 2012-03-29

Total Pages: 383

ISBN-13: 1461422000

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The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Key topics include vectors and vector fields, line integrals, regular k-surfaces, flux of a vector field, orientation of a surface, differential forms, Stokes' theorem, and divergence theorem. This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables. The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.

Multivariable and Vector Calculus

Author: Sarhan M. Musa

Publisher: Mercury Learning and Information

Published: 2023-02-08

Total Pages: 491

ISBN-13: 1683929179

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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

Basic Multivariable Calculus

Author: Jerrold E. Marsden

Publisher: Springer

Published: 2000-10-31

Total Pages: 540

ISBN-13: 9780387979762

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Basic Multivariable Calculus fills the need for a student-oriented text devoted exclusively to the third-semester course in multivariable calculus. In this text, the basic algebraic, analytic, and geometric concepts of multivariable and vector calculus are carefully explained, with an emphasis on developing the student's intuitive understanding and computational technique. A wealth of figures supports geometrical interpretation, while exercise sets, review sections, practice exams, and historical notes keep the students active in, and involved with, the mathematical ideas. All necessary linear algebra is developed within the text, and the material can be readily coordinated with computer laboratories. Basic Multivariable Calculus is the product of an extensive writing, revising, and class-testing collaboration by the authors of Calculus III (Springer-Verlag) and Vector Calculus (W.H. Freeman & Co.). Incorporating many features from these highly respected texts, it is both a synthesis of the authors' previous work and a new and original textbook.

Multivariable and Vector Calculus

Author: Joseph D. Fehribach

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-02-10

Total Pages: 201

ISBN-13: 3110660571

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This carefully-designed book covers multivariable and vector calculus, and is appropriate either as a text of a one-semester course, or for self-study. It includes many worked-through exercises, with answers to many of the basic computational ones and hints to many of those that are more involved, as well as lots of diagrams which illustrate the various theoretical concepts.

Multivariable Calculus with Linear Algebra and Series

Author: William F. Trench

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 771

ISBN-13: 148325920X

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Multivariable Calculus with Linear Algebra and Series presents a modern, but not extreme, treatment of linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples. Comprised of seven chapters, this book begins with an introduction to linear equations and matrices, including determinants. The next chapter deals with vector spaces and linear transformations, along with eigenvalues and eigenvectors. The discussion then turns to vector analysis and analytic geometry in R3; curves and surfaces; the differential calculus of real-valued functions of n variables; and vector-valued functions as ordered m-tuples of real-valued functions. Integration (line, surface, and multiple integrals) is also considered, together with Green's and Stokes's theorems and the divergence theorem. The final chapter is devoted to infinite sequences, infinite series, and power series in one variable. This monograph is intended for students majoring in science, engineering, or mathematics.

Advanced Calculus (Revised Edition)

Author: Lynn Harold Loomis

Publisher: World Scientific Publishing Company

Published: 2014-02-26

Total Pages: 595

ISBN-13: 9814583952

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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.

Multivariable Calculus and Mathematica®

Author: Kevin R. Coombes

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 282

ISBN-13: 1461216982

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Aiming to "modernise" the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents introductions to geometry, mathematical physics, and kinematics. The authors make it clear that Mathematica is not algorithms, but at the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The sets of problems give students an opportunity to practice their newly learned skills, covering simple calculations, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numerical integration, and also cover the practice of incorporating text and headings into a Mathematica notebook. The accompanying diskette contains both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students, which can be used with any standard multivariable calculus textbook. It is assumed that students will also have access to an introductory primer for Mathematica.

Multivariable Calculus with Applications

Author: Peter D. Lax

Publisher: Springer

Published: 2018-03-12

Total Pages: 483

ISBN-13: 3319740733

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This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics.