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Multivariable Calculus

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Multivariable Calculus

Multivariable Calculus Book
Author : Don Shimamoto
Publisher : Unknown
Release : 2019-11-17
ISBN : 9781708246990
Language : En, Es, Fr & De

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Book Description :

This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking, the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and, finally, the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise, the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required. Latest corrected printing: January 8, 2020. Updated information available online at the Open Textbook Library.

Calculus

Calculus Book
Author : Deborah Hughes-Hallett
Publisher : John Wiley & Sons Incorporated
Release : 1999-07-01
ISBN : 9780471323860
Language : En, Es, Fr & De

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Book Description :

Download Calculus book written by Deborah Hughes-Hallett, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Multivariable Calculus with Mathematica

Multivariable Calculus with Mathematica Book
Author : Robert P. Gilbert,Michael Shoushani,Yvonne Ou
Publisher : CRC Press
Release : 2020-11-25
ISBN : 1351665464
Language : En, Es, Fr & De

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Book Description :

Multivariable Calculus with Mathematica is a textbook addressing the calculus of several variables. Instead of just using Mathematica to directly solve problems, the students are encouraged to learn the syntax and to write their own code to solve problems. This not only encourages scientific computing skills but at the same time stresses the complete understanding of the mathematics. Questions are provided at the end of the chapters to test the student’s theoretical understanding of the mathematics, and there are also computer algebra questions which test the student’s ability to apply their knowledge in non-trivial ways. Features Ensures that students are not just using the package to directly solve problems, but learning the syntax to write their own code to solve problems Suitable as a main textbook for a Calculus III course, and as a supplementary text for topics scientific computing, engineering, and mathematical physics Written in a style that engages the students’ interest and encourages the understanding of the mathematical ideas

Calculus of Several Variables

Calculus of Several Variables Book
Author : Serge Lang
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461210682
Language : En, Es, Fr & De

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Book Description :

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.

Multivariable Calculus

Multivariable Calculus Book
Author : L. Corwin
Publisher : Routledge
Release : 2017-10-19
ISBN : 1351429523
Language : En, Es, Fr & De

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Book Description :

Classroom-tested and lucidly written, Multivariable Calculus gives a thorough and rigoroustreatment of differential and integral calculus of functions of several variables. Designed as ajunior-level textbook for an advanced calculus course, this book covers a variety of notions,including continuity , differentiation, multiple integrals, line and surface integrals, differentialforms, and infinite series. Numerous exercises and examples throughout the book facilitatethe student's understanding of important concepts.The level of rigor in this textbook is high; virtually every result is accompanied by a proof. Toaccommodate teachers' individual needs, the material is organized so that proofs can be deemphasizedor even omitted. Linear algebra for n-dimensional Euclidean space is developedwhen required for the calculus; for example, linear transformations are discussed for the treatmentof derivatives.Featuring a detailed discussion of differential forms and Stokes' theorem, Multivariable Calculusis an excellent textbook for junior-level advanced calculus courses and it is also usefulfor sophomores who have a strong background in single-variable calculus. A two-year calculussequence or a one-year honor calculus course is required for the most successful use of thistextbook. Students will benefit enormously from this book's systematic approach to mathematicalanalysis, which will ultimately prepare them for more advanced topics in the field.

Multivariable Calculus

Multivariable Calculus Book
Author : David Damiano,Margaret Freije
Publisher : Jones & Bartlett Publishers
Release : 2011-01-03
ISBN : 0763782475
Language : En, Es, Fr & De

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Book Description :

Written for mathematics, science, and engineering majors who have completed the traditional two-term course in single variable calculus, Multivariable Calculus bridges the gap between mathematical concepts and their real-world applications outside of mathematics. The ideas of multivariable calculus are presented in a context that is informed by their non-mathematical applications. It incorporates collaborative learning strategies and the sophisticated use of technology, which asks students to become active participants in the development of their own understanding of mathematical ideas. This teaching and learning strategy urges students to communicate mathematically, both orally and in writing. With extended examples and exercises and a student-friendly accessible writing style, Multivariable Calculus is an exciting and engaging journey into mathematics relevant to students everyday lives.

Multivariable Mathematics

Multivariable Mathematics Book
Author : Theodore Shifrin
Publisher : John Wiley & Sons
Release : 2004-01-26
ISBN : 047152638X
Language : En, Es, Fr & De

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Book Description :

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.

Multivariable Calculus with Applications

Multivariable Calculus with Applications Book
Author : Peter D. Lax,Maria Shea Terrell
Publisher : Springer
Release : 2018-03-12
ISBN : 3319740733
Language : En, Es, Fr & De

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Book Description :

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.

Multivariable Calculus Linear Algebra and Differential Equations

Multivariable Calculus  Linear Algebra  and Differential Equations Book
Author : Stanley I. Grossman
Publisher : Academic Press
Release : 2014-05-10
ISBN : 1483218031
Language : En, Es, Fr & De

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Book Description :

Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in "n" variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus.

An Illustrative Guide to Multivariable and Vector Calculus

An Illustrative Guide to Multivariable and Vector Calculus Book
Author : Stanley J. Miklavcic
Publisher : Springer Nature
Release : 2020-02-17
ISBN : 3030334597
Language : En, Es, Fr & De

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Book Description :

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.

Multivariable Calculus with MATLAB

Multivariable Calculus with MATLAB   Book
Author : Ronald L. Lipsman,Jonathan M. Rosenberg
Publisher : Springer
Release : 2017-12-06
ISBN : 331965070X
Language : En, Es, Fr & De

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Book Description :

This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.

A Course in Multivariable Calculus and Analysis

A Course in Multivariable Calculus and Analysis Book
Author : Sudhir R. Ghorpade,Balmohan V. Limaye
Publisher : Springer Science & Business Media
Release : 2009-12-10
ISBN : 1441916202
Language : En, Es, Fr & De

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Book Description :

This self-contained textbook gives a thorough exposition of multivariable calculus. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike.

Multivariable Calculus

Multivariable Calculus Book
Author : James Stewart
Publisher : Brooks/Cole
Release : 2011-09-27
ISBN : 9780538498869
Language : En, Es, Fr & De

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Book Description :

Success in your calculus course starts here! James Stewart's CALCULUS, 7e, International Metric texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With MULTIVARIABLE CALCULUS, 7e, International Metric Edition Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

A Course in Multivariable Calculus and Analysis

A Course in Multivariable Calculus and Analysis Book
Author : Sudhir R. Ghorpade,Balmohan V. Limaye
Publisher : Springer Science & Business Media
Release : 2010-03-20
ISBN : 1441916210
Language : En, Es, Fr & De

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Book Description :

This self-contained textbook gives a thorough exposition of multivariable calculus. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike.

Fractional and Multivariable Calculus

Fractional and Multivariable Calculus Book
Author : A.M. Mathai,H.J. Haubold
Publisher : Springer
Release : 2017-07-25
ISBN : 3319599933
Language : En, Es, Fr & De

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Book Description :

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable functions). Illustrative examples, input-output process, optimal recovery of functions and approximations are given; each section lists an ample number of exercises to heighten understanding of the material. Chapter three discusses deterministic/mathematical and optimization models evolving from differential equations, difference equations, algebraic models, power function models, input-output models and pathway models. Fractional integral and derivative models are examined. Chapter four covers non-deterministic/stochastic models. The random walk model, branching process model, birth and death process model, time series models, and regression type models are examined. The fifth chapter covers optimal design. General linear models from a statistical point of view are introduced; the Gauss–Markov theorem, quadratic forms, and generalized inverses of matrices are covered. Pathway, symmetric, and asymmetric models are covered in chapter six, the concepts are illustrated with graphs.

Multivariable Calculus and Mathematica

Multivariable Calculus and Mathematica   Book
Author : Kevin R. Coombes,Ronald L. Lipsman,Jonathan M. Rosenberg
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461216982
Language : En, Es, Fr & De

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Book Description :

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 Vectors

Multivariable Calculus with Vectors Book
Author : Hartley Rogers
Publisher : Unknown
Release : 1999
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Presents a conceptual underpinning for multivariable calculus that is as natural and intuitively simple as possible. This book focuses on modeling physical phenomena, especially from physics and engineering, and on developing geometric intuition. Geometric intuition is particularly stressed. The synthetic, coordinate-free geometries of 2- and 3-dimensional Euclidean spaces (E^2 and E^3) have a primary role. Wherever possible, coordinate-free definitions are used

Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series

Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series Book
Author : William F. Trench,Bernard Kolman
Publisher : Academic Press
Release : 2014-05-10
ISBN : 1483220451
Language : En, Es, Fr & De

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Book Description :

Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in 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. The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eigenvalues and eigenvectors; 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 covered, 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.

Multivariable Calculus

Multivariable Calculus Book
Author : Rolland Trapp
Publisher : Oxford University Press
Release : 2019-10-24
ISBN : 0192572288
Language : En, Es, Fr & De

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Book Description :

In this modern treatment of the topic, Rolland Trapp presents an accessible introduction to the topic of multivariable calculus, supplemented by the use of fully interactive three-dimensional graphics throughout the text. Multivariable Calculus opens with an introduction to points, curves and surfaces, easing student transitions from two- to three-dimensions, and concludes with the main theorems of vector calculus. All standard topics of multivariable calculus are covered in between, including a variety of applications within the physical sciences. The exposition combines rigor and intuition, resulting in a well-rounded resource for students of the subject. In addition, the interactive three-dimensional graphics, accessible through the electronic text or via the companion website, enhance student understanding while improving their acuity. The style of composition, sequencing of subjects, and interactive graphics combine to form a useful text that appeals to a broad audience: students in the sciences, technology, engineering, and mathematics alike.

Multivariable and Vector Calculus for Engineers and Scientists

Multivariable and Vector Calculus for Engineers and Scientists Book
Author : Sarhan M. Musa
Publisher : Unknown
Release : 2018-09-30
ISBN : 9781683922391
Language : En, Es, Fr & De

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Book Description :

Designed for undergraduates in mathematics, engineering, the physical sciences and for practicing engineers, the book focuses on practical applications of engineering and science used in industry. It first presents the theoretical concepts followed by practical applications of vector calculus, differentiation, and integration. MATLAB examples with source code appear on the companion files. Features: * Includes numerous computer illustrations and tutorials using * Covers the major topics of vector geometry, differentiation, and integration in several variables