An Introduction To Multivariable Mathematics
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An Introduction To Multivariable Mathematics
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Author : Leon Simon
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2008
An Introduction To Multivariable Mathematics written by Leon Simon and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The core material of this text is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in ten or eleven lectures, followed by a similar number of lectures on basic multivariable analysis, including first theorems on differentiable functions on domains in Euclidean space and a brief introduction to submanifolds.
Multivariable Mathematics
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Author : Theodore Shifrin
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-26
Multivariable Mathematics written by Theodore Shifrin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-26 with Mathematics categories.
Multivariable Mathematics combines linear algebra and multivariable calculus in a rigorous approach. The material is integrated to emphasize the role of linearity in all of calculus and the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author addresses 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 including complete proofs. By emphasizing the theoretical aspects and reviewing the linear algebra material quickly, the book can also be used as a text for an advanced calculus or multivariable analysis course culminating in a treatment of manifolds, differential forms, and the generalized Stokes’s Theorem.
An Introduction To Multivariable Mathematics
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Author : Leon Simon
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
An Introduction To Multivariable Mathematics written by Leon Simon and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.
The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. The core material of the book is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in the first ten or eleven lectures, followed by a similar number of lectures on basic multivariable analysis, including first theorems on differentiable functions on domains in Euclidean space and a brief introduction to submanifolds. The book then concludes with further essential linear algebra, including the theory of determinants, eigenvalues, and the spectral theorem for real symmetric matrices, and further multivariable analysis, including the contraction mapping principle and the inverse and implicit function theorems. There is also an appendix which provides a nine-lecture introduction to real analysis. There are various ways in which the additional material in the appendix could be integrated into a course--for example in the Stanford Mathematics honors program, run as a four-lecture per week program in the Autumn Quarter each year, the first six lectures of the nine-lecture appendix are presented at the rate of one lecture per week in weeks two through seven of the quarter, with the remaining three lectures per week during those weeks being devoted to the main chapters of the text. It is hoped that the text would be suitable for a quarter or semester course for students who have scored well in the BC Calculus advanced placement examination (or equivalent), particularly those who are considering a possible major in mathematics. The author has attempted to make the presentation rigorous and complete, with the clarity and simplicity needed to make it accessible to an appropriately large group of students. Table of Contents: Linear Algebra / Analysis in R / More Linear Algebra / More Analysis in R / Appendix: Introductory Lectures on Real Analysis
A Course In Multivariable Calculus And Analysis
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Author : Sudhir R. Ghorpade
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-20
A Course In Multivariable Calculus And Analysis written by Sudhir R. Ghorpade and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-20 with Mathematics categories.
This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. 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. Moreover, the emphasis is on a geometric approach to such basic notions as local extremum and saddle point. 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. There is also an informative section of "Notes and Comments’’ indicating some novel features of the treatment of topics in that chapter as well as references to relevant literature. The only prerequisite for this text is a course in one-variable calculus.
Calculus Of Several Variables
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Calculus Of Several Variables written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.
Multivariable Analysis
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Author : Griffith B Price
language : en
Publisher:
Release Date : 1984-06-01
Multivariable Analysis written by Griffith B Price and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-06-01 with categories.
Calculus On Manifolds
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Author : Michael Spivak
language : en
Publisher: Westview Press
Release Date : 1965
Calculus On Manifolds written by Michael Spivak and has been published by Westview Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Science categories.
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.
Multivariable And Vector Calculus
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Author : David A. Santos
language : en
Publisher: Mercury Learning and Information
Release Date : 2015-07-30
Multivariable And Vector Calculus written by David A. Santos and has been published by Mercury Learning and Information this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Mathematics categories.
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. It also provides numerous computer illustrations and tutorials using MATLAB® and Maple®, that bridge the gap between analysis and computation. 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
Derivatives And Integrals Of Multivariable Functions
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Author : Alberto Guzman
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-08-22
Derivatives And Integrals Of Multivariable Functions written by Alberto Guzman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-22 with Mathematics categories.
This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author’s previous text, "Continuous Functions of Vector Variables": specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. Topics encompass differentiability, partial derivatives, directional derivatives and the gradient; curves, surfaces, and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini, Stokes, and Gauss. Prerequisites include background in linear algebra, one-variable calculus, and some acquaintance with continuous functions and the topology of the real line. Written in a definition-theorem-proof format, the book is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths. "Derivatives and Integrals of Multivariable Functions" is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry.
Multivariable Mathematics
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Author : Richard E. Williamson
language : en
Publisher:
Release Date : 2004
Multivariable Mathematics written by Richard E. Williamson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Algebras, Linear categories.
For courses in second-year calculus, linear calculus and differential equations. This text explores the standard problem-solving techniques of multivariable mathematics - integrating vector algebra ideas with multivariable calculus and differential equations.