Multivariable Calculus And Differential Geometry Download Ebook PDF Epub Online

Author : Gerard Walschap
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2015-07-01
Page : 365
Category : Mathematics
ISBN 13 : 3110369540
Description :


This book offers an introduction to differential geometry for the non-specialist. It includes most of the required material from multivariable calculus, linear algebra, and basic analysis. An intuitive approach and a minimum of prerequisites make it a valuable companion for students of mathematics and physics. The main focus is on manifolds in Euclidean space and the metric properties they inherit from it. Among the topics discussed are curvature and how it affects the shape of space, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.


Author : Gerard Walschap
Publisher : De Gruyter
Release : 2015-05-15
Page : 365
Category : Mathematics
ISBN 13 : 9783110369496
Description :


This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.


Author : Seán Dineen
Publisher : Springer
Release : 2014-09-18
Page : 257
Category : Mathematics
ISBN 13 : 1447164199
Description :


Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook not only follows this programme, but additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.


Author : Lynn Harold Loomis
Shlomo Sternberg
Publisher : World Scientific Publishing Company
Release : 2014-02-26
Page : 596
Category : Mathematics
ISBN 13 : 9814583952
Description :


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.


Author : Theodore Shifrin
Publisher : John Wiley & Sons
Release : 2004-01-26
Page : 512
Category : Mathematics
ISBN 13 : 047152638X
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.


Author : Kevin R. Coombes
Ronald L. Lipsman
Publisher : Springer Science & Business Media
Release : 2012-12-06
Page : 283
Category : Mathematics
ISBN 13 : 1461216982
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.


Author : David Bachman
Publisher : Springer Science & Business Media
Release : 2012-02-02
Page : 156
Category : Mathematics
ISBN 13 : 0817683046
Description :


This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.


Author : Stephen T. Lovett
Publisher : A K Peters/CRC Press
Release : 2010-06-11
Page : 440
Category : Mathematics
ISBN 13 : 9781568814575
Description :


From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations. The three appendices provide background information on point set topology, calculus of variations, and multilinear algebra—topics that may not have been covered in the prerequisite courses of multivariable calculus and linear algebra. Differential Geometry of Manifolds takes a practical approach, containing extensive exercises and focusing on applications of differential geometry in physics, including the Hamiltonian formulation of dynamics (with a view toward symplectic manifolds), the tensorial formulation of electromagnetism, some string theory, and some fundamental concepts in general relativity.


Author : William F. Trench
Bernard Kolman
Publisher : Academic Press
Release : 2014-05-10
Page : 94
Category : Mathematics
ISBN 13 : 1483220451
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.


Author : Harold M. Edwards
Publisher : Springer Science & Business Media
Release : 2013-12-01
Page : 508
Category : Mathematics
ISBN 13 : 146120271X
Description :


This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.


Author : John Oprea
Publisher : MAA
Release : 2007-09-06
Page : 469
Category : Mathematics
ISBN 13 : 9780883857489
Description :


Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole, it mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors, it is also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only “see” geodesics on surfaces, but they will also see the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. Students will also see how particles move under constraints. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.


Author : Michael Spivak
Publisher : Hachette UK
Release : 1971-01-22
Page : 160
Category : Science
ISBN 13 : 0813346126
Description :


This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.


Author : John Hamal Hubbard
Barbara Burke Hubbard
Publisher :
Release : 2009
Page : 284
Category : Algebras, Linear
ISBN 13 : 9780971576674
Description :



Author : Steven H. Weintraub
Publisher : Academic Press
Release : 1997
Page : 256
Category : Mathematics
ISBN 13 : 9780127425108
Description :


This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods. * Treats vector calculus using differential forms * Presents a very concrete introduction to differential forms * Develops Stokess theorem in an easily understandable way * Gives well-supported, carefully stated, and thoroughly explained definitions and theorems. * Provides glimpses of further topics to entice the interested student


Author : James R. Munkres
Publisher : CRC Press
Release : 2018-02-19
Page : 384
Category : Mathematics
ISBN 13 : 042996269X
Description :


A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.


Author : William F. Trench
Bernard Kolman
Publisher : Academic Press
Release : 2014-05-10
Page : 770
Category : Mathematics
ISBN 13 : 148325920X
Description :


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.


Author : Ronald L. Lipsman
Jonathan M. Rosenberg
Publisher : Springer
Release : 2017-12-06
Page : 276
Category : Mathematics
ISBN 13 : 331965070X
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.


Author : A.N. Pressley
Publisher : Springer Science & Business Media
Release : 2013-11-11
Page : 332
Category : Mathematics
ISBN 13 : 1447136969
Description :


Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface geometry, it includes intersting and in-depth examples and goes into the subject in great detail and vigour. The book will cover three-dimensional Euclidean space only, and takes the whole book to cover the material and treat it as a subject in its own right.


Author : L. Corwin
Publisher : Routledge
Release : 2017-10-19
Page : 546
Category : Mathematics
ISBN 13 : 1351429523
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.


Author : George A. Duckett
Publisher : Createspace Independent Publishing Platform
Release : 2016-05-30
Page : 288
Category :
ISBN 13 : 9781533492333
Description :


If you have a question about Partial Differential Equations this is the book with the answers. Partial Differential Equations: Questions and Answers takes some of the best questions and answers asked on the math.stackexchange.com website. You can use this book to look up commonly asked questions, browse questions on a particular topic, compare answers to common topics, check out the original source and much more. This book has been designed to be very easy to use, with many internal references set up that makes browsing in many different ways possible. Topics covered include: Functional Analysis, Reference Request, Sobolev Spaces, Differential Geometry, Real Analysis, Analysis, Multivariable Calculus, Riemannian Geometry, Calculus, Fourier Analysis, Soft Question, Intuition, Stochastic Processes, Calculus Of Variations, Mathematical Physics and many more."