Basic Insights In Vector Calculus With A Supplement On Mathematical Understanding
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Basic Insights In Vector Calculus With A Supplement On Mathematical Understanding
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Author : Terrance J Quinn
language : en
Publisher: World Scientific
Release Date : 2020-07-24
Basic Insights In Vector Calculus With A Supplement On Mathematical Understanding written by Terrance J Quinn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-24 with Mathematics categories.
Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.
Basic Insights In Vector Calculus
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Author : RAI
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020-08-06
Basic Insights In Vector Calculus written by RAI and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-06 with Mathematics categories.
A Guided Tour Of Mathematical Methods
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Author : Roel Snieder
language : en
Publisher: Cambridge University Press
Release Date : 2004-09-23
A Guided Tour Of Mathematical Methods written by Roel Snieder and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-23 with Mathematics categories.
Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks.
A Student S Guide To Numerical Methods
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Author : Ian H. Hutchinson
language : en
Publisher: Cambridge University Press
Release Date : 2015-04-30
A Student S Guide To Numerical Methods written by Ian H. Hutchinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-30 with Computers categories.
The plain language style, worked examples and exercises in this book help students to understand the foundations of computational physics and engineering.
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.
Explorations In Mathematical Physics
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Author : Don Koks
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-15
Explorations In Mathematical Physics written by Don Koks 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 2006-09-15 with Science categories.
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
A First Course In Topology
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Author : Robert A Conover
language : en
Publisher: Courier Corporation
Release Date : 2014-02-20
A First Course In Topology written by Robert A Conover and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-20 with Mathematics categories.
Students must prove all of the theorems in this undergraduate-level text, which focuses on point-set topology and emphasizes continuity. The final chapter explores homotopy and the fundamental group. 1975 edition.
An Illustrative Guide To Multivariable And Vector Calculus
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Author : Stanley J. Miklavcic
language : en
Publisher: Springer Nature
Release Date : 2020-02-17
An Illustrative Guide To Multivariable And Vector Calculus written by Stanley J. Miklavcic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-17 with Mathematics categories.
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.
Teaching And Learning Of Calculus
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Author : David Bressoud
language : en
Publisher: Springer
Release Date : 2016-06-14
Teaching And Learning Of Calculus written by David Bressoud and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-14 with Education categories.
This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.
A Vector Space Approach To Geometry
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Author : Melvin Hausner
language : en
Publisher: Courier Dover Publications
Release Date : 2018-10-17
A Vector Space Approach To Geometry written by Melvin Hausner and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-17 with Mathematics categories.
A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.