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Vector Calculus

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Author : Paul C. Matthews
Category : Mathematics
Publisher : Springer Science & Business Media
Published : 2000-01-14
ISBN : 3540761802
Type : PDF & EPUB
Page : 196
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Reviews book: Vector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.

Vector Calculus In Regional Development Analysis

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Author : Kesra Nermend
Category : Business & Economics
Publisher : Springer Science & Business Media
Published : 2009-04-29
ISBN : 3790821799
Type : PDF & EPUB
Page : 174
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Reviews book: Methods used for regional development analysis are employed mainly to make forecasts and comparisons. Forecasting models of various types (e.g. econometric models) are usually used for forecasting. Recently, vector-autoregressive models (VAR) have become popular. These models were proposed by Sims in 1980. On the contrary, taxonomic methods (that are in the center of attention as far as the present publication is concerned) are most often employed to make comparisons. Linear ordering methods, including standard methods, are the most popular among ta- nomic methods. They are based on different distance and similarity measures, which leads to the fact that they do not always provide reliable information. When, for example, one construes the standard for a base year and then compares it with data for other years, it may turn out that the measure determined will have worse values than the standard for a real object (region, micro region) although this object is better from the standard. Hence, one must look for new methods employed in regional development analysis or improve hitherto existing ones in such a way so that information obtained re?ects the reality to a larger extent. The main aim of the present publication is to work out methodological basis for regional development analysis based on vector calculus together with assumptions about computer system supporting the implementation of the method suggested.

Vector Calculus

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Author : W. Cox
Category : Mathematics
Publisher : Butterworth-Heinemann
Published : 1998-05-15
ISBN : 9780340677414
Type : PDF & EPUB
Page : 257
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Reviews book: Written for second semester options, Vector Calculus introduces the student to some of the key techniques used by mathematicians, and includes historical contexts, real-life situations and links with other areas of mathematics.

Multivariable And Vector Calculus

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Author : David A. Santos
Category : Mathematics
Publisher : Mercury Learning and Information
Published : 2015-07-30
ISBN : 9781942270256
Type : PDF & EPUB
Page : 450
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Reviews book: 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

Basic Insights In Vector Calculus With A Supplement On Mathematical Understanding

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Author : Zine Boudhraa
Category : Mathematics
Publisher : World Scientific
Published : 2020-07-24
ISBN : 9789811222580
Type : PDF & EPUB
Page : 252
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Reviews book: 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.

An Illustrative Guide To Multivariable And Vector Calculus

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Author : Stanley J. Miklavcic
Category : Mathematics
Publisher : Springer Nature
Published : 2020-02-17
ISBN : 9783030334598
Type : PDF & EPUB
Page : 309
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Reviews book: 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.

Elementary Vector Calculus And Its Applications With Matlab Programming

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Author : Nita H. Shah
Category : Mathematics
Publisher : CRC Press
Published : 2023-01-31
ISBN : 9781000824230
Type : PDF & EPUB
Page : 226
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Reviews book: Sir Isaac Newton, one of the greatest scientists and mathematicians of all time, introduced the notion of a vector to define the existence of gravitational forces, the motion of the planets around the sun, and the motion of the moon around the earth. Vector calculus is a fundamental scientific tool that allows us to investigate the origins and evolution of space and time, as well as the origins of gravity, electromagnetism, and nuclear forces. Vector calculus is an essential language of mathematical physics, and plays a vital role in differential geometry and studies related to partial differential equations widely used in physics, engineering, fluid flow, electromagnetic fields, and other disciplines. Vector calculus represents physical quantities in two or three-dimensional space, as well as the variations in these quantities. The machinery of differential geometry, of which vector calculus is a subset, is used to understand most of the analytic results in a more general form. Many topics in the physical sciences can be mathematically studied using vector calculus techniques. This book is designed under the assumption that the readers have no prior knowledge of vector calculus. It begins with an introduction to vectors and scalars, and also covers scalar and vector products, vector differentiation and integrals, Gauss's theorem, Stokes's theorem, and Green's theorem. The MATLAB programming is given in the last chapter. This book includes many illustrations, solved examples, practice examples, and multiple-choice questions.

Multivariable Calculus

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Author : Rolland Trapp
Category : Calculus
Publisher : Oxford University Press, USA
Published : 2019-10-10
ISBN : 9780198835172
Type : PDF & EPUB
Page : 479
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Reviews book: 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 Calculus

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Author : Ron Larson
Category : Mathematics
Publisher : Cengage Learning
Published : 2022-01-02
ISBN : 9780357749425
Type : PDF & EPUB
Page : 480
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Reviews book: Discover the clear approach and learning support you need to truly understand calculus with MULTIVARIABLE CALCULUS, 12th Edition by award-winning authors Larson and Edwards. This edition effectively presents and demonstrates the concepts and rules of calculus using a thoroughly updated and refined learning experience specifically designed to remove any typical barriers to learning. New Big Ideas of Calculus notes present the overarching ideas behind chapter topics to place the principles you're learning within a meaningful context. Annotated examples and Concept Checks further reinforce your understanding. A variety of exercises, including visually driven exercises, provide the resources you need to develop a deeper conceptual understanding of calculus. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

An Introduction To Vectors Vector Operators And Vector Analysis

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Author : Pramod S. Joag
Category : Mathematical physics
Publisher : Cambridge University Press
Published : 2016
ISBN : 9781107154438
Type : PDF & EPUB
Page : 547
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Reviews book: Ideal for undergraduate and graduate students of science and engineering, this book covers fundamental concepts of vectors and their applications in a single volume. The first unit deals with basic formulation, both conceptual and theoretical. It discusses applications of algebraic operations, Levi-Civita notation, and curvilinear coordinate systems like spherical polar and parabolic systems and structures, and analytical geometry of curves and surfaces. The second unit delves into the algebra of operators and their types and also explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigen vectors and eigen values of a linear vector operator are elaborated using vector algebra. The third unit deals with vector analysis, discussing vector valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus covering both the scalar vector fields and vector integration.