Problems And Worked Solutions In Vector Analysis
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Problems And Worked Solutions In Vector Analysis
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Author : L.R. Shorter
language : en
Publisher: Courier Corporation
Release Date : 2014-06-01
Problems And Worked Solutions In Vector Analysis written by L.R. Shorter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-01 with Mathematics categories.
Devoted to fully worked out examples, this unique text constitutes a self-contained introductory course in vector analysis. Topics include vector addition, subtraction, multiplication, and applications. "Very comprehensive." — The Mathematical Gazette. 1931 edition.
Problems And Worked Solutions In Vector Analysis
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Author : L.R. Shorter
language : en
Publisher: Courier Corporation
Release Date : 2014-07-16
Problems And Worked Solutions In Vector Analysis written by L.R. Shorter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-16 with Mathematics categories.
"A handy book like this," noted The Mathematical Gazette, "will fill a great want." Devoted to fully worked out examples, this unique text constitutes a self-contained introductory course in vector analysis for undergraduate and graduate students of applied mathematics. Opening chapters define vector addition and subtraction, show how to resolve and determine the direction of two or more vectors, and explain systems of coordinates, vector equations of a plane and straight line, relative velocity and acceleration, and infinitely small vectors. The following chapters deal with scalar and vector multiplication, axial and polar vectors, areas, differentiation of vector functions, gradient, curl, divergence, and analytical properties of the position vector. Applications of vector analysis to dynamics and physics are the focus of the final chapter, including such topics as moving rigid bodies, energy of a moving rigid system, central forces, equipotential surfaces, Gauss's theorem, and vector flow. Dover (2014) republication of Introduction to Vector Analysis, originally published by Macmillan and Company, Ltd., London, 1931. See every Dover book in print at www.doverpublications.com
Problems And Worked Solutions In Vector Analysis
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Author : Lewis Richard Shorter
language : en
Publisher:
Release Date : 1931
Problems And Worked Solutions In Vector Analysis written by Lewis Richard Shorter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1931 with Vector analysis categories.
Problems And Worked Solutions In Vector Analysis By L R Shorter
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Author :
language : en
Publisher:
Release Date : 1930
Problems And Worked Solutions In Vector Analysis By L R Shorter written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1930 with categories.
Applications Of Vector Analysis And Complex Variables In Engineering
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Author : Otto D. L. Strack
language : en
Publisher: Springer Nature
Release Date : 2020-04-18
Applications Of Vector Analysis And Complex Variables In Engineering written by Otto D. L. Strack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-18 with Technology & Engineering categories.
This textbook presents the application of mathematical methods and theorems tosolve engineering problems, rather than focusing on mathematical proofs. Applications of Vector Analysis and Complex Variables in Engineering explains the mathematical principles in a manner suitable for engineering students, who generally think quite differently than students of mathematics. The objective is to emphasize mathematical methods and applications, rather than emphasizing general theorems and principles, for which the reader is referred to the literature. Vector analysis plays an important role in engineering, and is presented in terms of indicial notation, making use of the Einstein summation convention. This text differs from most texts in that symbolic vector notation is completely avoided, as suggested in the textbooks on tensor algebra and analysis written in German by Duschek and Hochreiner, in the 1960s. The defining properties of vector fields, the divergence and curl, are introduced in terms of fluid mechanics. The integral theorems of Gauss (the divergence theorem), Stokes, and Green are introduced also in the context of fluid mechanics. The final application of vector analysis consists of the introduction of non-Cartesian coordinate systems with straight axes, the formal definition of vectors and tensors. The stress and strain tensors are defined as an application. Partial differential equations of the first and second order are discussed. Two-dimensional linear partial differential equations of the second order are covered, emphasizing the three types of equation: hyperbolic, parabolic, and elliptic. The hyperbolic partial differential equations have two real characteristic directions, and writing the equations along these directions simplifies the solution process. The parabolic partial differential equations have two coinciding characteristics; this gives useful information regarding the character of the equation, but does not help in solving problems. The elliptic partial differential equations do not have real characteristics. In contrast to most texts, rather than abandoning the idea of using characteristics, here the complex characteristics are determined, and the differential equations are written along these characteristics. This leads to a generalized complex variable system, introduced by Wirtinger. The vector field is written in terms of a complex velocity, and the divergence and the curl of the vector field is written in complex form, reducing both equations to a single one. Complex variable methods are applied to elliptical problems in fluid mechanics, and linear elasticity. The techniques presented for solving parabolic problems are the Laplace transform and separation of variables, illustrated for problems of heat flow and soil mechanics. Hyperbolic problems of vibrating strings and bars, governed by the wave equation are solved by the method of characteristics as well as by Laplace transform. The method of characteristics for quasi-linear hyperbolic partial differential equations is illustrated for the case of a failing granular material, such as sand, underneath a strip footing. The Navier Stokes equations are derived and discussed in the final chapter as an illustration of a highly non-linear set of partial differential equations and the solutions are interpreted by illustrating the role of rotation (curl) in energy transfer of a fluid.
Problems And Worked Solutions In Vector Analysis
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Author : L. R. Shorter
language : en
Publisher:
Release Date : 1931
Problems And Worked Solutions In Vector Analysis written by L. R. Shorter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1931 with categories.
Vector And Tensor Analysis With Applications
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Author : A. I. Borisenko
language : en
Publisher: Courier Corporation
Release Date : 2012-08-28
Vector And Tensor Analysis With Applications written by A. I. Borisenko and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-28 with Mathematics categories.
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
An Introduction To Vectors Vector Operators And Vector Analysis
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Author : Pramod S. Joag
language : en
Publisher: Cambridge University Press
Release Date : 2016
An Introduction To Vectors Vector Operators And Vector Analysis written by Pramod S. Joag 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 2016 with Mathematics categories.
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.
Answers To Selected Problems In Multivariable Calculus With Linear Algebra And Series
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Author : William F. Trench
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Answers To Selected Problems In Multivariable Calculus With Linear Algebra And Series written by William F. Trench and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Understanding Vector Calculus
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Author : Jerrold Franklin
language : en
Publisher: Courier Dover Publications
Release Date : 2021-01-13
Understanding Vector Calculus written by Jerrold Franklin 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 2021-01-13 with Mathematics categories.
This concise text is a workbook for using vector calculus in practical calculations and derivations. Part One briefly develops vector calculus from the beginning; Part Two consists of answered problems. 2020 edition.