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# Vector Analysis

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• by Robert C Wrede , Language: English

This broad introduction to vector and tensor analysis is designed for the advanced undergraduate or graduate student in mathematics, physics, and engineering as well as for the practicing engineer or physicist who needs a theoretical understanding of these essential mathematical tools. In recent years, the vector approach has found its way even into writings on aspects of biology, economics, and other sciences.The many and various topics covered include: the algebra of vectors — linear dependence and independence, transformation equations, the inner product, the cross product, and the algebra of matrixes; the differentiation of vectors — geometry of space curves, kinematics, moving frames of reference, Newtonian orbits and special relativity theory; partial differentiation of vectors — geometry of space curves, kinematics, moving frames of reference, Newtonian orbits and special relativity theory; partial differentiation and associated concepts — surface representations, bases in general coordinate systems, and maxima and minima of functions of two variables; the integration of vectors — line integrals, surface integrals, surface tensors and volume integrals; tensor algebra and analysis — fundamental notions of n-space, transformations and tensors, Riemannian geometry, tensor processes of differentiation, geodesics, the curvature tensor and its algebraic properties, and general relativity theory.T

Throughout, Professor Wrede stresses the interrelationships between algebra and geometry, and moves frequently from one to the other. As he points out, vector and tensor analysis provides a kind of bridge between elementary aspects of linear algebra, geometry and analysis. He uses the classical notation for vector analysis, but introduces a more appropriate new notation for tensors, which he correlates with the common vector notation. He stresses proofs and concludes each section with a set of problems designed to help the student get a solid grasp of the ideas, and explore them more thoroughly on his own. His approach features a combination of important historical material with up-to-date developments in both fields. The knowledge of vector and tensor analysis gained in this way is excellent preparation for further studies in differential geometry, applied mathematics, and theoretical physics.

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## قیمت واقعی کتاب در آمازون : 18.95 دلار

• by Miroslav Lovric , Language: English

This manual contains solutions to all exercises from the textbook Vector Calculus by Miroslav Lovric, published by John Wiley & Sons.In most cases, all details of a solution are given. Occasionally, a related theoretical concept, a method or a formula are recalled in order to make the exposition clearer. Details of evaluation of definite integrals are sometimes skipped and the reader is referred to a table of integrals or advised to use a numeric method or appropriate software. (The objective of this course is not to master a dozen integration techniques but rather to understand what the integral involved is all about.)

)It is assumed that students have access to a table of integrals and a calculator. Instructors may wish to encourage their students to use a graphing/programmable calculator or, better yet, appropriate software packages (such as Maple or Mathematica). A separate Students’ Solutions Manual, containing solutions to all odd-numbered exercises, is available to students.In the Students’ Solutions Manual the following advice is given to students: "It is far more beneficial to try to solve an exercise on your own. Start, and see how far you can go. If you get stuck, identify the problem first – try to understand why you are having difficulties, and then look up the solution in the manual. This way, you will learn not only what the problem is (or what you have problems with), but also how that particular problem has been resolved. If you just read a solution, you might not recognize the hard part(s) – or, even worse, you might miss the whole point of the exercise."

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## قیمت واقعی کتاب در آمازون : 201.44 دلار

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