Advanced Calculus : A Geometric View - new book

2010, ISBN: 1441973311

[EAN: 9781441973313], Neubuch, [SC: 0.0], [PU: Springer-Verlag Gmbh Sep 2010], ANALYSIS; CALCULUS; APPROXIMATION - DIFFERENZENAPPROXIMATION; NÄHERUNGSRECHNUNG; RECHNEN / MATHEMATIK; DIFFE… More...

[EAN: 9781441973313], Neubuch, [SC: 0.0], [PU: Springer-Verlag Gmbh Sep 2010], ANALYSIS; CALCULUS; APPROXIMATION - DIFFERENZENAPPROXIMATION; NÄHERUNGSRECHNUNG; RECHNEN / MATHEMATIK; DIFFERENZIALGLEICHUNG; GLEICHUNG DIFFERENZIALRECHNUNG; INFINITESIMALRECHNUNG, Neuware - With a fresh geometric approach accompanied by approximately 300 figures, this textbook sets itself apart from all others in advanced calculus. Although this book presents classical capstones of advanced calculus, such as the divergence theorem for 3-dimensional regions and Stokes theorem for 2-dimensional surfaces in space, it devotes most of the book to the physical meaning of the theorems and their underlying concepts. All relevant analytic topics, such as convergence of sequences of functions, are purposefully left out of this book because the analysis aspect is typically covered in advanced calculus textbooks while the geometric aspects are rarely represented.The pace of Advanced Calculus: A Geometric View is designed deliberately for independent study, as it is abundant in figures, exercises, and visual examples that introduce ideas and topics. This book can be divided into two parts: Part 1: mappings; Part 2: integrals. There are many chapters in both parts, which go into extreme detail on the many different topics in advanced calculus, such as the geometry of linear maps, approximations, derivatives, implicit functions, surface integrals, and Stoke s theorem. Containing both calculus and geometry, this textbook is intended to be used by undergraduates in mathematics and the physical sciences who are taking a course in advanced calculus and/or geometry, or engaged in independent study. The prerequisites include linear algebra and multivariable calculus. With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study. 526 pp. Englisch<

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2010, ISBN: 1441973311

[EAN: 9781441973313], Neubuch, [PU: Springer-Verlag Gmbh Sep 2010], ANALYSIS; CALCULUS; APPROXIMATION - DIFFERENZENAPPROXIMATION; NÄHERUNGSRECHNUNG; RECHNEN / MATHEMATIK; DIFFERENZIALGLEI… More...

[EAN: 9781441973313], Neubuch, [PU: Springer-Verlag Gmbh Sep 2010], ANALYSIS; CALCULUS; APPROXIMATION - DIFFERENZENAPPROXIMATION; NÄHERUNGSRECHNUNG; RECHNEN / MATHEMATIK; DIFFERENZIALGLEICHUNG; GLEICHUNG DIFFERENZIALRECHNUNG; INFINITESIMALRECHNUNG, Neuware - With a fresh geometric approach accompanied by approximately 300 figures, this textbook sets itself apart from all others in advanced calculus. Although this book presents classical capstones of advanced calculus, such as the divergence theorem for 3-dimensional regions and Stokes theorem for 2-dimensional surfaces in space, it devotes most of the book to the physical meaning of the theorems and their underlying concepts. All relevant analytic topics, such as convergence of sequences of functions, are purposefully left out of this book because the analysis aspect is typically covered in advanced calculus textbooks while the geometric aspects are rarely represented.The pace of Advanced Calculus: A Geometric View is designed deliberately for independent study, as it is abundant in figures, exercises, and visual examples that introduce ideas and topics. This book can be divided into two parts: Part 1: mappings; Part 2: integrals. There are many chapters in both parts, which go into extreme detail on the many different topics in advanced calculus, such as the geometry of linear maps, approximations, derivatives, implicit functions, surface integrals, and Stoke s theorem. Containing both calculus and geometry, this textbook is intended to be used by undergraduates in mathematics and the physical sciences who are taking a course in advanced calculus and/or geometry, or engaged in independent study. The prerequisites include linear algebra and multivariable calculus. With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study. 526 pp. Englisch<

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ISBN: 9781441973313

A half-century ago, advanced calculus was a well-de?ned subject at the core of the undergraduate mathematics curriulum. The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan… More...

A half-century ago, advanced calculus was a well-de?ned subject at the core of the undergraduate mathematics curriulum. The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan [9], for example, show some of the ways it was approached. Over time, certain aspects of the course came to be seen as more signi?cant—those seen as giving a rigorous foundation to calculus—and they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core. Advanced calculus did not, in the process, become less important, but its role in the curriculum changed. In fact, a bifurcation occurred. In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal. The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III. In my experience, though, it does not manage to accomplish what the old advancedcalculus course did. Multivariable calculusnaturallysplits intothreeparts:(1)severalfunctionsofonevariable,(2)one function of several variables, and (3) several functions of several variables. The ?rst two are well-developed in Calculus III, but the third is really too large and varied to be treated satisfactorily in the time remaining at the end of a semester. To put it another way: Green’s theorem ?ts comfortably; Stokes’ and Gauss’ do not. Books > Mathematics Hard cover, Springer Shop<

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2010, ISBN: 9781441973313

[ED: Gebunden], [PU: Springer US], With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Bes… More...

[ED: Gebunden], [PU: Springer US], With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study., DE, [SC: 0.00], Neuware, gewerbliches Angebot, 526, [GW: 1159g], Sofortüberweisung, PayPal, Banküberweisung<

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2010, ISBN: 1441973311

Advanced Calculus ab 69.49 € als gebundene Ausgabe: A Geometric View. Auflage 2010. Aus dem Bereich: Bücher, Wissenschaft, Mathematik, Medien > Bücher, Springer-Verlag GmbH

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