Advanced Calculus: Fundamentals of Mathematics PDF Download
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Author: Carlos Polanco
Publisher: Bentham Science Publishers
ISBN: 9811415072
Category : Mathematics
Languages : en
Pages : 212
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Book Description
Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations. This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms. Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about advanced calculus as part of their college curriculum and equip themselves with the knowledge to apply theoretical concepts in practical situations.
Author: Carlos Polanco
Publisher: Bentham Science Publishers
ISBN: 9811415072
Category : Mathematics
Languages : en
Pages : 212
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Book Description
Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations. This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms. Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about advanced calculus as part of their college curriculum and equip themselves with the knowledge to apply theoretical concepts in practical situations.
Author: Frederick Shenstone Woods
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 420
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Book Description
Author: Henri Bourles
Publisher: Elsevier
ISBN: 0081023863
Category : Mathematics
Languages : en
Pages : 428
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Book Description
Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds), an analysis on Lie groups, the Haar measure, the convolution of functions and distributions, and the harmonic analysis over a Lie group. Finally, the theory of connections is (linear connections, principal connections, and Cartan connections) covered, as is the calculus of variations in Lagrangian and Hamiltonian formulations. This volume is the prerequisite to the analytic and geometric study of nonlinear systems. - Includes sections on differential and analytic manifolds, vector bundles, tensors, Lie derivatives, applications to algebraic topology, and more - Presents an ideal prerequisite resource on the analytic and geometric study of nonlinear systems - Provides theory as well as practical information
Author: Patrick Fitzpatrick
Publisher: American Mathematical Soc.
ISBN: 0821847910
Category : Mathematics
Languages : en
Pages : 610
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Book Description
"Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.
Author: David V. Widder
Publisher: Courier Corporation
ISBN: 0486134660
Category : Mathematics
Languages : en
Pages : 548
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Book Description
Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Includes exercises and selected answers.
Author: Kenneth A. Ross
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 9780817637071
Category : Education
Languages : en
Pages : 532
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Book Description
This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.
Author: Ellen F. Buck
Publisher:
ISBN: 9780070850767
Category : Calculus
Languages : en
Pages : 622
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Book Description
Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category : Mathematics
Languages : en
Pages : 595
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Book Description
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author: Gerald Atkins
Publisher: Larsen and Keller Education
ISBN: 9781641721400
Category :
Languages : en
Pages : 276
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Book Description
Calculus is a branch of mathematics that studies continuous change. It can be divided into the two branches of differential and integral calculus. The principles of limits and infinitesimals, the fundamental theorem of calculus and the convergence of infinite sequences and infinite series are fundamental to the development of calculus. Current studies in this field are in the areas of reformulations of calculus such as non-standard calculus, smooth infinitesimal analysis and constructive analysis. An understanding of this domain is crucial for developing a functional approach to advanced mathematical analysis. Besides advancing the frontiers of advanced mathematics, calculus is also instrumental in science, engineering and economics. This book provides comprehensive insights into the field of calculus. Some of the diverse topics covered herein address the varied branches that fall under this category. Coherent flow of topics, student-friendly language and extensive use of examples make this textbook an invaluable source of knowledge.
