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Advanced Calculus

Advanced Calculus Author Pietro-Luciano Buono
ISBN-10 9783110438222
Release 2016-09-12
Pages 313
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This textbook offers a high-level introduction to multi-variable differential calculus. Differential forms are introduced incrementally in the narrative, eventually leading to a unified treatment of Green’s, Stokes’ and Gauss’ theorems. Furthermore, the presentation offers a natural route to differential geometry. Contents: Calculus of Vector Functions Tangent Spaces and 1-forms Line Integrals Differential Calculus of Mappings Applications of Differential Calculus Double and Triple Integrals Wedge Products and Exterior Derivatives Integration of Forms Stokes’ Theorem and Applications

Multivariable Calculus and Differential Geometry

Multivariable Calculus and Differential Geometry Author Gerard Walschap
ISBN-10 9783110369540
Release 2015-07-01
Pages 365
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This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.

Groups and Manifolds

Groups and Manifolds Author Pietro Giuseppe Fré
ISBN-10 9783110551334
Release 2017-12-18
Pages 496
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Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.

Intermediate Calculus

Intermediate Calculus Author Murray H. Protter
ISBN-10 9781461210863
Release 2012-12-06
Pages 655
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Intermediate Calculus has been writing in one form or another for most of life. You can find so many inspiration from Intermediate Calculus also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Intermediate Calculus book for free.

Mathematical Analysis

Mathematical Analysis Author Andrew Browder
ISBN-10 9781461207153
Release 2012-12-06
Pages 335
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Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.

Multivariable Analysis

Multivariable Analysis Author Satish Shirali
ISBN-10 9780857291929
Release 2010-12-13
Pages 394
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This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are expounded in the last chapter. With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Much of the material included is published for the first time in textbook form, for example Schwarz' Theorem in Chapter 2 and double sequences and sufficient conditions for constrained extrema in Chapter 4. A wide selection of problems, ranging from simple to more challenging, are included with carefully formed solutions. Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.

Tensors and Riemannian Geometry

Tensors and Riemannian Geometry Author Nail H. Ibragimov
ISBN-10 9783110379501
Release 2015-08-31
Pages 197
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This graduate textbook begins by introducing Tensors and Riemannian Spaces, and then elaborates their application in solving second-order differential equations, and ends with introducing theory of relativity and de Sitter space. Based on 40 years of teaching experience, the author compiles a well-developed collection of examples and exercises to facilitate the reader’s learning.

A Course in Analysis

A Course in Analysis Author Niels Jacob
ISBN-10 9789813140981
Release 2016-06-29
Pages 788
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This is the second volume of "A Course in Analysis" and it is devoted to the study of mappings between subsets of Euclidean spaces. The metric, hence the topological structure is discussed as well as the continuity of mappings. This is followed by introducing partial derivatives of real-valued functions and the differential of mappings. Many chapters deal with applications, in particular to geometry (parametric curves and surfaces, convexity), but topics such as extreme values and Lagrange multipliers, or curvilinear coordinates are considered too. On the more abstract side results such as the Stone–Weierstrass theorem or the Arzela–Ascoli theorem are proved in detail. The first part ends with a rigorous treatment of line integrals. The second part handles iterated and volume integrals for real-valued functions. Here we develop the Riemann (–Darboux–Jordan) theory. A whole chapter is devoted to boundaries and Jordan measurability of domains. We also handle in detail improper integrals and give some of their applications. The final part of this volume takes up a first discussion of vector calculus. Here we present a working mathematician's version of Green's, Gauss' and Stokes' theorem. Again some emphasis is given to applications, for example to the study of partial differential equations. At the same time we prepare the student to understand why these theorems and related objects such as surface integrals demand a much more advanced theory which we will develop in later volumes. This volume offers more than 260 problems solved in complete detail which should be of great benefit to every serious student.

The Origins of Cauchy s Rigorous Calculus

The Origins of Cauchy s Rigorous Calculus Author Judith V. Grabiner
ISBN-10 9780486143743
Release 2012-05-11
Pages 272
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This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.

Lectures on the Topology of 3 Manifolds

Lectures on the Topology of 3 Manifolds Author Nikolai Saveliev
ISBN-10 9783110250367
Release 2012-01-01
Pages 218
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This textbook – now in its second revised and extended edition – introduces the topology of 3- and 4-dimensional manifolds. It also considers new developments especially related to the Heegaard Floer and contact homology. The book is accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poincaré duality on manifolds.

A Posteriori Estimates for Partial Differential Equations

A Posteriori Estimates for Partial Differential Equations Author Sergey I. Repin
ISBN-10 9783110203042
Release 2008-10-31
Pages 327
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This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis. After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by using methods of the theory of partial differential equations and functional analysis. These estimates are applicable to approximate solutions computed by various methods.

Methods of Mathematics Applied to Calculus Probability and Statistics

Methods of Mathematics Applied to Calculus  Probability  and Statistics Author Richard W. Hamming
ISBN-10 9780486138879
Release 2012-06-28
Pages 880
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This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.

Calculus of Several Variables

Calculus of Several Variables Author Serge Lang
ISBN-10 9781461210689
Release 2012-12-06
Pages 619
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This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

A Course in Analysis

A Course in Analysis Author Niels Jacob
ISBN-10 9789814689106
Release 2015-08-18
Pages 768
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Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis. Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions. Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers. Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions.

Easy Precalculus Step by Step

Easy Precalculus Step by Step Author Carolyn Wheater
ISBN-10 9780071767682
Release 2012-06-15
Pages 224
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Take it step-by-step for pre-calculus success! The quickest route to learning a subject is through a solid grounding in the basics. So what you won’t find in Easy Pre-calculus Step-by-Step is a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused exercises that are linked to core skills--enabling learners to grasp when and how to apply those techniques. This book features: Large step-by-step charts breaking down each step within a process and showing clear connections between topics and annotations to clarify difficulties Stay-in-step panels show how to cope with variations to the core steps Step-it-up exercises link practice to the core steps already presented Missteps and stumbles highlight common errors to avoid You can master pre-calculus as long as you take it Step-by-Step!

Functional Analysis

Functional Analysis Author Joseph Muscat
ISBN-10 9783319067285
Release 2014-07-23
Pages 420
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This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.

Introduction to Differential Geometry of Space Curves and Surfaces

Introduction to Differential Geometry of Space Curves and Surfaces Author Taha Sochi
ISBN-10 9781387103249
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Introduction to Differential Geometry of Space Curves and Surfaces has been writing in one form or another for most of life. You can find so many inspiration from Introduction to Differential Geometry of Space Curves and Surfaces also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Introduction to Differential Geometry of Space Curves and Surfaces book for free.