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Advanced Calculus

Advanced Calculus Author Pietro-Luciano Buono
ISBN-10 3110438216
Release 2016-09-12
Pages 313
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This textbook offers a high-level introduction to multi-variable differential calculus. By introducing differential forms early as a basic concept, the structures behind Stokes' and Gauss' theorems become much clearer. Furthermore, it offers a natural route to differential geometry.



Multivariable Calculus and Differential Geometry

Multivariable Calculus and Differential Geometry Author Gerard Walschap
ISBN-10 3110369494
Release 2015-05-15
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.



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.



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.



Functions of Several Real Variables

Functions of Several Real Variables Author Martin Moskowitz
ISBN-10 9789813100916
Release 2011-04-29
Pages 732
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This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration such as the Inverse and Implicit Function theorems, Lagrange's multiplier rule, Fubini's theorem, the change of variables formula, Green's, Stokes' and Gauss' theorems are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one result upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify matters and teach the reader how to apply these results and solve problems in mathematics, the other sciences and economics. Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Sard's theorem , the Weierstrass approximation theorem, the Fourier transform, Vector fields on spheres, Brouwer's fixed point theorem, Whitney's embedding theorem, Picard's theorem, and Hermite polynomials are discussed in stared sections.



Calculus and Analysis in Euclidean Space

Calculus and Analysis in Euclidean Space Author Jerry Shurman
ISBN-10 9783319493145
Release 2017-01-01
Pages 507
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The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skills of geometric intuition (the visual cortex being quickly instinctive) algebraic manipulation (symbol-patterns being precise and robust) incisive use of natural language (slogans that encapsulate central ideas enabling a large-scale grasp of the subject). Thinking in these ways renders mathematics coherent, inevitable, and fluid. The prerequisite is single-variable calculus, including familiarity with the foundational theorems and some experience with proofs.



Dynamics

Dynamics Author Carlos M. Roithmayr
ISBN-10 9781316060612
Release 2016-03-09
Pages
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This book is ideal for teaching students in engineering or physics the skills necessary to analyze motions of complex mechanical systems such as spacecraft, robotic manipulators, and articulated scientific instruments. Kane's method, which emerged recently, reduces the labor needed to derive equations of motion and leads to equations that are simpler and more readily solved by computer, in comparison to earlier, classical approaches. Moreover, the method is highly systematic and thus easy to teach. This book is a revision of Dynamics: Theory and Applications (1985), by T. R. Kane and D. A. Levinson, and presents the method for forming equations of motion by constructing generalized active forces and generalized inertia forces. Important additional topics include approaches for dealing with finite rotation, an updated treatment of constraint forces and constraint torques, an extension of Kane's method to deal with a broader class of nonholonomic constraint equations, and other recent advances.



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.



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.



Calculus Workbook For Dummies

Calculus Workbook For Dummies Author Mark Ryan
ISBN-10 047176275X
Release 2005-08-05
Pages 288
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Calculus Workbook For Dummies has been writing in one form or another for most of life. You can find so many inspiration from Calculus Workbook For Dummies also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Calculus Workbook For Dummies book for free.



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.



A Student s Guide to Geophysical Equations

A Student s Guide to Geophysical Equations Author William Lowrie
ISBN-10 9781139499248
Release 2011-05-26
Pages
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The advent of accessible student computing packages has meant that geophysics students can now easily manipulate datasets and gain first-hand modeling experience - essential in developing an intuitive understanding of the physics of the Earth. Yet to gain a more in-depth understanding of physical theory, and to develop new models and solutions, it is necessary to be able to derive the relevant equations from first principles. This compact, handy book fills a gap left by most modern geophysics textbooks, which generally do not have space to derive all of the important formulae, showing the intermediate steps. This guide presents full derivations for the classical equations of gravitation, gravity, tides, earth rotation, heat, geomagnetism and foundational seismology, illustrated with simple schematic diagrams. It supports students through the successive steps and explains the logical sequence of a derivation - facilitating self-study and helping students to tackle homework exercises and prepare for exams.



Introduction to Differential Geometry of Space Curves and Surfaces

Introduction to Differential Geometry of Space Curves and Surfaces Author Taha Sochi
ISBN-10 9781387103249
Release
Pages
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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.



Numerical Mathematics and Advanced Applications 2009

Numerical Mathematics and Advanced Applications 2009 Author Gunilla Kreiss
ISBN-10 3642117953
Release 2010-10-19
Pages 939
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Mathematical Thought From Ancient to Modern Times

Mathematical Thought From Ancient to Modern Times Author Morris Kline
ISBN-10 9780199770465
Release 1990-03-01
Pages 432
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The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.



Minimal Submanifolds in Pseudo Riemannian Geometry

Minimal Submanifolds in Pseudo Riemannian Geometry Author Henri Anciaux
ISBN-10 9789814291248
Release 2011
Pages 167
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Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemannian case. For the first time, this textbook provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian geometry, only assuming from the reader some basic knowledge about manifold theory. Several classical results, such as the Weierstrass representation formula for minimal surfaces, and the minimizing properties of complex submanifolds, are presented in full generality without sacrificing the clarity of exposition. Finally, a number of very recent results on the subject, including the classification of equivariant minimal hypersurfaces in pseudo-Riemannian space forms and the characterization of minimal Lagrangian surfaces in some pseudo-Khler manifolds are given.



Factorization Singular Operators and Related Problems

Factorization  Singular Operators and Related Problems Author Georgiĭ Semenovich Litvinchuk
ISBN-10 1402014074
Release 2003-07-31
Pages 333
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Proceedings of the Conference in Honour of Professor Georgii Litvinchuk