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Foundations of Differential Calculus

Foundations of Differential Calculus Author Euler
ISBN-10 9780387226453
Release 2006-05-04
Pages 194
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The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.



Local Analysis

Local Analysis Author Carl-Heinz Scriba
ISBN-10 3055014472
Release 1994
Pages 240
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A detailed introduction to those parts of finite-dimensional real calculus that deal with multidimensional differentiation and only one-dimensional integration. Uses the concepts of function and derivative to bypass coordinates and dependent variables. For undergraduate students of mathematics, physics, or engineering who are familiar with one-dimensional calculus and linear algebra. Annotation copyright by Book News, Inc., Portland, OR



Local Analysis Part A Foundations and Differential Calculus Part B First Order Differential Equations and Differential Forms

Local Analysis  Part A  Foundations and Differential Calculus  Part B  First Order Differential Equations and Differential Forms Author Carl-Heinz Schriba
ISBN-10 352740063X
Release 1996-10-28
Pages 591
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The first part of the "Local Analysis" textbook is self-consistent & provides a detailed introduction to those parts of finite-dimensional real calculus which go with multi-dimensional differentiation & only one-dimensional integration. The second part is based upon the first one & gives a detailed introduction to the initial value problems of certain systems of first order ordinary & partial differential equations as well as to the theory of differential forms.



Introduction to Differential Calculus

Introduction to Differential Calculus Author Ulrich L. Rohde
ISBN-10 9781118130148
Release 2012-01-12
Pages 736
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Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications. The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of theories, methods, and applications in differential calculus, including: Concepts of function, continuity, and derivative Properties of exponential and logarithmic function Inverse trigonometric functions and their properties Derivatives of higher order Methods to find maximum and minimum values of a function Hyperbolic functions and their properties Readers are equipped with the necessary tools to quickly learn how to understand a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. Introduction to Differential Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals alike who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.



Differential Calculus and Its Applications

Differential Calculus and Its Applications Author Michael J. Field
ISBN-10 9780486298849
Release 2013-04-10
Pages 336
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Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.



Introduction to Analysis of the Infinite

Introduction to Analysis of the Infinite Author Leonhard Euler
ISBN-10 9781461210214
Release 2012-12-06
Pages 327
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From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."



Differential and Integral Calculus

Differential and Integral Calculus Author Richard Courant
ISBN-10 9781118031490
Release 2011-08-15
Pages 640
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Differential and Integral Calculus has been writing in one form or another for most of life. You can find so many inspiration from Differential and Integral Calculus also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Differential and Integral Calculus book for free.



Foundations of Iso Differential Calculus Volume 5

Foundations of Iso Differential Calculus  Volume 5 Author Svetlin Georgiev
ISBN-10 1634821912
Release 2015-01-01
Pages 253
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This book is intended for readers who have had a course in iso-differential calculus and theory of probability. It can be used for a senior undergraduate course.



Foundations of Iso differential Calculus

Foundations of Iso differential Calculus Author Svetlin Georgiev
ISBN-10 1634850211
Release 2016-04-01
Pages 350
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This book is intended for readers who have had a course in theory of functions, isodifferential calculus and it can also be used for a senior undergraduate course. Chapter One deals with the infinite sets. We introduce the main operations on the sets. They are considered as the one-to-one correspondences, the denumerable sets and the nondenumerable sets, and their properties. Chapter Two introduces the point sets. They are defined as the limit points, the interior points, the open sets, and the closed sets. Also included are the structure of the bounded open and the closed sets, and an examination of some of their main properties. Chapter Three describes the measurable sets. They are defined and deducted as the main properties of the measure of a bounded open set, a bounded closed set, and the outer and the inner measures of a bounded set. Chapter Four is devoted to the theory of the measurable iso-functions. They are defined as the main classes of the measurable iso-functions and their associated properties are defined as well. In Chapter Five, the Lebesgue iso-integral of a bounded iso-function continue the discussion of the book. Their main properties are given. In Chapter Six the square iso-summable iso-functions, the iso-orthogonal systems, the iso-spaces Lp and l p, p > 1 are studied. The Stieltjes iso-integral and its properties are investigated in Chapter Seven.



The absolute differential calculus calculus of tensors

The absolute differential calculus  calculus of tensors Author Tullio Levi-Civita
ISBN-10 UCSC:32106002334958
Release 1961
Pages 452
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The absolute differential calculus calculus of tensors has been writing in one form or another for most of life. You can find so many inspiration from The absolute differential calculus calculus of tensors also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The absolute differential calculus calculus of tensors book for free.



Calculus Without Derivatives

Calculus Without Derivatives Author Jean-Paul Penot
ISBN-10 9781461445388
Release 2012-11-09
Pages 524
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Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.



Shapes and Geometries

Shapes and Geometries Author M. C. Delfour
ISBN-10 9780898719369
Release 2011-01-01
Pages 622
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Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.



The Convenient Setting of Global Analysis

The Convenient Setting of Global Analysis Author Andreas Kriegl
ISBN-10 9780821807804
Release 1997
Pages 618
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This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Frechet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.



Foundations of Analysis

Foundations of Analysis Author Edmund Landau
ISBN-10 9780821826935
Release 1966-01-01
Pages 136
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Certainly no clearer treatment of the foundations of the number system can be offered ... one can only be thankful to the author for this fundamental piece of exposition, which is alive with his vitality and genius. --American Mathematical Monthly Why does $2 \times 2 = 4$? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, what are numbers? And why do they have the properties we attribute to them? Thanks to the genius of Dedekind, Cantor, Peano, Frege, and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis answers these important questions.



Foundations of Differentiable Manifolds and Lie Groups

Foundations of Differentiable Manifolds and Lie Groups Author Frank W. Warner
ISBN-10 9781475717990
Release 2013-11-11
Pages 276
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Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.



Advanced Calculus

Advanced Calculus Author Harold M. Edwards
ISBN-10 9780817684129
Release 2013-11-10
Pages 508
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In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes’ theorem. The result is genuine mathematics, both in spirit and content, and an exciting choice for an honors or graduate course or indeed for any mathematician in need of a refreshingly informal and flexible reintroduction to the subject. For all these potential readers, the author has made the approach work in the best tradition of creative mathematics. This affordable softcover reprint of the 1994 edition presents the diverse set of topics from which advanced calculus courses are created in beautiful unifying generalization. The author emphasizes the use of differential forms in linear algebra, implicit differentiation in higher dimensions using the calculus of differential forms, and the method of Lagrange multipliers in a general but easy-to-use formulation. There are copious exercises to help guide the reader in testing understanding. The chapters can be read in almost any order, including beginning with the final chapter that contains some of the more traditional topics of advanced calculus courses. In addition, it is ideal for a course on vector analysis from the differential forms point of view. The professional mathematician will find here a delightful example of mathematical literature; the student fortunate enough to have gone through this book will have a firm grasp of the nature of modern mathematics and a solid framework to continue to more advanced studies. The most important feature...is that it is fun—it is fun to read the exercises, it is fun to read the comments printed in the margins, it is fun simply to pick a random spot in the book and begin reading. This is the way mathematics should be presented, with an excitement and liveliness that show why we are interested in the subject. —The American Mathematical Monthly (First Review) An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically rigorous, entertaining but serious. Remarkable diverse applications, physical and mathematical. —The American Mathematical Monthly (1994) Based on the Second Edition



The Foundations of Business Analysis

The Foundations of Business Analysis Author M. Douglas Berg
ISBN-10 1465222030
Release 2013-05-15
Pages 149
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The Foundations of Business Analysis has been writing in one form or another for most of life. You can find so many inspiration from The Foundations of Business Analysis also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Foundations of Business Analysis book for free.