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The History And Mathematics Of Integration In Finite Terms
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Book Synopsis The History and Mathematics of Integration in Finite Terms by : Laurence Eric Penn
Download or read book The History and Mathematics of Integration in Finite Terms written by Laurence Eric Penn and published by . This book was released on 1983 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integration in Finite Terms by : Joseph Fels Ritt
Download or read book Integration in Finite Terms written by Joseph Fels Ritt and published by . This book was released on 1948 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an account of Liouville's theory of integration in finite terms -- his determination of the form which the integral of an algebraic function must have when the integral can be expressed with the operations of elementary mathematical analysis, carried out a finite number of times -- and the work of some of his followers.
Book Synopsis Integration in Finite Terms: Fundamental Sources by : Clemens G. Raab
Download or read book Integration in Finite Terms: Fundamental Sources written by Clemens G. Raab and published by Springer Nature. This book was released on 2022-06-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
Book Synopsis The Integration of Functions of a Single Variable by : Godfrey Harold Hardy
Download or read book The Integration of Functions of a Single Variable written by Godfrey Harold Hardy and published by . This book was released on 1928 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Integration of Functions of a Single Variable by Godfrey Hardy Harold, first published in 1916, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
Book Synopsis Integration in Finite Terms by : Joseph Fels Ritt
Download or read book Integration in Finite Terms written by Joseph Fels Ritt and published by . This book was released on 1984 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Oxford Handbook of the History of Mathematics by : Eleanor Robson
Download or read book The Oxford Handbook of the History of Mathematics written by Eleanor Robson and published by Oxford University Press on Demand. This book was released on 2009 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook explores the history of mathematics, addressing what mathematics has been and what it has meant to practise it. 36 self-contained chapters provide a fascinating overview of 5000 years of mathematics and its key cultures for academics in mathematics, historians of science, and general historians.
Book Synopsis Integration in Finite Terms with Elementary Functions and Dilogarithms by : Mohamed Jamil Baddoura
Download or read book Integration in Finite Terms with Elementary Functions and Dilogarithms written by Mohamed Jamil Baddoura and published by . This book was released on 1994 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical and Modern Integration Theories by : Ivan N. Pesin
Download or read book Classical and Modern Integration Theories written by Ivan N. Pesin and published by Academic Press. This book was released on 2014-07-03 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical and Modern Integration Theories discusses classical integration theory, particularly that part of the theory directly associated with the problems of area. The book reviews the history and the determination of primitive functions, beginning from Cauchy to Daniell. The text describes Cauchy's definition of an integral, Riemann's definition of the R-integral, the upper and lower Darboux integrals. The book also reviews the origin of the Lebesgue-Young integration theory, and Borel's postulates that define measures of sets. W.H. Young's work provides a construction of the integral equivalent to Lebesque's construction with a different generalization of integrals leading to different approaches in solutions. Young's investigations aim at generalizing the notion of length for arbitrary sets by means of a process which is more general than Borel's postulates. The text notes that the Lebesgue measure is the unique solution of the measure problem for the class of L-measurable sets. The book also describes further modifications made into the Lebesgue definition of the integral by Riesz, Pierpont, Denjoy, Borel, and Young. These modifications bring the Lebesgue definition of the integral closer to the Riemann or Darboux definitions, as well as to have it associated with the concepts of classical analysis. The book can benefit mathematicians, students, and professors in calculus or readers interested in the history of classical mathematics.
Book Synopsis A History of Mathematical Impossibility by : Jesper Lützen
Download or read book A History of Mathematical Impossibility written by Jesper Lützen and published by Oxford University Press. This book was released on 2023-01-26 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat's last theorem, and the impossibility of proving the parallel postulate from the other axioms of Euclidean geometry. This book tells the history of these and many other impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square. Lützen argues that the role of impossibility results have changed over time. At first, they were considered rather unimportant meta-statements concerning mathematics but gradually they obtained the role of important proper mathematical results that can and should be proved. While mathematical impossibility proofs are more rigorous than impossibility arguments in other areas of life, mathematicians have employed great ingenuity to circumvent impossibilities by changing the rules of the game. For example, complex numbers were invented in order to make impossible equations solvable. In this way, impossibilities have been a strong creative force in the development of mathematics, mathematical physics, and social science.
Book Synopsis Deleuze and the History of Mathematics by : Simon Duffy
Download or read book Deleuze and the History of Mathematics written by Simon Duffy and published by A&C Black. This book was released on 2013-05-09 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. In the wake of Alain Badiou's recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze's work, Simon B.Duffy offers a robust defence of the structure of Deleuze's philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze's seemingly incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze's philosophy, rebuffing the recent challenges against it.
Book Synopsis The Real Numbers and Real Analysis by : Ethan D. Bloch
Download or read book The Real Numbers and Real Analysis written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2011-05-14 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
Book Synopsis Excursions in the History of Mathematics by : Israel Kleiner
Download or read book Excursions in the History of Mathematics written by Israel Kleiner and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.
Book Synopsis Introduction to Real Analysis by : William C. Bauldry
Download or read book Introduction to Real Analysis written by William C. Bauldry and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to real analysis and its connectionto elementary calculus Bridging the gap between the development and history of realanalysis, Introduction to Real Analysis: An EducationalApproach presents a comprehensive introduction to real analysiswhile also offering a survey of the field. With its balance ofhistorical background, key calculus methods, and hands-onapplications, this book provides readers with a solid foundationand fundamental understanding of real analysis. The book begins with an outline of basic calculus, including aclose examination of problems illustrating links and potentialdifficulties. Next, a fluid introduction to real analysis ispresented, guiding readers through the basic topology of realnumbers, limits, integration, and a series of functions in naturalprogression. The book moves on to analysis with more rigorousinvestigations, and the topology of the line is presented alongwith a discussion of limits and continuity that includes unusualexamples in order to direct readers' thinking beyond intuitivereasoning and on to more complex understanding. The dichotomy ofpointwise and uniform convergence is then addressed and is followedby differentiation and integration. Riemann-Stieltjes integrals andthe Lebesgue measure are also introduced to broaden the presentedperspective. The book concludes with a collection of advancedtopics that are connected to elementary calculus, such as modelingwith logistic functions, numerical quadrature, Fourier series, andspecial functions. Detailed appendices outline key definitions and theorems inelementary calculus and also present additional proofs, projects,and sets in real analysis. Each chapter references historicalsources on real analysis while also providing proof-orientedexercises and examples that facilitate the development ofcomputational skills. In addition, an extensive bibliographyprovides additional resources on the topic. Introduction to Real Analysis: An Educational Approach isan ideal book for upper- undergraduate and graduate-level realanalysis courses in the areas of mathematics and education. It isalso a valuable reference for educators in the field of appliedmathematics.
Book Synopsis Symbolic Integration I by : Manuel Bronstein
Download or read book Symbolic Integration I written by Manuel Bronstein and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume in the series "Algorithms and Computation in Mathematics", is destined to become the standard reference work in the field. Manuel Bronstein is the number-one expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.
Book Synopsis Mastering the History of Pure and Applied Mathematics by : Toke Knudsen
Download or read book Mastering the History of Pure and Applied Mathematics written by Toke Knudsen and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-06-04 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lützen. In a career that spans more than four decades, Professor Lützen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lützen's work. In addition to this noteworthy scholarship, Professor Lützen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lützen—as a scholarly role model, mentor, colleague, and friend.
Book Synopsis Joseph Liouville 1809–1882 by : Jesper Lützen
Download or read book Joseph Liouville 1809–1882 written by Jesper Lützen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scientific biography of the mathematician Joseph Liouville is divided into two parts. The first part is a chronological account of Liouville's career including a description of the institutions he worked in, his relations with his teachers, colleagues and students, and the historical context of his works. It portrays the French scientific community in a period when Germany and England had surpassed France as the leading nations in mathematics and physics. The second part of the book gives a detailed analysis of Liouville's major contributions to mathematics and mechanics. The gradual development of Liouville's ideas, as reflected in his publications and notebooks, are related to the works of his predecessors and his contemporaries as well as to later developments in the field. On the basis of Liouville's unpublished notes the book reconstructs Liouville's hitherto unknown theories of stability of rotating masses of fluid, potential theory, Galois theory and electrodynamics. It also incorporates valuable added information from Liouville's notes regarding his works on differentiation of arbitrary order, integration in finite terms, Sturm-Liouville theory, transcendental numbers, doubly periodic functions, geometry and mechanics.
Book Synopsis The Theory of Integration by : Laurence Chisholm Young
Download or read book The Theory of Integration written by Laurence Chisholm Young and published by . This book was released on 1927 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: