improper riemann integrals

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Improper Riemann Integrals

Author : Ioannis Markos Roussos
ISBN : 9781466588080
Genre : Mathematics
File Size : 85. 47 MB
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Improper Riemann Integrals is the first book to collect classical and modern material on the subject for undergraduate students. The book gives students the prerequisites and tools to understand the convergence, principal value, and evaluation of the improper/generalized Riemann integral. It also illustrates applications to science and engineering problems. The book contains the necessary background, theorems, and tools, along with two lists of the most important integrals and sums computed in the text. Numerous examples at various levels of difficulty illustrate the concepts and theorems. The book uses powerful tools of real and complex analysis not only to compute the examples and solve the problems but also to justify that the computation methods are legitimate. Enriched with many examples, applications, and problems, this book helps students acquire a deeper understanding of the subject, preparing them for further study. It shows how to solve the integrals without exclusively relying on tables and computer packages.

Measure Theory

Author : Vladimir I. Bogachev
ISBN : 9783540345145
Genre : Mathematics
File Size : 63. 61 MB
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This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.

The Generalized Riemann Integral

Author : Robert M. McLeod
ISBN : UCAL:B4406224
Genre : Mathematics
File Size : 82. 41 MB
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Mathematical Analysis

Author : Tom M. Apostol
ISBN : 0201002884
Genre : Mathematics
File Size : 25. 41 MB
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It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

Fundamental Ideas Of Analysis

Author : Michael C. Reed
ISBN : 0471159964
Genre : Mathematics
File Size : 40. 99 MB
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The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.

Introduction To Real Analysis

Author : Manfred Stoll
ISBN : 0321046250
Genre : Mathematics
File Size : 23. 62 MB
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This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces. The Real Number System; Sequence Of Real Numbers; Structure Of Point Sets; Limits And Continuity; Differentiation; The Riemann And Riemann-Stieltjes Integral; Series of Real Numbers; Sequences And Series Of Functions; Orthogonal Functions And Fourier Series; Lebesgue Measure And Integration; Logic and Proofs; Propositions and Connectives For all readers interested in real analysis.

Analytic Functions And Distributions In Physics And Engineering

Author : Bernard W. Roos
ISBN : UOM:39015004539618
Genre : Mathematics
File Size : 31. 90 MB
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Basic Real Analysis

Author : Houshang H. Sohrab
ISBN : 9781493918416
Genre : Mathematics
File Size : 56. 57 MB
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This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews

Advanced Calculus With Applications In Statistics

Author : André I. Khuri
ISBN : UOM:39076001371793
Genre : Mathematics
File Size : 59. 9 MB
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Designed to help motivate the learning of advanced calculus by demonstrating its relevance in the field of statistics. Features detailed coverage of optimization techniques and their applications in statistics. Introduces approximation theory. Each chapter contains a significant amount of examples and exercises as well as additional reading lists.


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ISBN : CORNELL:31924099658720
Genre : Mathematics
File Size : 50. 76 MB
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