Course In Analysis, A - Vol. Iv: Fourier Analysis, Ordinary Differential Equations, Calculus Of Variations

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Publisher : World Scientific
ISBN 13 : 9813273534
Total Pages : 768 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Course In Analysis, A - Vol. Iv: Fourier Analysis, Ordinary Differential Equations, Calculus Of Variations by : Niels Jacob

Download or read book Course In Analysis, A - Vol. Iv: Fourier Analysis, Ordinary Differential Equations, Calculus Of Variations written by Niels Jacob and published by World Scientific. This book was released on 2018-07-19 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindelöf and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail.The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.

A Course in Analysis

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Publisher : World Scientific Publishing Company
ISBN 13 : 9789813273511
Total Pages : 0 pages
Book Rating : 4.2/5 (735 download)

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Book Synopsis A Course in Analysis by : Niels Jacob

Download or read book A Course in Analysis written by Niels Jacob and published by World Scientific Publishing Company. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures. Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindelöf and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows. Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail. The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.

A Course in Analysis

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Publisher : World Scientific Publishing Company
ISBN 13 : 9789811216336
Total Pages : 0 pages
Book Rating : 4.2/5 (163 download)

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Book Synopsis A Course in Analysis by : Niels Jacob

Download or read book A Course in Analysis written by Niels Jacob and published by World Scientific Publishing Company. This book was released on 2020-01-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an advanced textbook and a reference text in functional analysis in the wide sense. It provides advanced undergraduate and graduate students with a coherent introduction to the field, i.e. the basic principles, and leads them to more demanding topics such as the spectral theorem, Choquet theory, interpolation theory, analysis of operator semigroups, Hilbert-Schmidt operators and Hille-Tamarkin operators, topological vector spaces and distribution theory, fundamental solutions, or the Schwartz kernel theorem.All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions.Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies.

A First Course in Fourier Analysis

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Publisher : Cambridge University Press
ISBN 13 : 1139469037
Total Pages : 39 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis A First Course in Fourier Analysis by : David W. Kammler

Download or read book A First Course in Fourier Analysis written by David W. Kammler and published by Cambridge University Press. This book was released on 2008-01-17 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions

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Publisher : World Scientific
ISBN 13 : 9811215510
Total Pages : 854 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions by : Niels Jacob

Download or read book Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions written by Niels Jacob and published by World Scientific. This book was released on 2020-01-22 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an advanced textbook and a reference text in functional analysis in the wide sense. It provides advanced undergraduate and graduate students with a coherent introduction to the field, i.e. the basic principles, and leads them to more demanding topics such as the spectral theorem, Choquet theory, interpolation theory, analysis of operator semigroups, Hilbert-Schmidt operators and Hille-Tamarkin operators, topological vector spaces and distribution theory, fundamental solutions, or the Schwartz kernel theorem.All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions.Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies.

A Course in Mathematical Analysis Volume 3

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Publisher : Courier Corporation
ISBN 13 : 0486446522
Total Pages : 756 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Course in Mathematical Analysis Volume 3 by : Edouard Goursat

Download or read book A Course in Mathematical Analysis Volume 3 written by Edouard Goursat and published by Courier Corporation. This book was released on 2013-04-04 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and differential equations. Volume 3 surveys variations of solutions and partial differential equations of the second order and integral equations and calculus of variations.

Advanced Mathematics for Engineers and Physicists

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Publisher : Springer Nature
ISBN 13 : 3031215028
Total Pages : 833 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Advanced Mathematics for Engineers and Physicists by : Sever Angel Popescu

Download or read book Advanced Mathematics for Engineers and Physicists written by Sever Angel Popescu and published by Springer Nature. This book was released on 2023-01-25 with total page 833 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to be an introductory course to some basic chapters of Advanced Mathematics for Engineering and Physics students, researchers in different branches of Applied Mathematics and anyone wanting to improve their mathematical knowledge by a clear, live, self-contained and motivated text. Here, one can find different topics, such as differential (first order or higher order) equations, systems of differential equations, Fourier series, Fourier and Laplace transforms, partial differential equations, some basic facts and applications of the calculus of variations and, last but not least, an original and more intuitive introduction to probability theory. All these topics are carefully introduced, with complete proofs, motivations, examples, applications, problems and exercises, which are completely solved at the end of the book. We added a generous supplementary material (11.1) with a self-contained and complete introduction to normed, metric and Hilbert spaces. Since we used some topics from complex function theory, we also introduced in Chapter 11 a section (11.2) with the basic facts in this important field. What a reader needs for a complete understanding of this book? For a deep understanding of this book, it is required to take a course in undergraduate calculus and linear algebra. We mostly tried to use the engineering intuition instead of insisting on mathematical tricks. The main feature of the material presented here is its clarity, motivation and the genuine desire of the authors to make extremely transparent the "mysterious" mathematical tools that are used to describe and organize the great variety of impressions that come to the searching mind, from the infinite complexity of Nature. The book is recommended not only to engineering and physics students or researchers but also to junior students in mathematics because it shows the connection between pure mathematics and physical phenomena, which always supply motivations for mathematical discoveries.

Course In Analysis, A -

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Publisher :
ISBN 13 : 9789814689939
Total Pages : 769 pages
Book Rating : 4.6/5 (899 download)

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Book Synopsis Course In Analysis, A - by : Niels Jacob

Download or read book Course In Analysis, A - written by Niels Jacob and published by . This book was released on 2015 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A First Course in Partial Differential Equations

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Publisher : Courier Corporation
ISBN 13 : 0486132048
Total Pages : 482 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis A First Course in Partial Differential Equations by : H. F. Weinberger

Download or read book A First Course in Partial Differential Equations written by H. F. Weinberger and published by Courier Corporation. This book was released on 2012-04-20 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.

Advanced Calculus

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Publisher : World Scientific Publishing Company
ISBN 13 : 9814583952
Total Pages : 596 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Advanced Calculus by : Lynn Harold Loomis

Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

A Course in Mathematical Analysis: pt.2. Differential equations. [c1917

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Publisher :
ISBN 13 :
Total Pages : 628 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis A Course in Mathematical Analysis: pt.2. Differential equations. [c1917 by : Edouard Goursat

Download or read book A Course in Mathematical Analysis: pt.2. Differential equations. [c1917 written by Edouard Goursat and published by . This book was released on 1916 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spaces: An Introduction to Real Analysis

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Publisher : American Mathematical Soc.
ISBN 13 : 1470440628
Total Pages : 369 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Spaces: An Introduction to Real Analysis by : Tom L. Lindstrøm

Download or read book Spaces: An Introduction to Real Analysis written by Tom L. Lindstrøm and published by American Mathematical Soc.. This book was released on 2017-11-28 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.

Engineering Mathematics Vol. One 4Th Ed.

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Publisher : PHI Learning Pvt. Ltd.
ISBN 13 : 812033616X
Total Pages : 690 pages
Book Rating : 4.1/5 (23 download)

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Book Synopsis Engineering Mathematics Vol. One 4Th Ed. by : S. S. Sastry

Download or read book Engineering Mathematics Vol. One 4Th Ed. written by S. S. Sastry and published by PHI Learning Pvt. Ltd.. This book was released on 2008-07-30 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised fourth edition begins with a detailed discussion of higher algebra, geometry, vectors and complex numbers. The text then goes on to give an indepth analysis of geometry, vectors and complex numbers; applications of differential calculus; integration; and ordinary differential equations of the first order. It concludes with a thorough treatment of numerical methods.

A Course in Analysis

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Publisher : World Scientific Publishing Company
ISBN 13 : 9814689106
Total Pages : 768 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis A Course in Analysis by : Niels Jacob

Download or read book A Course in Analysis written by Niels Jacob and published by World Scientific Publishing Company. This book was released on 2015-08-18 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course on Rough Paths

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Publisher : Springer Nature
ISBN 13 : 3030415562
Total Pages : 346 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis A Course on Rough Paths by : Peter K. Friz

Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH

Fourier Series and Orthogonal Functions

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Publisher : Courier Corporation
ISBN 13 : 0486140733
Total Pages : 436 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Fourier Series and Orthogonal Functions by : Harry F. Davis

Download or read book Fourier Series and Orthogonal Functions written by Harry F. Davis and published by Courier Corporation. This book was released on 2012-09-05 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging. The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics. Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.

The Philosophy of the Upanishads

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Publisher : New York : Dover Publications
ISBN 13 :
Total Pages : 474 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis The Philosophy of the Upanishads by : Paul Deussen

Download or read book The Philosophy of the Upanishads written by Paul Deussen and published by New York : Dover Publications. This book was released on 1906 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: