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 769 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.
Download or read book Course In Analysis A Volume I Introductory Calculus Analysis Of Functions Of One Real Variable written by Niels Jacob and published by World Scientific Publishing Company. This book was released on 2015-08-18 with total page 769 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.
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.
Download or read book Course In Analysis A Vol Ii Differentiation And Integration Of Functions Of Several Variables Vector Calculus written by Niels Jacob and published by World Scientific Publishing Company. This book was released on 2016-06-29 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The authors give many examples, illustrations and exercises to help students digest the theory and they employ use of clear and neat notation throughout. I really appreciate their selection of exercises, since many of the problems develop simple techniques to be used later in the book or make connections of analysis with other parts of mathematics. There are also solutions to all of the exercises in the back of the book. As in the first volume there are some real gems in volume II. A Course in Analysis seems to be full of these little gems where the authors use the material or ask the readers to use the material to obtain results or examples that the reader will certainly see again in another context later in their studies of mathematics. Generally, the quality of exposition in both of the first two volumes is very high. I recommend these books.' (See Full Review)MAA ReviewsThis is the second volume of 'A Course in Analysis' and it is devoted to the study of mappings between subsets of Euclidean spaces. The metric, hence the topological structure is discussed as well as the continuity of mappings. This is followed by introducing partial derivatives of real-valued functions and the differential of mappings. Many chapters deal with applications, in particular to geometry (parametric curves and surfaces, convexity), but topics such as extreme values and Lagrange multipliers, or curvilinear coordinates are considered too. On the more abstract side results such as the Stone-Weierstrass theorem or the Arzela-Ascoli theorem are proved in detail. The first part ends with a rigorous treatment of line integrals.The second part handles iterated and volume integrals for real-valued functions. Here we develop the Riemann (-Darboux-Jordan) theory. A whole chapter is devoted to boundaries and Jordan measurability of domains. We also handle in detail improper integrals and give some of their applications.The final part of this volume takes up a first discussion of vector calculus. Here we present a working mathematician's version of Green's, Gauss' and Stokes' theorem. Again some emphasis is given to applications, for example to the study of partial differential equations. At the same time we prepare the student to understand why these theorems and related objects such as surface integrals demand a much more advanced theory which we will develop in later volumes.This volume offers more than 260 problems solved in complete detail which should be of great benefit to every serious student.
Download or read book Course In Analysis A Vol Iii Measure And Integration Theory Complex valued Functions Of A Complex Variable written by Niels Jacob and published by World Scientific Publishing Company. This book was released on 2017-06-29 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'It is a great book for a first year (US) graduate student. One of the nice features of the book is that the book contains full solutions for all of the problems which make it useful as reference for self-study or qualifying exam prep.' (See Full Review)MAA ReviewsIn this third volume of 'A Course in Analysis', two topics indispensible for every mathematician are treated: Measure and Integration Theory; and Complex Function Theory.In the first part measurable spaces and measure spaces are introduced and Caratheodory's extension theorem is proved. This is followed by the construction of the integral with respect to a measure, in particular with respect to the Lebesgue measure in the Euclidean space. The Radon-Nikodym theorem and the transformation theorem are discussed and much care is taken to handle convergence theorems with applications, as well as Lp-spaces.Integration on product spaces and Fubini's theorem is a further topic as is the discussion of the relation between the Lebesgue integral and the Riemann integral. In addition to these standard topics we deal with the Hausdorff measure, convolutions of functions and measures including the Friedrichs mollifier, absolutely continuous functions and functions of bounded variation. The fundamental theorem of calculus is revisited, and we also look at Sard's theorem or the Riesz-Kolmogorov theorem on pre-compact sets in Lp-spaces.The text can serve as a companion to lectures, but it can also be used for self-studying. This volume includes more than 275 problems solved completely in detail which should help the student further.
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: This volume covers the contents of two typical modules in an undergraduate mathematics course: part 1 - introductory calculus and part 2 - analysis of functions of one variable. The book contains 360 problems with complete solutions
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.
Download or read book Advanced Calculus Revised Edition written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 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.
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.
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:
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 384 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.
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.
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.
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
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.
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:
Download or read book History of the Theory of Numbers Volume I written by Leonard Eugene Dickson and published by Courier Corporation. This book was released on 2005-06-03 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1st volume in the series History of the Theory of Numbers presents the material related to the subjects of divisibility and primality. This series is the work of a distinguished mathematician who taught at the University of Chicago for 4 decades and is celebrated for his many contributions to number theory and group theory. 1919 edition.
