A Brief Course in the Theory of Functions of a Real Variable PDF Download
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Author: Boris Zakharovich Vulikh
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Author: John Meigs Hubbell Olmsted
Publisher:
ISBN:
Category : Functions of real variables
Languages : en
Pages : 646
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Book Description
Author: James Pierpont
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 674
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Book Description
Author: R. L. Jeffery
Publisher: Toronto, Ont. : University of Toronto Press
ISBN:
Category : Mathematics
Languages : en
Pages : 252
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Book Description
Author: Lawrence Murray Graves
Publisher:
ISBN:
Category : Functions of real variables
Languages : en
Pages : 400
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Book Description
Author: Boris Zakharovich Vulikh
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Author: Ernest William Hobson
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 764
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Book Description
Author: Niels Jacob
Publisher: World Scientific Publishing Company
ISBN: 9789813273511
Category : Calculus
Languages : en
Pages : 0
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Book Description
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.
Author: Ralph Cooper
Publisher:
ISBN:
Category : Functions of real variables
Languages : en
Pages : 248
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Book Description
Author: Heinrich Burkhardt
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 458
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Book Description
Author: Miklós Laczkovich
Publisher: Springer
ISBN: 149397369X
Category : Mathematics
Languages : en
Pages : 396
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Book Description
This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Together, these volumes form the first English edition of the popular Hungarian original, Valós Analízis I & II, based on courses taught by the authors at Eötvös Loránd University, Hungary, for more than 30 years. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems. Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading. Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics. Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. By developing the student’s intuition throughout, many definitions and results become motivated by insights from their context.
