the lebesgue stieltjes integral a practical introduction undergraduate texts in mathematics

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The Lebesgue Stieltjes Integral

Author : M. Carter
ISBN : 9781461211747
Genre : Mathematics
File Size : 44. 95 MB
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While mathematics students generally meet the Riemann integral early in their undergraduate studies, those whose interests lie more in the direction of applied mathematics will probably find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral before they have acquired the necessary theoretical background. This book is aimed at exactly this group of readers. The authors introduce the Lebesgue-Stieltjes integral on the real line as a natural extension of the Riemann integral, making the treatment as practical as possible. They discuss the evaluation of Lebesgue-Stieltjes integrals in detail, as well as the standard convergence theorems, and conclude with a brief discussion of multivariate integrals and surveys of L spaces plus some applications. The whole is rounded off with exercises that extend and illustrate the theory, as well as providing practice in the techniques.

Analysis By Its History

Author : Ernst Hairer
ISBN : 9780387770314
Genre : Mathematics
File Size : 87. 15 MB
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This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

Introduction To Analytic Number Theory

Author : Tom M. Apostol
ISBN : 0387901639
Genre : Mathematics
File Size : 53. 50 MB
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"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS

Undergraduate Algebra

Author : Serge Lang
ISBN : 038797279X
Genre : Mathematics
File Size : 28. 24 MB
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The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group

Real Mathematical Analysis

Author : Charles C. Pugh
ISBN : 0387952977
Genre : Mathematics
File Size : 24. 37 MB
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Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Introduction To Calculus And Classical Analysis

Author : Omar Hijab
ISBN : 9780387693163
Genre : Mathematics
File Size : 39. 54 MB
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Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.

Computing The Continuous Discretely

Author : Matthias Beck
ISBN : 9780387461120
Genre : Mathematics
File Size : 58. 29 MB
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This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.


Author : New Zealand Mathematical Society
ISBN : UOM:39015057377932
Genre : Mathematics
File Size : 40. 99 MB
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Author :
ISBN : STANFORD:36105111050477
Genre : American literature
File Size : 52. 54 MB
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Introduction To Cryptography

Author : Johannes Buchmann
ISBN : 0387950346
Genre : Computers
File Size : 59. 87 MB
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A text written for students with only basic mathematical knowledge interested in the science of cryptography. Explains the basic methods, showing how to crack electronic codes, how to measure the efficiency and security of a code, and understand the basic techniques. DLC: Coding theory.

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