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Author: Marian Muresan Publisher: Springer Science & Business Media ISBN: 0387789332 Category : Mathematics Languages : en Pages : 433
Book Description
Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.
Author: Marian Muresan Publisher: Springer Science & Business Media ISBN: 0387789332 Category : Mathematics Languages : en Pages : 433
Book Description
Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.
Author: Nicholas J. Daras Publisher: Springer Nature ISBN: 3031464877 Category : Mathematics Languages : en Pages : 474
Book Description
This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Author: Elimhan Mahmudov Publisher: Springer Science & Business Media ISBN: 9491216864 Category : Mathematics Languages : en Pages : 386
Book Description
The book “Single variable Differential and Integral Calculus” is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in single variable differential and integral calculus, as well as giving application examples in important business fields. Some elementary concepts such as the power of a set, cardinality, measure theory, measurable functions are introduced. It also covers real and complex numbers, vector spaces, topological properties of sets, series and sequences of functions (including complex-valued functions and functions of a complex variable), polynomials and interpolation and extrema of functions. Although analysis is based on the single variable models and applications, theorems and examples are all set to be converted to multi variable extensions. For example, Newton, Riemann, Stieltjes and Lebesque integrals are studied together and compared.
Author: Anatoly B. Bakushinsky Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110557355 Category : Mathematics Languages : en Pages : 342
Book Description
This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. ContentsIntroductionRegularization Methods For Linear EquationsFinite Difference MethodsIterative Regularization MethodsFinite-Dimensional Iterative ProcessesVariational Inequalities and Optimization Problems
Author: Tom Leinster Publisher: Cambridge University Press ISBN: 1108962173 Category : Mathematics Languages : en Pages : 458
Book Description
The global biodiversity crisis is one of humanity's most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question 'what is diversity?' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.
Author: Marian Mureşan Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3111412040 Category : Mathematics Languages : en Pages : 692
Book Description
The book concerns with solving about 650 ordinary and partial differential equations. Each equation has at least one solution and each solution has at least one coloured graph. The coloured graphs reveal different features of the solutions. Some graphs are dynamical as for Clairaut differential equations. Thus, one can study the general and the singular solutions. All the equations are solved by Mathematica. The first chapter contains mathematical notions and results that are used later through the book. Thus, the book is self-contained that is an advantage for the reader. The ordinary differential equations are treated in Chapters 2 to 4, while the partial differential equations are discussed in Chapters 5 to 10. The book is useful for undergraduate and graduate students, for researchers in engineering, physics, chemistry, and others. Chapter 9 treats parabolic partial differential equations while Chapter 10 treats third and higher order nonlinear partial differential equations, both with modern methods. Chapter 10 discusses the Korteweg-de Vries, Dodd-Bullough-Mikhailov, Tzitzeica-Dodd-Bullough, Benjamin, Kadomtsev-Petviashvili, Sawada-Kotera, and Kaup-Kupershmidt equations.
Author: Ronald L. Graham Publisher: Addison-Wesley Professional ISBN: 0134389980 Category : Computers Languages : en Pages : 811
Book Description
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
Author: Sacha Friedli Publisher: Cambridge University Press ISBN: 1107184827 Category : Mathematics Languages : en Pages : 643
Book Description
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author: Henri Cohen Publisher: American Mathematical Soc. ISBN: 0821849476 Category : Forms (Mathematics). Languages : en Pages : 700
Book Description
The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.
Author: Ernst Hairer Publisher: Springer Science & Business Media ISBN: 0387770364 Category : Mathematics Languages : en Pages : 390
Book Description
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.
Author: Marian Muresan
Author: Marian Muresan
Author: Nicholas J. Daras
Author: Elimhan Mahmudov
Author: Anatoly B. Bakushinsky
Author: Tom Leinster
Author: Marian Mureşan
Author: Ronald L. Graham
Author: Sacha Friedli
Author: Henri Cohen
Author: Ernst Hairer