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English
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Geared toward undergraduate mathematics majors, engineering students, and future high school mathematics teachers, this text offers an understanding of the principles involved in numerical analysis. Its main theme is interpolation from the standpoint of finite differences, least squares theory, and harmonic analysis. Additional considerations include the numerical solutions of ordinary differential equations and approximations through Fourier series....
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Español
Description
En este libro se realizan ejercicios sobre los siguientes temas matemáticos:integrales definidas e indefinidasintegrales impropiasaplicaciones geométricas y teoremas notables del cálculo integral.También se presentan indicaciones teóricas iniciales para que se comprenda la realización de los ejercicios.
Author
Language
Español
Description
En este libro se realizan ejercicios sobre los siguientes temas matemáticos:derivadas y calculo diferencialaplicaciones geométricas y físicas de las derivadasteoremas notables de cálculo diferencialTambién se presentan indicaciones teóricas iniciales para que se entienda la realización de los ejercicios.
Author
Series
Language
English
Description
Practical text strikes fine balance between students' requirements for theoretical treatment and needs of practitioners, with best methods for large- and small-scale computing. Prerequisites are minimal (calculus, linear algebra, and preferably some acquaintance with computer programming). Text includes many worked examples, problems, and an extensive bibliography.
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Series
Language
English
Description
Olivier Druet is Researcher at CNRS, Ecole Normale Supérieure de Lyon. Emmanuel Hebey is Professor at Université de Cergy-Pontoise. Frédéric Robert is Associate Professor at Université de Nice Sophia-Antipolis.
Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe...
Author
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English
Description
A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Suitable for advanced undergraduates and graduate-level industrial engineers and management science majors, it proposes modeling systems in terms of their simulation, regardless of whether simulation is employed for analysis. Beginning with a view of the conditions...
Author
Language
English
Description
In this book, exercises are carried out regarding the following mathematical topics:
solving integral equations
solving integral-differential equations
calculus of variations
Initial theoretical hints are also presented to make the conduct of the exercises understandable.
Author
Series
Language
English
Description
This text offers upper-level undergraduates and graduate students a survey of practical elements of real function theory, general topology, and functional analysis. Beginning with a brief discussion of proof and definition by mathematical induction, it freely uses these notions and techniques. The maximality principle is introduced early but used sparingly; an appendix provides a more thorough treatment. The notion of convergence is stated in basic...
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English
Description
A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings. Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces....
Author
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English
Description
In this book exercises are carried out regarding the following mathematical topics:exact differential forms and primitivesconservative fields and potentialsremarkable theorems of differential analysisInitial theoretical hints are also presented to make the performance of the exercises understood.
11) Complex Analysis
Author
Language
English
Description
Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset,...
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Language
English
Description
These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing...
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English
Description
Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely reading about mathematics is no substitute for doing mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics. Journey into Mathematics offers a coherent...
Author
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English
Description
Geared toward upper-level undergraduates and graduate students, this text explores the applications of nonstandard analysis without assuming any knowledge of mathematical logic. It develops the key techniques of nonstandard analysis at the outset from a single, powerful construction; then, beginning with a nonstandard construction of the real number system, it leads students through a nonstandard treatment of the basic topics of elementary real analysis,...
Author
Language
Español
Description
En este libro se presentan los siguientes temas matemáticos:funciones reales con varias variablesfunciones implícitascálculo integral para funciones de varias variablesdesarrollos en series de potencias, series de Taylor y series de Fourieranálisis en el campo complejo
Author
Language
English
Description
Designed for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on generality and careful formulation rather than problem-solving. Its author, a member of the distinguished National Academy of Science, based this graduate-level text on the course he taught at Harvard University. Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and...
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English
Description
Numerical analysis is a subject of extreme interest to mathematicians and computer scientists, who will welcome this first inexpensive paperback edition of a groundbreaking classic text on the subject. In an introductory chapter on numerical methods and their relevance to computing, well-known mathematician Richard Hamming ("the Hamming code," "the Hamming distance," and "Hamming window," etc.), suggests that the purpose of computing is insight, not...
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Language
Français
Description
Dans ce livre, des exercices sont effectués sur les sujets mathématiques suivants :Systèmes différentiels linéaires 2x2 et 3x3Problèmes de Cauchy liés aux systèmes linéaires à coefficients constantsrecherche et détermination des valeurs propres liées aux systèmes linéairesDes indications théoriques initiales concernant la théorie des matrices sont également présentées pour rendre compréhensible la réalisation des exercices.
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Language
English
Description
This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain...
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