An Introduction to Capstone in Applied Analysis: A Fundamental Guide for Students and Instructors, Narayan Thapa

Автор: Jan Vries
Название: Topological Dynamical Systems: An Introduction to the Dynamics of Continuous Mappings
ISBN: 3110340739 ISBN-13(EAN): 9783110340730
Издательство: Walter de Gruyter
Цена: 148700.00 T
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Описание: There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.

Автор: David L. Chopp
Название: Introduction to High Performance Scientific Computing
ISBN: 1611975638 ISBN-13(EAN): 9781611975635
Издательство: Mare Nostrum (Eurospan)
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Цена: 76910.00 T
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Описание: Based on a course developed by the author, Introduction to High Performance Scientific Computing introduces methods for adding parallelism to numerical methods for solving differential equations. It contains exercises and programming projects that facilitate learning as well as examples and discussions based on the C programming language, with additional comments for those already familiar with C . The text provides an overview of concepts and algorithmic techniques for modern scientific computing and is divided into six self-contained parts that can be assembled in any order to create an introductory course using available computer hardware.Part I introduces the C programming language for those not already familiar with programming in a compiled language. Part II describes parallelism on shared memory architectures using OpenMP. Part III details parallelism on computer clusters using MPI for coordinating a computation. Part IV demonstrates the use of graphical programming units (GPUs) to solve problems using the CUDA language for NVIDIA graphics cards. Part V addresses programming on GPUs for non-NVIDIA graphics cards using the OpenCL framework. Finally, Part VI contains a brief discussion of numerical methods and applications, giving the reader an opportunity to test the methods on typical computing problems. Introduction to High Performance Scientific Computing is intended for advanced undergraduate or beginning graduate students who have limited exposure to programming or parallel programming concepts. Extensive knowledge of numerical methods is not assumed. The material can be adapted to the available computational hardware, from OpenMP on simple laptops or desktops to MPI on computer clusters or CUDA and OpenCL for computers containing NVIDIA or other graphics cards. Experienced programmers unfamiliar with parallel programming will benefit from comparing the various methods to determine the type of parallel programming best suited for their application. The book can be used for courses on parallel scientific computing, high performance computing, and numerical methods for parallel computing.

Автор: Daniel J. Arrigo
Название: An Introduction to Partial Differential Equations
ISBN: 1681732548 ISBN-13(EAN): 9781681732541
Издательство: Mare Nostrum (Eurospan)
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Цена: 72070.00 T
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Описание: Provides an introduction to methods for solving partial differential equations (PDEs). After the introduction of the main four PDEs that could be considered the cornerstone of Applied Mathematics, the reader is introduced to a variety of PDEs that come from a variety of fields in the Natural Sciences and Engineering and is a springboard into this wonderful subject.

Автор: David Nualart, Eulalia Nualart
Название: Introduction to Malliavin Calculus
ISBN: 1107039126 ISBN-13(EAN): 9781107039124
Издательство: Cambridge Academ
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Цена: 116160.00 T
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Описание: This textbook offers a compact introduction to Malliavin calculus. It covers recent applications, and includes a self-contained presentation of preliminary material on Brownian motion and stochastic calculus. Accessible to non-experts, graduate students and researchers can use this book to master the core techniques necessary for further study.

Автор: Daniel J. Arrigo
Название: An Introduction to Partial Differential Equations
ISBN: 1681732564 ISBN-13(EAN): 9781681732565
Издательство: Mare Nostrum (Eurospan)
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Цена: 92400.00 T
Наличие на складе: Невозможна поставка.
Описание: Provides an introduction to methods for solving partial differential equations (PDEs). After the introduction of the main four PDEs that could be considered the cornerstone of Applied Mathematics, the reader is introduced to a variety of PDEs that come from a variety of fields in the Natural Sciences and Engineering and is a springboard into this wonderful subject.

Автор: Lin Lin, Jianfeng Lu
Название: A Mathematical Introduction to Electronic Structure Theory
ISBN: 1611975794 ISBN-13(EAN): 9781611975796
Издательство: Mare Nostrum (Eurospan)
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Цена: 40970.00 T
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Описание: Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area.A Mathematical Introduction to Electronic Structure Theory begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree–Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn–Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy.The book is written for advanced undergraduate and beginning graduate students, specifically those with mathematical backgrounds but without a priori knowledge of quantum mechanics, and can be used for self-study by researchers, instructors, and other scientists. The book can also serve as a starting point to learn about many-body perturbation theory, a topic at the frontier of the study of interacting electrons.

Автор: Timo Heister, Leo G. Rebholz, Fei Xue
Название: Numerical Analysis: An Introduction
ISBN: 311057330X ISBN-13(EAN): 9783110573305
Издательство: Walter de Gruyter
Цена: 53250.00 T
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Описание: Numerical analysis deals with the development and analysis of algorithms for scientific computing, and is in itself a very important part of mathematics, which has become more and more prevalent across the mathematical spectrum. This book is an introduction to numerical methods for solving linear and nonlinear systems of equations as well as ordinary and partial differential equations, and for approximating curves, functions, and integrals.

Автор: Chakraborty Kalyan, Kanemitsu Shigeru, Kuzumaki Takako
Название: A Quick Introduction to Complex Analysis
ISBN: 9813108509 ISBN-13(EAN): 9789813108509
Издательство: World Scientific Publishing
Цена: 65470.00 T
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Описание:

The aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels.

If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to do self-study on complex analysis can concentrate on Chapter 1 in which the two mainstreams of the theory -- the power series method due to Weierstrass and the integration method due to Cauchy -- are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can refer to Chapter 2, where numerous practical applications are provided. They will master the art of problem solving by following the step by step guidance given in the worked-out examples.

This book helps the reader to acquire fundamental skills of understanding complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermodynamics and fluid mechanics, information theory, and control theory. One of the main features of the book is that it presents different approaches to the same topic that aids the reader to gain a deeper understanding of the subject.

Автор: Martin Stynes, David Stynes
Название: Convection-Diffusion Problems: An Introduction to Their Analysis and Numerical Solution
ISBN: 1470448688 ISBN-13(EAN): 9781470448684
Издательство: Mare Nostrum (Eurospan)
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Цена: 112860.00 T
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Описание: Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this class of problems. At first they examine finite-difference methods for two-point boundary value problems, as their analysis requires little theoretical background. Upwinding, artificial diffusion, uniformly convergent methods, and Shishkin meshes are some of the topics presented. Throughout, the authors are concerned with the accuracy of solutions when the diffusion coefficient is close to zero. Later in the book they concentrate on finite element methods for problems posed in one and two dimensions.This lucid yet thorough account of convection-dominated convection-diffusion problems and how to solve them numerically is meant for beginning graduate students, and it includes a large number of exercises. An up-to-date bibliography provides the reader with further reading. This book is published in cooperation with Atlantic Association for Research in the Mathematical Sciences.

Автор: Biebler Karl-Ernst & Wodny Michael
Название: Splines And Compartment Models: An Introduction
ISBN: 9814522228 ISBN-13(EAN): 9789814522229
Издательство: World Scientific Publishing
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Цена: 116160.00 T
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Описание: This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given.In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics.

Автор: Luis Tenorio
Название: An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems
ISBN: 1611974917 ISBN-13(EAN): 9781611974911
Издательство: Mare Nostrum (Eurospan)
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Цена: 61870.00 T
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Описание: Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics.This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications.An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems includes:many examples that explain techniques which are useful to address general problems arising in uncertainty quantification; Bayesian and non-Bayesian statistical methods and discussions of their complementary roles; and analysis of a real data set to illustrate the methodology covered throughout the book.Audience: This book is intended for senior undergraduates and beginning graduate students in mathematics, engineering and physical sciences. The material spans from undergraduate statistics and probability to data analysis for inverse problems and probability distributions on infinite-dimensional spaces. It is also intended for researchers working on inverse problems and uncertainty quantification in geophysics, astrophysics, physics, and engineering. Because the statistical and probability methods covered have applications beyond inverse problems, the book may also be of interest to those people working in data science or in other applications of uncertainty quantification.

Автор: Kasso A. Okoudjou
Название: Finite Frame Theory: A Complete Introduction to Overcompleteness
ISBN: 1470420198 ISBN-13(EAN): 9781470420192
Издательство: Mare Nostrum (Eurospan)
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Цена: 107850.00 T
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Описание: Frames are overcomplete sets of vectors that can be used to stably and faithfully decompose and reconstruct vectors in the underlying vector space. Frame theory stands at the intersection of many areas in mathematics such as functional and harmonic analysis, numerical analysis, matrix theory, numerical linear algebra, algebraic and differential geometry, probability, statistics, and convex geometry. At the same time its applications in engineering, medicine, computer science, and quantum computing are motivating new research problems in applied and pure mathematics.This volume is based on lectures delivered at the 2015 AMS Short Course ``Finite Frame Theory: A Complete Introduction to Overcompleteness'', held January 8-9, 2015 in San Antonio, TX.Mostly written in a tutorial style, the seven chapters contained in this volume survey recent advances in the theory and applications of finite frames. In particular, it presents state-of-the-art results on foundational frame problems, and on the analysis and design of various frames, mostly motivated by specific applications. Carefully assembled, the volume quickly introduces the non-expert to the basic tools and techniques of frame theory. It then moves to develop many recent results in the area and presents some important applications. As such, the volume is designed for a diverse audience including researchers in applied and computational harmonic analysis, as well as engineers and graduate students.