Foundations Of Applied Mathematics Volume I
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Foundations Of Applied Mathematics Volume I
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Author : Jeffrey Humpherys
language : en
Publisher: SIAM
Release Date : 2017-07-07
Foundations Of Applied Mathematics Volume I written by Jeffrey Humpherys and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-07 with Mathematics categories.
This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?
Foundations Of Applied Mathematics Volume 2
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Author : Jeffrey Humpherys
language : en
Publisher: SIAM
Release Date : 2020-03-10
Foundations Of Applied Mathematics Volume 2 written by Jeffrey Humpherys and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.
In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization—essential topics in modern applied and computational mathematics. This material is the introductory framework upon which algorithm analysis, optimization, probability, statistics, machine learning, and control theory are built. This text gives a unified treatment of several topics that do not usually appear together: the theory and analysis of algorithms for mathematicians and data science students; probability and its applications; the theory and applications of approximation, including Fourier series, wavelets, and polynomial approximation; and the theory and practice of optimization, including dynamic optimization. When used in concert with the free supplemental lab materials, Foundations of Applied Mathematics, Volume 2: Algorithms, Approximation, Optimization teaches not only the theory but also the computational practice of modern mathematical methods. Exercises and examples build upon each other in a way that continually reinforces previous ideas, allowing students to retain learned concepts while achieving a greater depth. The mathematically rigorous lab content guides students to technical proficiency and answers the age-old question “When am I going to use this?” This textbook is geared toward advanced undergraduate and beginning graduate students in mathematics, data science, and machine learning.
Introduction To The Foundations Of Applied Mathematics
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Author : Mark H. Holmes
language : en
Publisher: Springer Nature
Release Date : 2019-10-02
Introduction To The Foundations Of Applied Mathematics written by Mark H. Holmes and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-02 with Mathematics categories.
The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change. What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book. The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. This provides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered. Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful. The material, and topics, have been updated to include recent developments in mathematical modeling. The exercises have also been expanded to include these changes, as well as enhance those from the first edition. Review of first edition: "The goal of this book is to introduce the mathematical tools needed for analyzing and deriving mathematical models. ... Holmes is able to integrate the theory with application in a very nice way providing an excellent book on applied mathematics. ... One of the best features of the book is the abundant number of exercises found at the end of each chapter. ... I think this is a great book, and I recommend it for scholarly purposes by students, teachers, and researchers." Joe Latulippe, The Mathematical Association of America, December, 2009
Algorithms As A Basis Of Modern Applied Mathematics
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Author : Šárka Hošková-Mayerová
language : en
Publisher: Springer Nature
Release Date : 2021-01-13
Algorithms As A Basis Of Modern Applied Mathematics written by Šárka Hošková-Mayerová and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-13 with Technology & Engineering categories.
This book offers a self-contained guide to advanced algorithms and their applications in various fields of science. Gathering contributions by authoritative researchers in the field of mathematics, statistics and computer science, it aims at offering a comprehensive and up-to-date view of algorithms, including the theory behind them, as well as practical considerations, current limitations and solutions. It covers applications in energy management, decision making, computer networks, materials science, mechanics and process optimization. It offers an integrated and timely guide to important algorithms, and represents a valuable reference resource for graduate students and researchers in various fields of applied mathematics, statistics and engineering.
Mathematics In Medicine And The Life Sciences
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Author : Frank C. Hoppensteadt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Mathematics In Medicine And The Life Sciences written by Frank C. Hoppensteadt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The aim of this book is to introduce the subject of mathematical modeling in the life sciences. It is intended for students of mathematics, the physical sciences, and engineering who are curious about biology. Additionally, it will be useful to students of the life sciences and medicine who are unsatisfied with mere description and who seek an understanding of biological mechanism and dynamics through the use of mathematics. The book will be particularly useful to premedical students, because it will introduce them not only to a collection of mathematical methods but also to an assortment of phenomena involving genetics, epidemics, and the physiology of the heart, lung, and kidney. Because of its introductory character, mathematical prerequisites are kept to a minimum; they involve only what is usually covered in the first semester of a calculus sequence. The authors have drawn on their extensive experience as modelers to select examples which are simple enough to be understood at this elementary level and yet realistic enough to capture the essence of significant biological phenomena drawn from the areas of population dynamics and physiology. Because the models presented are realistic, the book can serve not only as an introduction to mathematical methods but also as a mathematical introduction to the biological material itself. For the student, who enjoys mathematics, such an introduction will be far more stimulating and satisfying than the purely descriptive approach that is traditional in the biological sciences.
Foundations Of Discrete Mathematics
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Author :
language : en
Publisher:
Release Date : 2014
Foundations Of Discrete Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
The Fundamentals Of Mathematical Analysis
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Author : G. M. Fikhtengol'ts
language : en
Publisher: Elsevier
Release Date : 1965-01-01
The Fundamentals Of Mathematical Analysis written by G. M. Fikhtengol'ts and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965-01-01 with Mathematics categories.
The Fundamentals of Mathematical Analysis, Volume 2 focuses on the fundamental concepts of mathematical analysis. This book discusses the theorems on the comparison of series, condition for uniform convergence, and application of the fundamental formula of integral calculus. The differentiation under the integral sign, Lagrange's method of undetermined multipliers, and definition of curvilinear integrals of the second kind are also elaborated. This text likewise covers the transformation of plane domains, case of a piece-wise smooth surface, and problem of calculating the mass of a solid. Other topics include the flow of a vector through a surface, determination of coefficients by the Euler-Fourier method, and generalized equation of closure. This volume is a good reference for students and researchers conducting work on mathematical analysis.
Foundations Of Computational Mathematics Budapest 2011
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Author : Society for the Foundation of Computational Mathematics
language : en
Publisher: Cambridge University Press
Release Date : 2013
Foundations Of Computational Mathematics Budapest 2011 written by Society for the Foundation of Computational Mathematics and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
A diverse collection of articles by leading experts in computational mathematics, written to appeal to established researchers and non-experts.
Mathematical Foundations Of Neuroscience
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Author : G. Bard Ermentrout
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-01
Mathematical Foundations Of Neuroscience written by G. Bard Ermentrout and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.
This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.
Topology Geometry And Gauge Fields
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Author : Gregory L. Naber
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Topology Geometry And Gauge Fields written by Gregory L. Naber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development ofnewcourses is a natural consequence of a high levelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface In Egypt, geometry was created to measure the land. Similar motivations, on a somewhat larger scale, led Gauss to the intrinsic differential geometry of surfaces in space. Newton created the calculus to study the motion of physical objects (apples, planets, etc.) and Poincare was similarly impelled toward his deep and far-reaching topological view of dynamical systems.