Foundations of Applied Mathematics

Author: Michael D. Greenberg
Publisher: Courier Corporation
ISBN: 9780486492797
Release Date: 2013
Genre: Mathematics

"A longtime classic text in applied mathematics, this volume also serves as a reference for undergraduate and graduate students of engineering. Topics include real variable theory, complex variables, linear analysis, partial and ordinary differential equations, and other subjects. Answers to selected exercises are provided, along with Fourier and Laplace transformation tables and useful formulas. 1978 edition"--

Foundations of Applied Mathematics Volume I

Author: Jeffrey Humpherys
Publisher: SIAM
ISBN: 9781611974898
Release Date: 2017-07-07
Genre: Mathematics

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?

Introduction to the Foundations of Applied Mathematics

Author: Mark H. Holmes
Publisher: Springer Science & Business Media
ISBN: 9780387877495
Release Date: 2009-07-01
Genre: Mathematics

FOAM. This acronym has been used for over ?fty years at Rensselaer to designate an upper-division course entitled, Foundations of Applied Ma- ematics. This course was started by George Handelman in 1956, when he came to Rensselaer from the Carnegie Institute of Technology. His objective was to closely integrate mathematical and physical reasoning, and in the p- cess enable students to obtain a qualitative understanding of the world we live in. FOAM was soon taken over by a young faculty member, Lee Segel. About this time a similar course, Introduction to Applied Mathematics, was introduced by Chia-Ch’iao Lin at the Massachusetts Institute of Technology. Together Lin and Segel, with help from Handelman, produced one of the landmark textbooks in applied mathematics, Mathematics Applied to - terministic Problems in the Natural Sciences. This was originally published in 1974, and republished in 1988 by the Society for Industrial and Applied Mathematics, in their Classics Series. This textbook comes from the author teaching FOAM over the last few years. In this sense, it is an updated version of the Lin and Segel textbook.

Mathematical Foundations of Neuroscience

Author: G. Bard Ermentrout
Publisher: Springer Science & Business Media
ISBN: 9780387877082
Release Date: 2010-07-01
Genre: Mathematics

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.

Foundations of Abstract Mathematics

Author: David C. Kurtz
Publisher: McGraw-Hill College
ISBN: STANFORD:36105129676024
Release Date: 1992
Genre: Mathematics

This text is designed for the average to strong mathematics major taking a course called Transition to Higher Mathematics, Introduction to Proofs, or Fundamentals of Mathematics. It provides a transition to topics covered in advanced mathematics and covers logic, proofs and sets and emphasizes two important mathematical activities - finding examples of objects with specified properties and writing proofs.

Mathematics Applied to Deterministic Problems in the Natural Sciences

Author: C. C. Lin
Publisher: SIAM
ISBN: 1611971349
Release Date: 1988
Genre: Mathematics

Addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences. The authors' case studies approach leads to excitement in teaching realistic problems. The many problems and exercises reinforce, test and extend the reader's understanding. This reprint volume may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers working on fluid mechanics, elasticity, perturbation methods, dimensional analysis, numerical analysis, continuum mechanics and differential equations.

Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh
Publisher: Courier Corporation
ISBN: 9780486134772
Release Date: 2012-09-11
Genre: Mathematics

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Handbook of Analysis and Its Foundations

Author: Eric Schechter
Publisher: Academic Press
ISBN: 0080532993
Release Date: 1996-10-24
Genre: Mathematics

Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/

Introduction to Perturbation Methods

Author: Mark H. Holmes
Publisher: Springer Science & Business Media
ISBN: 9781461454779
Release Date: 2012-12-05
Genre: Mathematics

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.

Applied Mathematics

Author: Alain Goriely
Publisher: Oxford University Press
ISBN: 9780198754046
Release Date: 2018-02-22
Genre: Mathematics

Mathematics is playing an increasingly important role in society and the sciences, enhancing our ability to use models and handle data. While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world in which we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields. This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics and engineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Topology Geometry and Gauge Fields

Author: Gregory Naber
Publisher: Springer Science & Business Media
ISBN: 9781475727425
Release Date: 2013-04-17
Genre: Mathematics

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

Applied Mathematics for Database Professionals

Author: Lex deHaan
Publisher: Apress
ISBN: 143020348X
Release Date: 2007-10-25
Genre: Computers

This book touches on an area seldom explored: the mathematical underpinnings of the relational database. The topic is important, but far too often ignored. This is the first book to explain the underlying math in a way that’s accessible to database professionals. Just as importantly, if not more so, this book goes beyond the abstract by showing readers how to apply that math in ways that will make them more productive in their jobs. What’s in this book will "open the eyes" of most readers to the great power, elegance, and simplicity inherent in relational database technology.

Fundamentals of Technical Mathematics

Author: Sarhan M. Musa
Publisher: Academic Press
ISBN: 9780128020166
Release Date: 2015-10-16
Genre: Mathematics

Fundamentals of Technical Mathematics introduces key, applied mathematics for engineering technologists and technicians. Through a simple, engaging approach, the book reviews basic mathematics, including whole numbers, fractions, mixed numbers, decimals, percentages, ratios, and proportions. The book covers conversions to different units of measure (standard and/or metric) and other topics as required by specific businesses and industries, providing a go-to resource on the topic. Building on these foundations, it then explores concepts in arithmetic, introductory algebra, equations, inequalities, and modeling, graphs and functions, measurement, geometry, and trigonometry, all the while supporting these concepts with practical applications in a variety of technical and career vocations, including automotive, allied health, welding, plumbing, machine tool, carpentry, auto mechanics, HVAC, and many other fields. In addition, the book provides practical examples from a vast number of technologies. Presents foundational math concepts in a concise, engaging way Covers conversions to different units of measure (standard and/or metric) and other topics as required by specific businesses and industries Reviews basic mathematics, including whole numbers, fractions, mixed numbers, decimals, percentages, ratios, and proportions Connects concepts with recent applications in technology, engineering, manufacturing, and science Includes many practice and review problems

Mathematical Models in Biology

Author: Leah Edelstein-Keshet
Publisher: SIAM
ISBN: 0898719143
Release Date: 1988
Genre: Biology

Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.