Foundations Of Applied Mathematics Volume I

Author : Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans
Publisher : SIAM
Page : 710 pages
File Size : 43,5 Mb
Release : 2017-07-07
Category : Mathematics
ISBN : 9781611974898

Get Book

Foundations of Applied Mathematics, Volume I by Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans Pdf

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?

Author : Jeffrey Humpherys,Tyler J. Jarvis
Publisher : SIAM
Page : 806 pages
File Size : 50,7 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9781611976069

Get Book

Foundations of Applied Mathematics, Volume 2 by Jeffrey Humpherys,Tyler J. Jarvis Pdf

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.

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 55,9 Mb
Release : 2009-06-18
Category : Mathematics
ISBN : 9780387877655

Get Book

Introduction to the Foundations of Applied Mathematics by Mark H. Holmes Pdf

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.

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 46,7 Mb
Release : 2009-07-01
Category : Mathematics
ISBN : 9780387877495

Get Book

Introduction to the Foundations of Applied Mathematics by Mark H. Holmes Pdf

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.

Author : Michael D. Greenberg
Publisher : Courier Corporation
Page : 660 pages
File Size : 54,9 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486492797

Get Book

Foundations of Applied Mathematics by Michael D. Greenberg Pdf

"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"--

Author : Raymond L. Wilder
Publisher : Courier Corporation
Page : 352 pages
File Size : 55,9 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486276205

Get Book

Introduction to the Foundations of Mathematics by Raymond L. Wilder Pdf

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

Author : Nolan R. Wallach
Publisher : Courier Dover Publications
Page : 384 pages
File Size : 46,8 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9780486836430

Get Book

Harmonic Analysis on Homogeneous Spaces by Nolan R. Wallach Pdf

This book is suitable for advanced undergraduate and graduate students in mathematics with a strong background in linear algebra and advanced calculus. Early chapters develop representation theory of compact Lie groups with applications to topology, geometry, and analysis, including the Peter-Weyl theorem, the theorem of the highest weight, the character theory, invariant differential operators on homogeneous vector bundles, and Bott's index theorem for such operators. Later chapters study the structure of representation theory and analysis of non-compact semi-simple Lie groups, including the principal series, intertwining operators, asymptotics of matrix coefficients, and an important special case of the Plancherel theorem. Teachers will find this volume useful as either a main text or a supplement to standard one-year courses in Lie groups and Lie algebras. The treatment advances from fairly simple topics to more complex subjects, and exercises appear at the end of each chapter. Eight helpful Appendixes develop aspects of differential geometry, Lie theory, and functional analysis employed in the main text.

Author : Bernard Friedman
Publisher : Courier Dover Publications
Page : 338 pages
File Size : 44,8 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 9780486664446

Get Book

Principles and Techniques of Applied Mathematics by Bernard Friedman Pdf

Stimulating, thought-provoking study shows how abstract methods of pure mathematics can be used to systematize problem-solving techniques in applied mathematics. Topics include methods for solving integral equations, finding Green’s function for ordinary or partial differential equations, and for finding the spectral representation of ordinary differential operators.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 44,9 Mb
Release : 2014
Category : Electronic
ISBN : 812243598X

Get Book

Foundations of Discrete Mathematics by Anonim Pdf

Author : Gerald D. Mahan
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461513155

Get Book

Applied Mathematics by Gerald D. Mahan Pdf

This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I realized that my own research students did not learn much in this course at my university. Then I learned that the available textbooks were too introduc tory. While teaching this course without an assigned text, I wrote up my lecture notes and gave them to the students. This textbook is a result of that endeavor. When I took this course many, many, years ago, the primary references were the two volumes of P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953). The present text returns the contents to a similar level, although the syllabus is quite different than given in this venerable pair of books.

Author : G. M. Fikhtengol'ts
Publisher : Elsevier
Page : 540 pages
File Size : 55,8 Mb
Release : 2014-08-01
Category : Mathematics
ISBN : 9781483154138

Get Book

The Fundamentals of Mathematical Analysis by G. M. Fikhtengol'ts Pdf

The Fundamentals of Mathematical Analysis, Volume 2 is a continuation of the discussion of the fundamentals of mathematical analysis, specifically on the subject of curvilinear and surface integrals, with emphasis on the difference between the curvilinear and surface ""integrals of first kind"" and ""integrals of second kind."" The discussions in the book start with an introduction to the elementary concepts of series of numbers, infinite sequences and their limits, and the continuity of the sum of a series. The definition of improper integrals of unbounded functions and that of uniform convergence of integrals are explained. Curvilinear integrals of the first and second kinds are analyzed mathematically. The book then notes the application of surface integrals, through a parametric representation of a surface, and the calculation of the mass of a solid. The text also highlights that Green's formula, which connects a double integral over a plane domain with curvilinear integral along the contour of the domain, has an analogue in Ostrogradski's formula. The periodic values and harmonic analysis such as that found in the operation of a steam engine are analyzed. The volume ends with a note of further developments in mathematical analysis, which is a chronological presentation of important milestones in the history of analysis. The book is an ideal reference for mathematicians, students, and professors of calculus and advanced mathematics.

Author : G. Bard Ermentrout,David H. Terman
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 44,5 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9780387877082

Get Book

Mathematical Foundations of Neuroscience by G. Bard Ermentrout,David H. Terman Pdf

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.

Author : Šárka Hošková-Mayerová,Cristina Flaut,Fabrizio Maturo
Publisher : Springer Nature
Page : 515 pages
File Size : 55,6 Mb
Release : 2021-01-13
Category : Technology & Engineering
ISBN : 9783030613341

Get Book

Algorithms as a Basis of Modern Applied Mathematics by Šárka Hošková-Mayerová,Cristina Flaut,Fabrizio Maturo Pdf

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.

Author : Jorge Rebaza
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 52,8 Mb
Release : 2021-04-27
Category : Mathematics
ISBN : 9781118229620

Get Book

A First Course in Applied Mathematics by Jorge Rebaza Pdf

Explore real-world applications of selected mathematical theory, concepts, and methods Exploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation for transitioning to more advanced subjects. The author utilizes MATLAB® to showcase the presented theory and illustrate interesting real-world applications to Google's web page ranking algorithm, image compression, cryptography, chaos, and waste management systems. Additional topics covered include: Linear algebra Ranking web pages Matrix factorizations Least squares Image compression Ordinary differential equations Dynamical systems Mathematical models Throughout the book, theoretical and applications-oriented problems and exercises allow readers to test their comprehension of the presented material. An accompanying website features related MATLAB® code and additional resources. A First Course in Applied Mathematics is an ideal book for mathematics, computer science, and engineering courses at the upper-undergraduate level. The book also serves as a valuable reference for practitioners working with mathematical modeling, computational methods, and the applications of mathematics in their everyday work.

Author : Masayoshi Nagata
Publisher : Unknown
Page : 288 pages
File Size : 42,8 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015038842566

Get Book

Field Theory by Masayoshi Nagata Pdf