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Foundations of Applied Mathematics, Volume I

Author: Jeffrey Humpherys

Publisher: SIAM

Published: 2017-07-07

Total Pages: 710

ISBN-13: 1611974895

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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?

Book Synopsis Foundations of Applied Mathematics, Volume I by : Jeffrey Humpherys

Download or read book Foundations of Applied Mathematics, Volume I written by Jeffrey Humpherys and published by SIAM. This book was released on 2017-07-07 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author: Jeffrey Humpherys

Publisher: SIAM

Published: 2020-03-10

Total Pages: 806

ISBN-13: 1611976065

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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.

Book Synopsis Foundations of Applied Mathematics, Volume 2 by : Jeffrey Humpherys

Download or read book Foundations of Applied Mathematics, Volume 2 written by Jeffrey Humpherys and published by SIAM. This book was released on 2020-03-10 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Applied Mathematics

Author: Michael D. Greenberg

Publisher: Courier Corporation

Published: 2013-01-01

Total Pages: 660

ISBN-13: 0486492796

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"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"--

Book Synopsis Foundations of Applied Mathematics by : Michael D. Greenberg

Download or read book Foundations of Applied Mathematics written by Michael D. Greenberg and published by Courier Corporation. This book was released on 2013-01-01 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--

Introduction to the Foundations of Applied Mathematics

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

Published: 2009-06-18

Total Pages: 477

ISBN-13: 0387877657

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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.

Book Synopsis Introduction to the Foundations of Applied Mathematics by : Mark H. Holmes

Download or read book Introduction to the Foundations of Applied Mathematics written by Mark H. Holmes and published by Springer Science & Business Media. This book was released on 2009-06-18 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A First Course in Applied Mathematics

Author: Jorge Rebaza

Publisher: John Wiley & Sons

Published: 2021-04-27

Total Pages: 464

ISBN-13: 1118229622

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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.

Book Synopsis A First Course in Applied Mathematics by : Jorge Rebaza

Download or read book A First Course in Applied Mathematics written by Jorge Rebaza and published by John Wiley & Sons. This book was released on 2021-04-27 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to the Foundations of Mathematics

Author: Raymond L. Wilder

Publisher: Courier Corporation

Published: 2013-09-26

Total Pages: 352

ISBN-13: 0486276201

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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.

Book Synopsis Introduction to the Foundations of Mathematics by : Raymond L. Wilder

Download or read book Introduction to the Foundations of Mathematics written by Raymond L. Wilder and published by Courier Corporation. This book was released on 2013-09-26 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Principles and Techniques of Applied Mathematics

Author: Bernard Friedman

Publisher: Courier Dover Publications

Published: 1990-01-01

Total Pages: 338

ISBN-13: 0486664449

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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.

Book Synopsis Principles and Techniques of Applied Mathematics by : Bernard Friedman

Download or read book Principles and Techniques of Applied Mathematics written by Bernard Friedman and published by Courier Dover Publications. This book was released on 1990-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Applied Electrodynamics

Author: Wen Geyi

Publisher: John Wiley & Sons

Published: 2011-07-05

Total Pages: 398

ISBN-13: 1119957486

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Foundations of Applied Electrodynamics takes a fresh look at the essential concepts and methods of electrodynamics as a whole, uniting the most relevant contemporary topics under a common mathematical framework. It contains clear explanations of high-level concepts as well as the mutual relationships between the essential ideas of electromagnetic theory. Starting with the fundamentals of electrodynamics, it methodically covers a wide spectrum of research and applications that stem from electromagnetic phenomena, before concluding with more advanced topics such as quantum mechanics. Includes new advances and methodologies in applied electrodynamics, and provides the whole picture of the theory of electrodynamics in most active areas of engineering applications Systematically deals with eigenvalue problems, integral equation formulations and transient phenomena in various areas of applied electrodynamics Introduces the complete theory of spherical vector wave functions, and presents the upper bounds of the product of gain and bandwidth for an arbitrary antenna Presents the field approach to multiple antenna system, which provides a theoretical tool for the prediction of channel models of MIMO, and is also the basis of wireless power transmission system One of the first books on electromagnetics that contains the general theory of relativity, which is needed in the design of mobile systems such as global positioning system (GPS) By summarising both engineering and theoretical electromagnetism in one volume, this book is an essential reference for practicing engineers, as well as a guide for those who wish to advance their analytical techniques for studying applied electrodynamics.

Book Synopsis Foundations of Applied Electrodynamics by : Wen Geyi

Download or read book Foundations of Applied Electrodynamics written by Wen Geyi and published by John Wiley & Sons. This book was released on 2011-07-05 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Applied Electrodynamics takes a fresh look at the essential concepts and methods of electrodynamics as a whole, uniting the most relevant contemporary topics under a common mathematical framework. It contains clear explanations of high-level concepts as well as the mutual relationships between the essential ideas of electromagnetic theory. Starting with the fundamentals of electrodynamics, it methodically covers a wide spectrum of research and applications that stem from electromagnetic phenomena, before concluding with more advanced topics such as quantum mechanics. Includes new advances and methodologies in applied electrodynamics, and provides the whole picture of the theory of electrodynamics in most active areas of engineering applications Systematically deals with eigenvalue problems, integral equation formulations and transient phenomena in various areas of applied electrodynamics Introduces the complete theory of spherical vector wave functions, and presents the upper bounds of the product of gain and bandwidth for an arbitrary antenna Presents the field approach to multiple antenna system, which provides a theoretical tool for the prediction of channel models of MIMO, and is also the basis of wireless power transmission system One of the first books on electromagnetics that contains the general theory of relativity, which is needed in the design of mobile systems such as global positioning system (GPS) By summarising both engineering and theoretical electromagnetism in one volume, this book is an essential reference for practicing engineers, as well as a guide for those who wish to advance their analytical techniques for studying applied electrodynamics.

Introduction to the Foundations of Applied Mathematics

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

Published: 2009-07-01

Total Pages: 476

ISBN-13: 0387877495

DOWNLOAD EBOOK

Book Synopsis Introduction to the Foundations of Applied Mathematics by : Mark H. Holmes

Download or read book Introduction to the Foundations of Applied Mathematics written by Mark H. Holmes and published by Springer Science & Business Media. This book was released on 2009-07-01 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Mathematics

Author: Gerald D. Mahan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 374

ISBN-13: 1461513154

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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.

Book Synopsis Applied Mathematics by : Gerald D. Mahan

Download or read book Applied Mathematics written by Gerald D. Mahan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.