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, DaniellLebesgue 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: Michael D. Greenberg
Publisher: Courier Corporation
Release Date: 2013
"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: Mark H. Holmes
Publisher: Springer Science & Business Media
Release Date: 2009-07-01
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.
Der 3-bändige Grundkurs für Studienanfänger verbindet die mathematische Analysis (Soul) mit numerischer Berechnung (Body) und einer Fülle von Anwendungen. Die Autoren haben die Inhalte im Unterricht erprobt. Band 1 behandelt die Grundlagen der Analysis.
Das Buch ist für Studenten der angewandten Mathematik und der Ingenieurwissenschaften auf Vordiplomniveau geeignet. Der Schwerpunkt liegt auf der Verbindung der Theorie linearer partieller Differentialgleichungen mit der Theorie finiter Differenzenverfahren und der Theorie der Methoden finiter Elemente. Für jede Klasse partieller Differentialgleichungen, d.h. elliptische, parabolische und hyperbolische, enthält der Text jeweils ein Kapitel zur mathematischen Theorie der Differentialgleichung gefolgt von einem Kapitel zu finiten Differenzenverfahren sowie einem zu Methoden der finiten Elemente. Den Kapiteln zu elliptischen Gleichungen geht ein Kapitel zum Zweipunkt-Randwertproblem für gewöhnliche Differentialgleichungen voran. Ebenso ist den Kapiteln zu zeitabhängigen Problemen ein Kapitel zum Anfangswertproblem für gewöhnliche Differentialgleichungen vorangestellt. Zudem gibt es ein Kapitel zum elliptischen Eigenwertproblem und zur Entwicklung nach Eigenfunktionen. Die Darstellung setzt keine tiefer gehenden Kenntnisse in Analysis und Funktionalanalysis voraus. Das erforderliche Grundwissen über lineare Funktionalanalysis und Sobolev-Räume wird im Anhang im Überblick besprochen.
Author: Steven Strogatz
Publisher: Kein & Aber AG
Release Date: 2014-04-23
Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.
Author: Hang Lee
Publisher: Springer Science & Business Media
Release Date: 2013-11-08
This is a text in methods of applied statistics for researchers who design and conduct experiments, perform statistical inference, and write technical reports. These research activities rely on an adequate knowledge of applied statistics. The reader both builds on basic statistics skills and learns to apply it to applicable scenarios without over-emphasis on the technical aspects. Demonstrations are a very important part of this text. Mathematical expressions are exhibited only if they are defined or intuitively comprehensible. This text may be used as a self review guidebook for applied researchers or as an introductory statistical methods textbook for students not majoring in statistics. Discussion includes essential probability models, inference of means, proportions, correlations and regressions, methods for censored survival time data analysis, and sample size determination. The author has over twenty years of experience on applying statistical methods to study design and data analysis in collaborative medical research setting as well as on teaching. He received his PhD from University of Southern California Department of Preventive Medicine, received a post-doctoral training at Harvard Department of Biostatistics, has held faculty appointments at UCLA School of Medicine and Harvard Medical School, and currently a biostatistics faculty member at Massachusetts General Hospital and Harvard Medical School in Boston, Massachusetts, USA.
Author: Wen Geyi
Publisher: John Wiley & Sons
Release Date: 2011-07-05
Genre: Technology & Engineering
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.
Author: Glenn E Sjoden
Publisher: World Scientific Publishing Company
Release Date: 2015-01-13
Foundations in Applied Nuclear Engineering Analysis (2nd Edition) covers a fast-paced one semester course to address concepts of modeling in mathematics, engineering analysis, and computational problem solving needed in subjects such as radiation interactions, heat transfer, reactor physics, radiation transport, numerical modeling, etc., for success in a nuclear engineering/medical physics curriculum. While certain topics are covered tangentially, others are covered in depth to target on the appropriate amalgam of topics for success in navigating nuclear-related disciplines. Software examples and programming are used throughout the book, since computational capabilities are essential for new engineers. The book contains a array of topics that cover the essential subjects expected for students to successfully navigate into nuclear-related disciplines. The text assumes that students have familiarity with undergraduate mathematics and physics, and are ready to apply those skills to problems in nuclear engineering. Applications and problem sets are directed toward problems in nuclear science. Software examples using Mathematica software are used in the text. This text was developed as part of a very applied course in mathematical physics methods for nuclear engineers. The course in Nuclear Engineering Analysis that follows this text began at the University of Florida; the 2nd edition was released while at the Georgia Institute of Technology.
Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodynamics, such as physics, engineering, and chemistry.