Book Title : Understanding Analysis

understanding analysis

Release Date : 2012-12-06
ISBN Code : 9780387215068
Book Author : Stephen Abbott
Book Publisher : Springer Science & Business Media
Total Pages : 260

Book Summary :

This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

Book Title : An Introduction to Multivariable Mathematics

an introduction to multivariable mathematics

Release Date : 2008
ISBN Code : 9781598298017
Book Author : Leon Simon
Book Publisher : Morgan & Claypool Publishers
Total Pages : 132

Book Summary :

The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. The core material of the book is arranged to allow for the main introductory material on linear algebra, including basic vector space theory in Euclidean space and the initial theory of matrices and linear systems, to be covered in the first ten or eleven lectures, followed by a similar number of lectures on basic multivariable analysis, including first theorems on differentiable functions on domains in Euclidean space and a brief introduction to submanifolds. The book then concludes with further essential linear algebra, including the theory of determinants, eigenvalues, and the spectral theorem for real symmetric matrices, and further multivariable analysis, including the contraction mapping principle and the inverse and implicit function theorems. There is also an appendix which provides a nine-lecture introduction to real analysis. There are various ways in which the additional material in the appendix could be integrated into a course--for example in the Stanford Mathematics honors program, run as a four-lecture per week program in the Autumn Quarter each year, the first six lectures of the nine-lecture appendix are presented at the rate of one lecture per week in weeks two through seven of the quarter, with the remaining three lectures per week during those weeks being devoted to the main chapters of the text. It is hoped that the text would be suitable for a quarter or semester course for students who have scored well in the BC Calculus advanced placement examination (or equivalent), particularly those who are considering a possible major in mathematics. The author has attempted to make the presentation rigorous and complete, with the clarity and simplicity needed to make it accessible to an appropriately large group of students. Table of Contents: Linear Algebra / Analysis in R / More Linear Algebra / More Analysis in R / Appendix: Introductory Lectures on Real Analysis

Book Title : Adhesion Measurement Methods

adhesion measurement methods

Release Date : 2005-11-21
ISBN Code : 9781420028829
Book Author : Robert Lacombe
Book Publisher : CRC Press
Total Pages : 456

Book Summary :

Adhesion Measurement Methods: Theory and Practice provides practical information on the most important measurement techniques, their unique advantages and disadvantages, and the selection of the proper method for a given application. It includes useful information and formulae on adhesion related matters such as driving force formulae for various modes of delamination, methods for estimating stress buildup, and material property data in support of "back of the envelope" calculations. The author presents optimal methods and tools used for measuring the adhesion of coatings and thin films as well as setting appropriate adhesion strength requirements. He provides a detailed overview of uses, implementation, and drawbacks for qualitative, semi-quantitative, and fully quantitative adhesion measurement techniques and self-loading systems. The book discusses thermal-mechanical behavior assessment, the application of the continuum theory of solids, and fracture mechanics, highlighting useful measures of adhesion strength such as stress intensity factor and strain energy release rate. It provides specific examples of how adhesion testing is carried out in practice, including the peel test, the scratch test, and the pull test, and describes the measurement of residual stress in a coating or other laminate structure. The book concludes with examples taken from the author's experience in the microelectronics industry and contains several appendices for looking up simple formulae and material property data for performing everyday calculations. Adhesion Measurement Methods is an ideal addition for courses on materials science, mechanics of materials, or engineering design of laminate structures at the advanced undergraduate or graduate level.

Book Title : Topology

topology

Release Date : 2014-08-05
ISBN Code : 9783319096803
Book Author : Stefan Waldmann
Book Publisher : Springer
Total Pages : 136

Book Summary :

This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.

Book Title : Calculus of One Variable

calculus of one variable

Release Date : 2006-01-27
ISBN Code : 9781846282225
Book Author : K.E. Hirst
Book Publisher : Springer Science & Business Media
Total Pages : 268

Book Summary :

Adopts a user-friendly approach, with an emphasis on worked examples and exercises, rather than abstract theory The computer algebra and graphical package MAPLE is used to illustrate many of the ideas and provides an additional aid to teaching and learning Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web

Book Title : Ecological Statistics

ecological statistics

Release Date : 2015-01-29
ISBN Code : 9780191652882
Book Author : Gordon A. Fox
Book Publisher : OUP Oxford
Total Pages : 400

Book Summary :

The application and interpretation of statistics are central to ecological study and practice. Ecologists are now asking more sophisticated questions than in the past. These new questions, together with the continued growth of computing power and the availability of new software, have created a new generation of statistical techniques. These have resulted in major recent developments in both our understanding and practice of ecological statistics. This novel book synthesizes a number of these changes, addressing key approaches and issues that tend to be overlooked in other books such as missing/censored data, correlation structure of data, heterogeneous data, and complex causal relationships. These issues characterize a large proportion of ecological data, but most ecologists' training in traditional statistics simply does not provide them with adequate preparation to handle the associated challenges. Uniquely, Ecological Statistics highlights the underlying links among many statistical approaches that attempt to tackle these issues. In particular, it gives readers an introduction to approaches to inference, likelihoods, generalized linear (mixed) models, spatially or phylogenetically-structured data, and data synthesis, with a strong emphasis on conceptual understanding and subsequent application to data analysis. Written by a team of practicing ecologists, mathematical explanations have been kept to the minimum necessary. This user-friendly textbook will be suitable for graduate students, researchers, and practitioners in the fields of ecology, evolution, environmental studies, and computational biology who are interested in updating their statistical tool kits. A companion web site provides example data sets and commented code in the R language.

Book Title : Network Calculus

network calculus

Release Date : 2003-08-06
ISBN Code : 9783540453185
Book Author : Jean-Yves Le Boudec
Book Publisher : Springer
Total Pages : 276

Book Summary :

Network Calculus is a set of recent developments that provide deep insights into flow problems encountered in the Internet and in intranets. The first part of the book is a self-contained, introductory course on network calculus. It presents the core of network calculus, and shows how it can be applied to the Internet to obtain results that have physical interpretations of practical importance to network engineers. The second part serves as a mathematical reference used across the book. It presents the results from Min-plus algebra needed for network calculus. The third part contains more advanced material. It is appropriate reading for a graduate course and a source of reference for professionals in networking by surveying the state of the art of research and pointing to open problems in network calculus and its application in different fields, such as mulitmedia smoothing, aggegate scheduling, adaptive guarantees in Internet differential services, renegotiated reserved services, etc.

Book Title : Publication

publication

Release Date : 1967
ISBN Code : CORNELL:31924065150280
Book Author : Commission on Undergraduate Education in the Biological Sciences
Book Publisher :
Total Pages :

Book Summary :

Book Title : Modern Methods in the Calculus of Variations

modern methods in the calculus of variations

Release Date : 2007-08-22
ISBN Code : 9780387690063
Book Author : Irene Fonseca
Book Publisher : Springer Science & Business Media
Total Pages : 600

Book Summary :

This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Book Title : Numerical Methods in Software and Analysis

numerical methods in software and analysis

Release Date : 2014-05-19
ISBN Code : 9781483295688
Book Author : John R. Rice
Book Publisher : Elsevier
Total Pages : 720

Book Summary :

Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithms. The book is organized into three parts. Part I presents the background material. Part II presents the principal methods and ideas of numerical computation. Part III contains material about software engineering and performance evaluation. A uniform approach is used in each area of numerical computation. First, an intuitive development is made of the problems and the basic methods for their solution. Then, relevant mathematical software is reviewed and its use outlined. Many areas provide extensive examples and case studies. Finally, a deeper analysis of the methods is presented as in traditional numerical analysis texts. Emphasizes the use of high-quality mathematical software for numerical computation Extensive use of IMSL routines Features extensive examples and case studies

Book Title : Calculus in Context

calculus in context

Release Date : 2017-03-15
ISBN Code : 9781421422305
Book Author : Alexander J. Hahn
Book Publisher : JHU Press
Total Pages : 712

Book Summary :

Breaking the mold of existing calculus textbooks, Calculus in Context draws students into the subject in two new ways. Part I develops the mathematical preliminaries (including geometry, trigonometry, algebra, and coordinate geometry) within the historical frame of the ancient Greeks and the heliocentric revolution in astronomy. Part II starts with comprehensive and modern treatments of the fundamentals of both differential and integral calculus, then turns to a wide-ranging discussion of applications. Students will learn that core ideas of calculus are central to concepts such as acceleration, force, momentum, torque, inertia, and the properties of lenses. Classroom-tested at Notre Dame University, this textbook is suitable for students of wide-ranging backgrounds because it engages its subject at several levels and offers ample and flexible problem set options for instructors. Parts I and II are both supplemented by expansive Problems and Projects segments. Topics covered in the book include: • the basics of geometry, trigonometry, algebra, and coordinate geometry and the historical, scientific agenda that drove their development• a brief, introductory calculus from the works of Newton and Leibniz• a modern development of the essentials of differential and integral calculus• the analysis of specific, relatable applications, such as the arc of the George Washington Bridge; the dome of the Pantheon; the optics of a telescope; the dynamics of a bullet; the geometry of the pseudosphere; the motion of a planet in orbit; and the momentum of an object in free fall. Calculus in Context is a compelling exploration—for students and instructors alike—of a discipline that is both rich in conceptual beauty and broad in its applied relevance.

Book Title : Calculus

calculus

Release Date : 1998
ISBN Code : 0486404536
Book Author : Morris Kline
Book Publisher : Courier Corporation
Total Pages : 943

Book Summary :

Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request.

Book Title : Research in Collegiate Mathematics Education VII

research in collegiate mathematics education vii

Release Date : 2010-03-05
ISBN Code : 9780821849965
Book Author : Fernando Hitt
Book Publisher : American Mathematical Soc.
Total Pages : 261

Book Summary :

The present volume of Research in Collegiate Mathematics Education, like previous volumes in this series, reflects the importance of research in mathematics education at the collegiate level. The editors in this series encourage communication between mathematicians and mathematics educators, and as pointed out by the International Commission of Mathematics Instruction (ICMI), much more work is needed in concert with these two groups. Indeed, editors of RCME are aware of this need and the articles published in this series are in line with that goal. Nine papers constitute this volume. The first two examine problems students experience when converting a representation from one particular system of representations to another. The next three papers investigate students learning about proofs. In the next two papers, the focus is instructor knowledge for teaching calculus. The final two papers in the volume address the nature of ``conception'' in mathematics. Whether they are specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas that they can use.

Book Title : Noninvasive Instrumentation and Measurement in Medical Diagnosis

noninvasive instrumentation and measurement in medical diagnosis

Release Date : 2001-09-26
ISBN Code : 9781420041200
Book Author : Robert B. Northrop
Book Publisher : CRC Press
Total Pages : 544

Book Summary :

Noninvasive medical diagnosis (NIMD) is as old as medical practice itself. From the earliest healers' observations of odors, skin color, and breath sounds to today's wealth of technologies, the basics remain the same and keep the role of NIMD essential to effective medical care. Noninvasive Instrumentation and Measurement in Medical Diagnosis is the first book dedicated to NIMD tools and techniques. Featuring emerging technologies along with traditional instruments, it describes how these non-invasive tools and techniques work and explores developments that will make NIMD simpler, more reliable, less expensive, and risk-free. Much of the material is descriptive, but the author includes rigorous mathematical analysis where appropriate. The treatment is readily accessible to readers with a background in basic algebra and ordinary differential equations, basic circuit theory, and concepts such as frequency response and transient response of linear systems. The rapid evolution of biomedical instrumentation has meant that books just five years old are already outdated. Whether used for an upper-level, biomedical engineering class or as a reference for medical students, healthcare professional, physicists, or physiologists, Noninvasive Instrumentation and Measurement in Medical Diagnosis stands alone in presenting the state of NIMD art and science.

Book Title : Direct Methods in the Calculus of Variations

direct methods in the calculus of variations

Release Date : 2007-11-21
ISBN Code : 9780387552491
Book Author : Bernard Dacorogna
Book Publisher : Springer Science & Business Media
Total Pages : 622

Book Summary :

This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.

Book Title : Convex Optimization in Normed Spaces

convex optimization in normed spaces

Release Date : 2015-03-18
ISBN Code : 9783319137100
Book Author : Juan Peypouquet
Book Publisher : Springer
Total Pages : 124

Book Summary :

This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.