How to do your Student Project in Chemistry

Book Description

This book is for undergraduate and diploma chemistry students who are about to begin their project work. Student projects are now an essential part of most undergraduate and diploma chemistry courses in the UK, and are an important component of the later years of chemistry degree courses in Australia, South Africa and New Zealand. The book covers all aspects of project work, from choosing a suitable topic and supervisor to communicating research results effectively. There is advice on the best way to use libraries and on how to gather relevant references. Students are taught how to work safely and effectively, and to present their results in report, seminar or conference poster form. Additionally, the author offers guidance on engaging a keyboard operator, on how to prepare artwork and visual aids, and coaching tips on effective communication. The work is a distillation of the author's many years of experience of guiding students of all abilities to success in their project work. This book should be of interest to second and third year undergraduates and diploma students in chemistry.

How to do your Student Project in Chemistry

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How to do your Student Project in Chemistry
Fred H. Jardine
Manufacturer: NY
ProductGroup: Book
Binding: Paperback
ASIN: B000MUA64I

Book Description

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics.

This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.

Key features include:

* Applications to a wide variety of physical problems in numerous interdisciplinary areas

* Over 900 worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry

* Historical comments on partial differential equations

* Solutions and hints to selected exercises

* A comprehensive bibliography—comprised of many standard texts and reference books, as well as a set of selected classic and recent papers—for readers interested in learning more about the modern treatment of the subject

Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields.

Also by L. Debnath: Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition, ISBN 0-8176-4323-0.

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Aimed at the Person who needs to do Real Work.......2007-04-05

Partial Differential equations are really the first time that the science or entineering student begins to see that math can really represent real life situations that are more complex than the almost trivial examples he has studied up until now.

This book, now in its fourth edition reflects comments made by users: students, faculty and researchers as well as covering the major new discoveries of methods for the solution of partial differential equations in the years since the last edition. The book is aimed at the advanced undergraduate or beginning graduate student, and it should be useful as a research reference for professionals in mathematics, science, engineering and the other applied sciences. In addition other fields of study from the social sciented to financial analysis have begin to use more advanced mathematics in their calculations.

The intent in this book is to provide the working physicist/engineer or whatever with the tools he needs to perform his work. In a few places this has meant a slight slacking of the rigor normally required by the pure mathematician in favor of producing solutions that give the user the answers he needs.

Fractional Differential Equations (Mathematics in Science and Engineering)

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Fractional Differential Equations (Mathematics in Science and Engineering)
Igor Podlubny
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0125588402

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This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.
This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.
In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.
A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications.

Key Features
* A unique survey of many applications of fractional calculus
* Presents basic theory
* Includes a unified presentation of selected classical results, which are important for applications
* Provides many examples
* Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory
* The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches
* Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives

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Physics of Fractal Operators
Bruce West , Mauro Bologna , and Paolo Grigolini
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Dover Books on Mathematics)

ASIN: 0387955542

Book Description

This text describes how fractal phenomena, both deterministic and random, change over time, using the fractional calculus. The intent is to identify those characteristics of complex physical phenomena that require fractional derivatives or fractional integrals to describe how the process changes over time. The discussion emphasizes the properties of physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. In many cases, classic analytic function theory cannot serve for modeling complex phenomena; "Physics of Fractal Operators" shows how classes of less familiar functions, such as fractals, can serve as useful models in such cases. Because fractal functions, such as the Weierstrass function (long known not to have a derivative), do in fact have fractional derivatives, they can be cast as solutions to fractional differential equations. The traditional techniques for solving differential equations, including Fourier and Laplace transforms as well as Green's functions, can be generalized to fractional derivatives. Physics of Fractal Operators addresses a general strategy for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of various forms of transport in heterogeneous materials. This strategy builds on traditional approaches and explains why the historical techniques fail as phenomena become more and more complicated.

Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations (De Gruyter Series in Nonlinear Analysis and Applications, 3)

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Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations (De Gruyter Series in Nonlinear Analysis and Applications, 3)
Thomas Runst , and Winfried Sickel
Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Hardcover

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ASIN: 3110151138

Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering

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Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Functional Fractional Calculus for System Identification and Controls

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ASIN: 1402060416

Product Description

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation.

As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Analysis in Integer and Fractional Dimensions (Cambridge Studies in Advanced Mathematics)

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Analysis in Integer and Fractional Dimensions (Cambridge Studies in Advanced Mathematics)
Ron Blei
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521650844

Book Description

This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on "dimension" as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Fréchet measures in stochastic analysis. This book is primarily aimed at graduate students specializing in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable as a textbook. It is also of interest to computer scientists, physicists, statisticians, biologists and economists.

Download Description

This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists.

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Fractional Analysis
IU.V. Novozhilov
Manufacturer: Birkhauser Verlag AG
ProductGroup: Book
Binding: Hardcover

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ASIN: 376433889X

Book Description

This book offers a new method for the formalized construction of approximate mathematical models of dynamic systems described by ordinary differential equations (ODE). The models illustrate the separated components of the motion of initial systems. This procedure, termed by Kline as "fractional analysis", consists of two stages. First, appropriate small parameters are introduced into initial equations by normalization, and then appropriate methods of small parameter are used to obtain equations of the separated "fractions". As shown in the book, a wide range of problems can be investigated in this way. The author suggests a new means of introducing small parameters, and surveys existing various methods of small parameter such as Poincare method, the method of averaging, and the method of boundary-layer expansions. Their applicability is discussed. The book is application oriented, so proofs of theorems are omitted and mathematical formulations are simplified. Emphasis is on approximate modeling in mechanics, the theory of gyroscopic transport, and robotic systems.

Fractional Integrals and Potentials (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)

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Fractional Integrals and Potentials (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)
Boris Rubin
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Loose Leaf

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ASIN: 0582253411

Book Description

This volume presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. Beyond some basic properties of fractional integrals in one and many dimensions, it contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaudís approach and its generalization, leading to wavelet type representations.

Generalized Analytic Functions in Fractional Spaces (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)

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Generalized Analytic Functions in Fractional Spaces (Chapman and Hall /Crc Monographs and Surveys in Pure and Applied Mathematics)
N K Bliev
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Loose Leaf

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ASIN: 0582288614

Book Description

This book studies the foundations of the general theory of generalized analytic functions in fractional spaces. The employment of fractional spaces and embedding theorems support applications of the theory of generalized analytic functions. The results obtained are applicable to the theory of singular integral equations, boundary value problems for elliptic differential equations, functions of a complex variable, as well as the theory of plates and shells. The book will be of interest to scientific workers and specialists interested in these questions and likewise to advanced students in mechanical engineering faculties.

Generalized Fractional Calculus and Applications

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Generalized Fractional Calculus and Applications
Virginia S Kiryakova
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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Book Description

In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed.This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.

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