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Ordinary Differential Equations

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook not only follows this programme, but additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations.

Written for undergraduate students with a mathematical background, this book is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. It features numerous theoretical and computational examples.

Mathematics for Finance: An Introduction to Financial Engineering combines financial motivation with mathematical style. Assuming only basic knowledge of probability and calculus, it presents three major areas of mathematical finance, namely Option pricing based on the no-arbitrage principle in discrete and continuous time setting, Markowitz portfolio optimisation and Capital Asset Pricing Model, and basic stochastic interest rate models in discrete setting.

In Europe's Space Programme - to Ariane and Beyond, author Brian Harvey begins with the fledgling European rocket effort of the 1930s and the key pioneers of the period, examining the significance of the V-2 and the technological advances represented by its development. He shows how the Russians and Americans put their captured V-2s to work, but the European countries were slower to respond. Both Britain and France developed national space programmes in the 1950s and 1960s and the early attempts at European co-operation for launcher development - ELDO and ESRO - are described. The formation of the European Space Agency and the origins of the successful Ariane launcher programme are discussed and Europe's subsequent success in the world launcher market, its cutting-edge role in space applications and European manned spaceflight, are all described in detail.

This book presents the human hand from an overall perspective – from the first appearance of hand-like structures in the fins of big fishes living millions of years ago to today´s and the future’s mind-controlled artificial hands.

Essential Mathematical Biology is a self-contained introduction to the fast-growing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. This book will appeal to 3rd and 4th year undergraduate students studying mathematical biology. A background in calculus and differential equations is assumed, although the main results required are collected in the appendices. A dedicated website at www springer.co.uk/britton/ accompanies the book and provides further exercises, more detailed solutions to exercises in the book, and links to other useful sites.

Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise.Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion.

This rigorous yet accessible introduction to complex analysis and differential equations covers complex numbers, holomorphic functions, analytic functions, ordinary differential equations, Fourier series and applications to partial differential equations.

This self-contained, mathematical introduction to the development and theory of linear models is aimed primarily at undergraduate students of mathematics. It includes numerous worked examples and exercises with full solutions.

This is a user-friendly introduction to the methods of differential and integral calculus of one real variable. The key feature of this book is the care that has been taken to ease the transition from school to university maths. It presents new ideas in the context of existing mathematical experience, building on students A-level knowledge and extending it to the level encountered in first year degree courses in mathematics and the physical sciences. The emphasis is on both helping readers to understand the critical ideas, and developing their manipulative skills, so topics are explained using worked examples and exercises. Many of the explanations are based on geometry through studying graphs. The plotting capabilities of Maple are used to enhance understanding, although the book is written in such a way that the use of Maple is not essential, just an additional - and fun - aid to learning. Supplementary material, including further exercises, more detailed solutions to the exercises, and exam questions, will also be available via the web. Suitable for first year undergraduates in the mathematical sciences, and for courses such as engineering, where methods are important.

All researchers need to write or speak about their work, and to have research  that is worth presenting. Based on the author's decades of experience as a researcher and advisor, this third edition provides detailed guidance on writing and presentations and a comprehensive introduction to research methods, the how-to of being a successful scientist. Topics include:·         Development of ideas into research questions;·         How to find, read, evaluate and referee other research;·         Design and evaluation of experiments and appropriate use of statistics;·         Ethics, the principles of science and examples of science gone wrong.Much of the book is a step-by-step guide to effective communication, with advice on:·         Writing style and editing;·         Figures, graphs and tables;·         Mathematics and algorithms;·         Literature reviews and referees’ reports;·         Structuring of arguments and results into papers and theses;·         Writing of other professional documents;·         Presentation of talks and posters.Written in an accessible style and including handy checklists and exercises, Writing for Computer Science is not only an introduction to the doing and describing of research, but is a valuable reference for working scientists in the computing and mathematical sciences.

Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.

"Risks in Technological Systems" is an interdisciplinary university textbook and a book for the educated reader on the risks of today’s society. In order to understand and analyze risks associated with the engineering systems on which modern society relies, other concerns have to be addressed, besides technical aspects. In contrast to many academic textbooks dealing with technological risks, this book has a unique interdisciplinary character that presents technological risks in their own context.Twenty-four scientists have come together to present their views on risks in technological systems. Their scientific disciplines cover not only engineering, economics and medicine, but also history, psychology, literature and philosophy. Taken together these contributions provide a broad, but accurate, interdisciplinary introduction to a field of increasing global interest, as well as rich opportunities to achieve in-depth knowledge of the subject.

New edition of the classic complete reference book for cardiologists and trainee cardiologists on the theory and practice of electrocardiography, one of the key modalities used for evaluating cardiology patients and deciding on appropriate management strategies.

Taking a direct route, "Essential Topology" brings the most important aspects of modern topology within reach of a second-year undergraduate student.

The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology impacts all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies…, new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The environmental aspects of all of our society’s activities are extremely important if the countryside; the sea and wildernesses are to be fully enjoyed by future generations. Urban waste in all its manifestations presents a particularly difficult disposal problem, which must be tackled conscientiously to prevent long lasting damage to the environment. Technological solutions should be seen as part of the available options. In this monograph, the authors M. R. Katebi, M. A. Johnson and J. Wilkie seek to introduce a comprehensive technological framework to the particular measurement and control problems of wastewater processing plants. Of course the disposal of urban sewage is a long-standing process but past solutions have used options (disposal at sea) which are no longer acceptable. Thus to meet new effluent regulations it is necessary to develop a new technological paradigm based on process control methods, and this is what the authors attempt to provide.

Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances.In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors.

Model Predictive Control System Design and Implementation Using MATLAB® proposes methods for design and implementation of MPC systems using basis functions that confer the following advantages: - continuous- and discrete-time MPC problems solved in similar design frameworks;

From power plants to sugar refining, model predictive control (MPC) schemes have established themselves as the preferred control strategies for a wide variety of processes. The second edition of Model Predictive Control provides a thorough introduction to theoretical and practical aspects of the most commonly used MPC strategies. It bridges the gap between the powerful but often abstract techniques of control researchers and the more empirical approach of practitioners. Model Predictive Control demonstrates that a powerful technique does not always require complex control algorithms. The text features material on the following subjects: general MPC elements and algorithms; commercial MPC schemes; generalized predictive control multivariable, robust, constrained nonlinear and hybrid MPC; fast methods for MPC implementation; applications.All of the material is thoroughly updated for the second edition with the chapters on nonlinear MPC, MPC and hybrid systems and MPC implementation being entirely new. Many new exercises and examples have also been added throughout and Matlab programs to aid in their solution can be downloaded from the authors' website at http://www esi.us.es/MPCBOOK.The text is an excellent aid for graduate and advanced undergraduate students and will also be of use to researchers and industrial practitioners wishing to keep abreast of a fast-moving field.

This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are expounded in the last chapter.With a focus on clarity rather than brevity, this text gives clear motivation, definitions and examples with transparent proofs. Much of the material included is published for the first time in textbook form, for example Schwarz' Theorem in Chapter 2 and double sequences and sufficient conditions for constrained extrema in Chapter 4. A wide selection of problems, ranging from simple to more challenging, are included with carefully formed solutions.Ideal as a classroom text or a self study resource for students, this book will appeal to higher level undergraduates in Mathematics.

Discrete mathematics has now established its place in most undergraduate mathematics courses. This textbook provides a concise, readable and accessible introduction to a number of topics in this area, such as enumeration, graph theory, Latin squares and designs. It is aimed at second-year undergraduate mathematics students, and provides them with many of the basic techniques, ideas and results. It contains many worked examples, and each chapter ends with a large number of exercises, with hints or solutions provided for most of them. As well as including standard topics such as binomial coefficients, recurrence, the inclusion-exclusion principle, trees, Hamiltonian and Eulerian graphs, Latin squares and finite projective planes, the text also includes material on the ménage problem, magic squares, Catalan and Stirling numbers, and tournament schedules.

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

It is increasingly clear that good quantitative work in the environmental sciences must be genuinely interdisciplinary. This volume, the proceedings of the first combined TIES/SPRUCE conference held at the University of Sheffield in September 2000, well demonstrates the truth of this assertion, highlighting the successful use of both statistics and mathematics in important practical problems.It brings together distinguished scientists and engineers to present the most up-to-date and practical methods for quantitative measurement and prediction and is organised around four themes:- spatial and temporal models and methods;- environmental sampling and standards;- atmosphere and ocean;- risk and uncertainty.Quantitative Methods for Current Environmental Issues is an invaluable resource for statisticians, applied mathematicians and researchers working on environmental problems, and for those in government agencies and research institutes involved in the analysis of environmental issues.

This book contains everything an astronomer needs to know about binocular observing. The book takes an in-depth look at the instruments themselves. It has sections on evaluating and buying binoculars and binocular telescopes, their care, mounting, and accessories. In addition there is a selection of fifty fine objects to be seen with 50mm and 100mm binoculars. The advantages of using both eyes for astronomical observing are many and considerable, largely because of the way the human brain processes visual information. This book enables the astronomer to maximize those advantages.

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing.

Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises.

Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance.