This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background.

Author: Nicholas F. Britton

Publisher: Springer Science & Business Media

ISBN: 9781447100492

Category: Mathematics

Page: 335

View: 237

This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. 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. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.

Mathematical Biology is a richly illustrated textbook in an exciting and fast growing field.

Author: James D. Murray

Publisher: Springer Science & Business Media

ISBN: 0387952233

Category: Mathematics

Page: 553

View: 778

Mathematical Biology is a richly illustrated textbook in an exciting and fast growing field. Providing an in-depth look at the practical use of math modeling, it features exercises throughout that are drawn from a variety of bioscientific disciplines - population biology, developmental biology, physiology, epidemiology, and evolution, among others. It maintains a consistent level throughout so that graduate students can use it to gain a foothold into this dynamic research area.

Math. Comput., 24, 809–820. Brauer, G.M., Steiberger, D.R., and Stansbury, J.W.
(1986). Dependence of Curing Time Peak Temperature and Mechanical ... Essential Mathematical Biology (Springer Undergraduate Mathematics Series).

Author: Jirí Nedoma

Publisher: John Wiley & Sons

ISBN: 1118006461

Category: Science

Page: 592

View: 907

Cutting-edge solutions to current problems in orthopedics, supported by modeling and numerical analysis Despite the current successful methods and achievements of good joint implantations, it is essential to further optimize the shape of implants so they may better resist extreme long-term mechanical demands. This book provides the orthopedic, biomechanical, and mathematical basis for the simulation of surgical techniques in orthopedics. It focuses on the numerical modeling of total human joint replacements and simulation of their functions, along with the rigorous biomechanics of human joints and other skeletal parts. The book includes: An introduction to the anatomy and biomechanics of the human skeleton, biomaterials, and problems of alloarthroplasty The definition of selected simulated orthopedic problems Constructions of mathematical model problems of the biomechanics of the human skeleton and its parts Replacement parts of the human skeleton and corresponding mathematical model problems Detailed mathematical analyses of mathematical models based on functional analysis and finite element methods Biomechanical analyses of particular parts of the human skeleton, joints, and corresponding replacements A discussion of the problems of data processing from nuclear magnetic resonance imaging and computer tomography This timely book offers a wealth of information on the current research in this field. The theories presented are applied to specific problems of orthopedics. Numerical results are presented and discussed from both biomechanical and orthopedic points of view and treatment methods are also briefly addressed. Emphasis is placed on the variational approach to the investigated model problems while preserving the orthopedic nature of the investigated problems. The book also presents a study of algorithmic procedures based on these simulation models. This is a highly useful tool for designers, researchers, and manufacturers of joint implants who require the results of suggested experiments to improve existing shapes or to design new shapes. It also benefits graduate students in orthopedics, biomechanics, and applied mathematics.

J. Math. Mech., 18:1025–1042, 1968/69. [27] G. W. Bluman and J. D. Cole.
Similarity methods for differential equations, volume 13 of Applied Mathematical
... Essential mathematical biology. Springer Undergraduate Mathematics Series.

Author: Roman Cherniha

Publisher: CRC Press

ISBN: 9781498776196

Category: Mathematics

Page: 238

View: 537

It is well known that symmetry-based methods are very powerful tools for investigating nonlinear partial differential equations (PDEs), notably for their reduction to those of lower dimensionality (e.g. to ODEs) and constructing exact solutions. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated problems. The book summarises the results derived by the authors during the last 10 years and those obtained by some other authors.

Springer Undergraduate Mathematics Series Springer Verlag , London ( 2003 ) .
xii + 270 pages . ... The continuum description is suitable for physical , biological ,
chemical phenomena , where large numbers of individual particles determine ...

The biological content of the book is self-contained and includes many basic biology topics such as the genetic code, Mendelian genetics, population dynamics, predator-prey relationships, epidemiology, and immunology.

Author: Glenn Ledder

Publisher: Springer Science & Business Media

ISBN: 9781461472766

Category: Mathematics

Page: 431

View: 324

Mathematics for the Life Sciences provides present and future biologists with the mathematical concepts and tools needed to understand and use mathematical models and read advanced mathematical biology books. It presents mathematics in biological contexts, focusing on the central mathematical ideas, and providing detailed explanations. The author assumes no mathematics background beyond algebra and precalculus. Calculus is presented as a one-chapter primer that is suitable for readers who have not studied the subject before, as well as readers who have taken a calculus course and need a review. This primer is followed by a novel chapter on mathematical modeling that begins with discussions of biological data and the basic principles of modeling. The remainder of the chapter introduces the reader to topics in mechanistic modeling (deriving models from biological assumptions) and empirical modeling (using data to parameterize and select models). The modeling chapter contains a thorough treatment of key ideas and techniques that are often neglected in mathematics books. It also provides the reader with a sophisticated viewpoint and the essential background needed to make full use of the remainder of the book, which includes two chapters on probability and its applications to inferential statistics and three chapters on discrete and continuous dynamical systems. The biological content of the book is self-contained and includes many basic biology topics such as the genetic code, Mendelian genetics, population dynamics, predator-prey relationships, epidemiology, and immunology. The large number of problem sets include some drill problems along with a large number of case studies. The latter are divided into step-by-step problems and sorted into the appropriate section, allowing readers to gradually develop complete investigations from understanding the biological assumptions to a complete analysis.

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, ...

Author: Fred Brauer

Publisher: Springer Science & Business Media

ISBN: 9783540789109

Category: Medical

Page: 414

View: 513

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).

With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, ...

Author: Sebastian Aniţa

Publisher: Springer Science & Business Media

ISBN: 0817680985

Category: Mathematics

Page: 232

View: 565

Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance.

This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of one science into another. The book focuses on problems of contemporary interest, such as cancer, genetics, and the rapidly growing field of genomics.

The essential assumption of the model is the bistability of the network with
neurons firing on the odd or even cycles of the ... Therefore , I recommend it as a
good paper to be read and discussed in mathematical biology seminars . ...
accessible to neuroscientists as well as advanced undergraduate math students (
indeed , the level of accessibility is similar to ... biology , morphogenesis and
neurosciences ( Kyoto , 1985 ) , 267 – 281 , Lecture Notes in Biomath . , 71 , Springer , Berlin ...

Author: Michel Eduardo Beleza YamagishiPublish On: 2017-08-31

This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA.

Author: Michel Eduardo Beleza Yamagishi

Publisher: Springer

ISBN: 9783319626895

Category: Mathematics

Page: 82

View: 297

This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.

Author: American Mathematical SocietyPublish On: 1984

Wissenschaften in Mathematics mainstream topics. theories in mathematical biology, range of modern mathematics. ... Just recently, several important books
on nonlinear systems and bifurcation theory appeared. ... engineering, political
science, psychology, and other areas are the central Your library cannot be
complete without these Springer Series. ... Undergraduate Texts in Mathematics
The books in this series are trendsetters, and not merely standard introductory
textbooks.

In this book, there is a strong emphasis on application with the necessary mathematical grounding.

Author: Phil Dyke

Publisher: Springer Science & Business Media

ISBN: 9781447163954

Category: Mathematics

Page: 318

View: 374

In this book, there is a strong emphasis on application with the necessary mathematical grounding. There are plenty of worked examples with all solutions provided. This enlarged new edition includes generalised Fourier series and a completely new chapter on wavelets. Only knowledge of elementary trigonometry and calculus are required as prerequisites. An Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems.

A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as ...

Author: Susanne Brenner

Publisher: Springer Science & Business Media

ISBN: 9781475736588

Category: Mathematics

Page: 363

View: 183

A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide

This highly readable book aims to ease the many challenges of starting undergraduate research.

Author: Aaron Wootton

Publisher: Birkhäuser

ISBN: 9783319660653

Category: Mathematics

Page: 313

View: 397

This highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading. The content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them.

Institute is probably the leading mathematics institute in India . ... ISBN 0 387
95223 3 , 0 387 95228 4 ( Springer ) . ... A book on mathematical biology cannot
follow the pattern we would expect in physics : basic theory leading on to
applications . ... Mathematical Biology would be eminently suitable as a text for a
final year undergraduate or postgraduate course in mathematical biology – not
the whole of it ...

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior.

Author: Alan Garfinkel

Publisher: Springer

ISBN: 9783319597317

Category: Mathematics

Page: 445

View: 510

This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?