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| Author | : Jacques Istas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 170 |
| Release | : 2005-10-04 |
| Genre | : Mathematics |
| ISBN | : 354027877X |
Provides a wide range of mathematical models currently used in the life sciences Each model is thoroughly explained and illustrated by example Includes three appendices to allow for independent reading
| Author | : Paul Doucet |
| Publisher | : Prentice Hall |
| Total Pages | : 490 |
| Release | : 1992-01-01 |
| Genre | : Biomathematics. |
| ISBN | : 9780135620182 |
Combining mathematics, biology, statistics and computer applications, this text applies mathematical methods to the solution of biological and related problems. It demonstrates how to formulate mathematical models of dynamic processes and how to study their behaviour analytically and numerically.
| Author | : Alan Garfinkel |
| Publisher | : Springer |
| Total Pages | : 456 |
| Release | : 2017-09-06 |
| Genre | : Mathematics |
| ISBN | : 3319597310 |
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?
| Author | : Giovanni Naldi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 437 |
| Release | : 2010-08-12 |
| Genre | : Mathematics |
| ISBN | : 0817649468 |
Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.
| Author | : James L. Cornette |
| Publisher | : MAA Press |
| Total Pages | : 713 |
| Release | : 2015-12-30 |
| Genre | : |
| ISBN | : 9781614446156 |
Freshman and sophomore life sciences students respond well to the modeling approach to calculus, difference equations, and differential equations presented in this book. Examples of population dynamics, pharmacokinetics, and biologically relevant physical processes are introduced in Chapter 1, and these and other life sciences topics are developed throughout the text. The students should have studied algebra, geometry, and trigonometry, but may be life sciences students because they have not enjoyed their previous mathematics courses.
| Author | : Urszula Ledzewicz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 426 |
| Release | : 2012-10-20 |
| Genre | : Mathematics |
| ISBN | : 1461441781 |
Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.
| Author | : Frank C. Hoppensteadt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 257 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475741316 |
The aim of this book is to introduce the subject of mathematical modeling in the life sciences. It is intended for students of mathematics, the physical sciences, and engineering who are curious about biology. Additionally, it will be useful to students of the life sciences and medicine who are unsatisfied with mere description and who seek an understanding of biological mechanism and dynamics through the use of mathematics. The book will be particularly useful to premedical students, because it will introduce them not only to a collection of mathematical methods but also to an assortment of phenomena involving genetics, epidemics, and the physiology of the heart, lung, and kidney. Because of its introductory character, mathematical prerequisites are kept to a minimum; they involve only what is usually covered in the first semester of a calculus sequence. The authors have drawn on their extensive experience as modelers to select examples which are simple enough to be understood at this elementary level and yet realistic enough to capture the essence of significant biological phenomena drawn from the areas of population dynamics and physiology. Because the models presented are realistic, the book can serve not only as an introduction to mathematical methods but also as a mathematical introduction to the biological material itself. For the student, who enjoys mathematics, such an introduction will be far more stimulating and satisfying than the purely descriptive approach that is traditional in the biological sciences.
| Author | : Erin N. Bodine |
| Publisher | : Princeton University Press |
| Total Pages | : 630 |
| Release | : 2014-08-17 |
| Genre | : Mathematics |
| ISBN | : 0691150729 |
An accessible undergraduate textbook on the essential math concepts used in the life sciences The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone. Proven in the classroom and requiring only a background in high school math, Mathematics for the Life Sciences doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences. Provides undergraduate life science students with a succinct overview of major mathematical concepts that are essential for modern biology Covers all the major quantitative concepts that national reports have identified as the ideal components of an entry-level course for life science students Provides good background for the MCAT, which now includes data-based and statistical reasoning Explicitly links data and math modeling Includes end-of-chapter homework problems, end-of-unit student projects, and select answers to homework problems Uses MATLAB throughout, and MATLAB m-files with an R supplement are available online Prepares students to read with comprehension the growing quantitative literature across the life sciences A solutions manual for professors and an illustration package is available
| Author | : Frank C. Hoppensteadt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 362 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0387215719 |
The result of lectures given by the authors at New York University, the University of Utah, and Michigan State University, the material is written for students who have had only one term of calculus, but it contains material that can be used in modeling courses in applied mathematics at all levels through early graduate courses. Numerous exercises are given as well as solutions to selected exercises, so as to lead readers to discover interesting extensions of that material. Throughout, illustrations depict physiological processes, population biology phenomena, corresponding models, and the results of computer simulations. Topics covered range from population phenomena to demographics, genetics, epidemics and dispersal; in physiological processes, including the circulation, gas exchange in the lungs, control of cell volume, the renal counter-current multiplier mechanism, and muscle mechanics; to mechanisms of neural control. Each chapter is graded in difficulty, so a reading of the first parts of each provides an elementary introduction to the processes and their models.
| Author | : Edward Beltrami |
| Publisher | : Academic Press |
| Total Pages | : 281 |
| Release | : 2013-06-19 |
| Genre | : Social Science |
| ISBN | : 0124046932 |
Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. - Offers 40% more content – 5 new chapters in addition to revisions to existing chapters - Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general - Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book
