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Author : James L. Cornette,Ralph A. Ackerman
Publisher : Unknown
Page : 128 pages
File Size : 46,6 Mb
Release : 2013
Category : Mathematics
ISBN : OCLC:1148174223
Author : James L. Cornette,Ralph A. Ackerman
Publisher : American Mathematical Soc.
Page : 713 pages
File Size : 53,5 Mb
Release : 2019-05-25
Category : Calculus
ISBN : 9781470451424
Calculus for the Life Sciences is an entire reimagining of the standard calculus sequence with the needs of life science students as the fundamental organizing principle. Those needs, according to the National Academy of Science, include: the mathematical concepts of change, modeling, equilibria and stability, structure of a system, interactions among components, data and measurement, visualization, and algorithms. This book addresses, in a deep and significant way, every concept on that list. The book begins with a primer on modeling in the biological realm and biological modeling is the theme and frame for the entire book. The authors build models of bacterial growth, light penetration through a column of water, and dynamics of a colony of mold in the first few pages. In each case there is actual data that needs fitting. In the case of the mold colony that data is a set of photographs of the colony growing on a ruled sheet of graph paper and the students need to make their own approximations. Fundamental questions about the nature of mathematical modeling—trying to approximate a real-world phenomenon with an equation—are all laid out for the students to wrestle with. The authors have produced a beautifully written introduction to the uses of mathematics in the life sciences. The exposition is crystalline, the problems are overwhelmingly from biology and interesting and rich, and the emphasis on modeling is pervasive. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to [email protected] for more information. Online question content and interactive step-by-step tutorials are available for this title in WebAssign. WebAssign is a leading provider of online instructional tools for both faculty and students.
Author : James L. Cornette,Ralph A. Ackerman
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2011
Category : Mathematics
ISBN : OCLC:1319300236
Author : James L. Cornette
Publisher : Unknown
Page : 560 pages
File Size : 46,5 Mb
Release : 2012-02-04
Category : Biomathematics
ISBN : 1470025884
Volume II is suitable for students who have studied calculus and are interested in difference and differential equation models in the life sciences. Volume II consists of Chapter 1 of Volume I, the differential equations content of Chapters 3, 5, 7, and 10 of Volume I, and five chapters on linear and non-linear first and second order difference equations and differential equations.
Author : Frederick R. Adler
Publisher : Cengage Learning Canada Inc
Page : 128 pages
File Size : 54,9 Mb
Release : 2015-05-11
Category : Mathematics
ISBN : 9780176728076
Mathematics has played a major role in breakthroughs in epidemiology, genetics, physiology, and other biological areas. Calculus for the Life Sciences: Modelling the Dynamics of Life provides life science students with a thorough grounding in mathematics while helping them to understand the role mathematics has in biological science.
Author : Erin N. Bodine,Suzanne Lenhart,Louis J. Gross
Publisher : Princeton University Press
Page : 630 pages
File Size : 49,9 Mb
Release : 2014-08-17
Category : Mathematics
ISBN : 9780691150727
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 : Alan Garfinkel,Jane Shevtsov,Yina Guo
Publisher : Springer
Page : 445 pages
File Size : 53,5 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9783319597317
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 : Glenn Ledder
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 43,7 Mb
Release : 2013-08-29
Category : Mathematics
ISBN : 9781461472766
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.
Author : Frederick R Adler,Miroslav Lovrić
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 2014-02-15
Category : Calculus
ISBN : 0176530789
Mathematics has played a major role in breakthroughs in epidemiology, genetics, physiology, and other biological areas. Calculus for the Life Sciences: Modelling the Dynamics of Life provides life science students with a thorough grounding in mathematics while helping them to understand the role mathematics has in biological science.
Author : James P. Keener
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 52,9 Mb
Release : 2021-06-02
Category : Education
ISBN : 9781470454289
How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.
Author : Joseph M. Mahaffy,Alexandra Chávez-Ross
Publisher : Unknown
Page : 339 pages
File Size : 46,7 Mb
Release : 2004
Category : Calculus
ISBN : 0536839891
Author : Michael Olinick
Publisher : John Wiley & Sons
Page : 594 pages
File Size : 46,5 Mb
Release : 2014-05-05
Category : Mathematics
ISBN : 9781118642696
Olinick’s Mathematical Models in the Social and Life Sciences concentrates not on physical models, but on models found in biology, social science, and daily life. This text concentrates on a relatively small number of models to allow students to study them critically and in depth, and balances practice and theory in its approach. Each chapter concluded with suggested projects that encourage students to build their own models, and space is set aside for historical and biographical notes about the development of mathematical models.
Author : Wan Frederic Y M
Publisher : World Scientific
Page : 476 pages
File Size : 53,5 Mb
Release : 2019-08-29
Category : Mathematics
ISBN : 9789813274624
Biological processes are evolutionary in nature and often evolve in a noisy environment or in the presence of uncertainty. Such evolving phenomena are necessarily modeled mathematically by stochastic differential/difference equations (SDE), which have been recognized as essential for a true understanding of many biological phenomena. Yet, there is a dearth of teaching material in this area for interested students and researchers, notwithstanding the addition of some recent texts on stochastic modelling in the life sciences. The reason may well be the demanding mathematical pre-requisites needed to 'solve' SDE.A principal goal of this volume is to provide a working knowledge of SDE based on the premise that familiarity with the basic elements of a stochastic calculus for random processes is unavoidable. Through some SDE models of familiar biological phenomena, we show how stochastic methods developed for other areas of science and engineering are also useful in the life sciences. In the process, the volume introduces to biologists a collection of analytical and computational methods for research and applications in this emerging area of life science. The additions broaden the available tools for SDE models for biologists that have been limited by and large to stochastic simulations.
Author : Frederic Y M Wan
Publisher : World Scientific Publishing Company
Page : 400 pages
File Size : 43,6 Mb
Release : 2017-08-16
Category : Mathematics
ISBN : 9789813143357
Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) the case study approach, and 2) the method based approach (that teaches mathematical techniques with applications to relevant mathematical models). This text emphasizes instead the scientific issues for modeling different phenomena. For the natural or harvested growth of a fish population, we may be interested in the evolution of the population, whether it reaches a steady state (equilibrium or cycle), stable or unstable with respect to a small perturbation from equilibrium, or whether a small change in the environment would cause a catastrophic change, etc. Each scientific issue requires an appropriate model and a different set of mathematical tools to extract information from the model. Models examined are chosen to help explain or justify empirical observations such as cocktail drug treatments are more effective and regenerations after injuries or illness are fast-tracked (compared to original developments). Volume I of this three-volume set limits its scope to phenomena and scientific issues that are modeled by ordinary differential equations (ODE). Scientific issues such as signal and wave propagation, diffusion, and shock formation involving spatial dynamics to be modeled by partial differential equations (PDE) will be treated in Vol. II. Scientific issues involving randomness and uncertainty are examined in Vol. III. Request Inspection Copy Contents: Mathematical Models and the Modeling CycleGrowth of a Population:Evolution and EquilibriumStability and BifurcationInteracting Populations:Linear InteractionsNonlinear Autonomous InteractionsHIV Dynamics and Drug TreatmentsIndex Theory, Bistability and FeedbackOptimization:The Economics of GrowthOptimization over a Planning PeriodModifications of the Basic ProblemBoundary Value Problems are More ComplexConstraints and Control:"Do Your Best" and the Maximum PrincipleChlamydia TrachomatisGenetic Instability and CarcinogenesisMathematical Modeling RevisitedAppendices:First Order ODEBasic Numerical MethodsAssignments Readership: Undergraduates in mathematical biology, mathematical modeling of dynamical systems, optimization and control, viral dynamics (infectious diseases), oncology.
Author : Sebastian J. Schreiber,Karl Smith,Wayne Getz
Publisher : Wiley Global Education
Page : 744 pages
File Size : 45,5 Mb
Release : 2014-01-17
Category : Mathematics
ISBN : 9781118893357
In this much anticipated first edition, the authors present the basic canons of first-year calculus, but motivated through real biological problems. The two main goals of the text are to provide students with a thorough grounding in calculus concepts and applications, analytical techniques, and numerical methods and to have students understand how, when, and why calculus can be used to model biological phenomena.Ê Both students and instructors will find the book to be a gateway to the exciting interface of mathematics and biology.