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Calculus for Biology and Medicine: A Vital Tool for Understanding Life's Processes
The intricacies of the biological world, from the rhythmic beating of a heart to the complex growth patterns of a population, are often best understood through the language of mathematics. While the image of a biologist might conjure up test tubes and microscopes, an increasing number rely on a surprisingly powerful tool: calculus. This post delves into the essential role of calculus in biology and medicine, exploring its applications and demonstrating why it's becoming an indispensable skill for aspiring scientists and healthcare professionals. We'll unpack its core concepts and show you how it illuminates the hidden mathematical elegance underlying biological systems.
Why is Calculus Important in Biological and Medical Fields?
Calculus, with its powerful tools of differentiation and integration, provides the framework for analyzing dynamic systems. In the biological sciences, many processes are continuous and constantly changing – population growth, drug concentration in the bloodstream, the spread of diseases, and the electrical activity of the heart are just a few examples. Understanding these dynamic processes requires the ability to model change, predict future states, and analyze rates of change, all of which are central to calculus.
#### Modeling Biological Growth and Decay:
One of the most common applications of calculus in biology is modeling exponential growth and decay. Whether it's the growth of bacterial colonies in a petri dish or the decay of a radioactive isotope used in medical imaging, calculus provides the tools to describe, predict, and analyze these processes precisely. Differential equations, a cornerstone of calculus, are used to construct models that capture the essence of these dynamic systems.
#### Analyzing Physiological Processes:
Calculus allows biologists and medical researchers to delve into the intricate workings of the human body. For instance, understanding the flow of blood through the circulatory system requires analyzing fluid dynamics, a field heavily reliant on calculus. Similarly, understanding the spread of nerve impulses involves analyzing changes in electrical potential over time, again requiring the tools of calculus.
#### Pharmacokinetics and Pharmacodynamics:
The study of how drugs are absorbed, distributed, metabolized, and excreted (pharmacokinetics) and the effects of drugs on the body (pharmacodynamics) are both deeply intertwined with calculus. Calculus is used to model drug concentration in the bloodstream over time, allowing researchers to optimize drug dosages and schedules to achieve the desired therapeutic effect while minimizing side effects. It helps determine the optimal drug delivery methods and the precise timing of administration.
Specific Applications of Calculus in Biology and Medicine
1. Population Dynamics: Calculus is crucial in studying how populations of organisms change over time, considering factors like birth rates, death rates, and migration. Differential equations help build models that predict future population sizes and analyze the impact of environmental changes or interventions.
2. Epidemiology: Understanding the spread of infectious diseases requires mathematical modeling. Calculus helps model the rate of infection spread, predict the peak of an epidemic, and evaluate the effectiveness of various control measures.
3. Biomechanics: The study of forces and their effects on biological systems, like the movement of limbs or the flow of blood, heavily relies on calculus. It's used to analyze muscle forces, joint stresses, and the biomechanics of various organs.
4. Genetics: While seemingly unrelated, calculus finds its place in population genetics, helping analyze gene frequencies and their changes over generations. It helps understand evolutionary processes and the spread of genetic traits.
Mastering Calculus for a Successful Career in Biology or Medicine
The benefits of a strong foundation in calculus extend far beyond textbook problems. It cultivates analytical and problem-solving skills crucial for interpreting experimental data, designing research studies, and comprehending complex scientific literature. For those aspiring to careers in research, the ability to develop and analyze mathematical models is invaluable.
Conclusion
Calculus is no longer a niche subject within biology and medicine; it's rapidly becoming an essential tool. Its ability to model dynamic systems, analyze change, and predict future states makes it indispensable for understanding the complex processes at play in living organisms. By mastering calculus, students equip themselves with the analytical power to contribute significantly to scientific advancements and improve healthcare practices.
FAQs
1. What level of calculus is needed for biology and medicine? A solid understanding of single and multivariable calculus, including differential and integral calculus, is generally sufficient for most biological and medical applications.
2. Are there specific calculus courses tailored to biology and medicine? Yes, many universities offer calculus courses specifically designed for students in biology, pre-med, and related fields. These courses often emphasize applications relevant to life sciences.
3. Can I learn calculus online if I don't have access to formal courses? Yes, many online resources, including MOOCs (Massive Open Online Courses) and online textbooks, offer comprehensive calculus instruction.
4. How can I apply calculus concepts to my current biology studies? Start by identifying dynamic processes in your coursework (e.g., population growth, enzyme kinetics). Then, search for relevant examples and models using calculus to understand them more deeply.
5. Are there software tools that can help me with calculus calculations related to biology? Yes, several software packages, such as MATLAB, R, and Python with scientific libraries, are widely used for modeling and analyzing biological data using calculus.
| calculus for biology and medicine: Calculus for Biology and Medicine Claudia Neuhauser, 2011 Calculus for Biology and Medicine, Third Edition, addresses the needs of students in the biological sciences by showing them how to use calculus to analyze natural phenomena. While the table of contents aligns well with a traditional calculus text, all the concepts are presented through biological and medical applications. The text provides students with the knowledge and skills necessary to analyze and interpret mathematical models of a diverse array of phenomena in the living world. Since this text is written for college freshmen, the examples were chosen so that no formal training in biology is needed. --From the Publisher. |
| calculus for biology and medicine: Calculus for Biology and Medicine Claudia Neuhauser, Marcus Roper, 2018-01-12 NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value; this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. For Books a la Carte editions that include MyLab(TM) or Mastering(TM), several versions may exist for each title - including customized versions for individual schools - and registrations are not transferable. In addition, you may need a Course ID, provided by your instructor, to register for and use MyLab or Mastering products. For one-semester or two-semester courses in Calculus for Life Sciences. Shows students how calculus is used to analyze phenomena in nature--while providing flexibility for instructors to teach at their desired level of rigor Calculus for Biology and Medicine motivates life and health science majors to learn calculus through relevant and strategically placed applications to their chosen fields. It presents the calculus in such a way that the level of rigor can be adjusted to meet the specific needs of the audience, from a purely applied course to one that matches the rigor of the standard calculus track. In the 4th Edition, new co-author Marcus Roper (UCLA) partners with author Claudia Neuhauser to preserve these strengths while adding an unprecedented number of real applications and infusing more modeling and technology. Also available with MyLab Math MyLab(TM) Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. For the first time, instructors teaching with Calculus for Biology and Medicine can assign text-specific online homework and other resources to students outside of the classroom. Learn more about MyLab Math. |
| calculus for biology and medicine: Calculus for Biology and Medicine Claudia Neuhauser, 2004 For a two-semester course in Calculus for Life Sciences. This text addresses the needs of students in the biological sciences by teaching calculus in a biological context without reducing the course level. It is a calculus text, written so that a math professor without a biology background can teach from it successfully. New concepts are introduced in a three step manner. First, a biological example motivates the topic; second, the topic is then developed via a simple mathematical example; and third the concept is tied to deeper biological examples. This allows students: to see why a concept is important; to understand how to use the concept computationally; to make sure that they can apply the concept. |
| calculus for biology and medicine: Calculus for Biology and Medicine Claudia Neuhauser, 2001 |
| calculus for biology and medicine: Applications Of Calculus To Biology And Medicine: Case Studies From Lake Victoria Nathan Ryan, Dorothy I Wallace, 2017-08-17 Biology majors and pre-health students at many colleges and universities are required to take a semester of calculus but rarely do such students see authentic applications of its techniques and concepts. Applications of Calculus to Biology and Medicine: Case Studies from Lake Victoria is designed to address this issue: it prepares students to engage with the research literature in the mathematical modeling of biological systems, assuming they have had only one semester of calculus. The text includes projects, problems and exercises: the projects ask the students to engage with the research literature, problems ask the students to extend their understanding of the materials and exercises ask the students to check their understanding as they read the text. Students who successfully work their way through the text will be able to engage in a meaningful way with the research literature to the point that they would be able to make genuine contributions to the literature. |
| calculus for biology and medicine: Fractional Calculus in Medical and Health Science Devendra Kumar, Jagdev Singh, 2020-07-09 This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them. The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies. The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science. |
| calculus for biology and medicine: Modeling Life Alan Garfinkel, Jane Shevtsov, Yina Guo, 2017-09-06 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? |
| calculus for biology and medicine: Calculus For Biology and Medicine: Pearson New International Edition PDF eBook Claudia Neuhauser, 2013-08-27 For a two-semester or three-semester course in Calculus for Life Sciences. Calculus for Biology and Medicine, Third Edition, addresses the needs of students in the biological sciences by showing them how to use calculus to analyze natural phenomena–without compromising the rigorous presentation of the mathematics. While the table of contents aligns well with a traditional calculus text, all the concepts are presented through biological and medical applications. The text provides students with the knowledge and skills necessary to analyze and interpret mathematical models of a diverse array of phenomena in the living world. Since this text is written for college freshmen, the examples were chosen so that no formal training in biology is needed. |
| calculus for biology and medicine: Physics in Biology and Medicine Paul Davidovits, 2008 This third edition covers topics in physics as they apply to the life sciences, specifically medicine, physiology, nursing and other applied health fields. It includes many figures, examples and illustrative problems and appendices which provide convenient access to the most important concepts of mechanics, electricity, and optics. |
| calculus for biology and medicine: Modeling and Simulation in Medicine and the Life Sciences Frank C. Hoppensteadt, Charles S. Peskin, 2012-12-06 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. |
| calculus for biology and medicine: Mathematics for Life Science and Medicine Yasuhiro Takeuchi, Yoh Iwasa, Kazunori Sato, 2007-01-25 The purpose of this volume is to present and discuss the many rich properties of the dynamical systems that appear in life science and medicine. It provides a fascinating survey of the theory of dynamical systems in biology and medicine. Each chapter will serve to introduce students and scholars to the state-of-the-art in an exciting area, to present new results, and to inspire future contributions to mathematical modeling in life science and medicine. |
| calculus for biology and medicine: Calculus for the Life Sciences James L. Cornette, Ralph A. Ackerman, 2015-12-30 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. |
| calculus for biology and medicine: Student Solutions Manual for Calculus for Biology and Medicine Claudia Neuhauser, Marcus Roper, 2018-01-25 Provides fully worked-out solutions to the odd-numbered exercises in the section and Chapter Review problems. Available in print (ISBN-13: 978-013-412269-4) or downloadable within MyLab(TM) Math. |
| calculus for biology and medicine: Optimization in Medicine Carlos J. S. Alves, Panos M. Pardalos, Luis Nunes Vicente, 2007-12-20 This volume presents a wide range of medical applications that can utilize mathematical computing. This work grew out of a workshop on optimization which was held during the 2005 CIM Thematic Term on Optimization in Coimbra, Portugal. It provides an overview of the state-of-the-art in optimization in medicine and will serve as an excellent reference for researchers in the medical computing community and for those working in applied mathematics and optimization. |
| calculus for biology and medicine: Introduction to Mathematics for Life Scientists E. Batschelet, 2012-12-06 A few decades ago mathematics played a modest role in life sciences. Today, however, a great variety of mathematical methods is applied in biology and medicine. Practically every mathematical procedure that is useful in physics, chemistry, engineering, and economics has also found an important application in the life sciences. The past and present training of life scientists does by no means reflect this development. However, the impact ofthe fast growing number of applications of mathematical methods makes it indispensable that students in the life sciences are offered a basic training in mathematics, both on the undergraduate and the graduate level. This book is primarily designed as a textbook for an introductory course. Life scientists may also use it as a reference to find mathematical methods suitable to their research problems. Moreover, the book should be appropriate for self-teaching. It will also be a guide for teachers. Numerous references are included to assist the reader in his search for the pertinent literature. |
| calculus for biology and medicine: Student's Solutions Manual, Calculus for Biology and Medicine, Third Edition Max Sterelyukhin, Claudia Neuhauser, 2010-01-22 Normal 0 false false false This manual contains completely worked-out solutions for all the odd-numbered exercises in the text. |
| calculus for biology and medicine: Quick Calculus Daniel Kleppner, Norman Ramsey, 1991-01-16 Quick Calculus 2nd Edition A Self-Teaching Guide Calculus is essential for understanding subjects ranging from physics and chemistry to economics and ecology. Nevertheless, countless students and others who need quantitative skills limit their futures by avoiding this subject like the plague. Maybe that's why the first edition of this self-teaching guide sold over 250,000 copies. Quick Calculus, Second Edition continues to teach the elementary techniques of differential and integral calculus quickly and painlessly. Your calculus anxiety will rapidly disappear as you work at your own pace on a series of carefully selected work problems. Each correct answer to a work problem leads to new material, while an incorrect response is followed by additional explanations and reviews. This updated edition incorporates the use of calculators and features more applications and examples. .makes it possible for a person to delve into the mystery of calculus without being mystified. --Physics Teacher |
| calculus for biology and medicine: Mathematical Methods in Biology J. David Logan, William Wolesensky, 2009-08-17 A one-of-a-kind guide to using deterministic and probabilistic methods for solving problems in the biological sciences Highlighting the growing relevance of quantitative techniques in scientific research, Mathematical Methods in Biology provides an accessible presentation of the broad range of important mathematical methods for solving problems in the biological sciences. The book reveals the growing connections between mathematics and biology through clear explanations and specific, interesting problems from areas such as population dynamics, foraging theory, and life history theory. The authors begin with an introduction and review of mathematical tools that are employed in subsequent chapters, including biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The following chapters examine standard discrete and continuous models using matrix algebra as well as difference and differential equations. Finally, the book outlines probability, statistics, and stochastic methods as well as material on bootstrapping and stochastic differential equations, which is a unique approach that is not offered in other literature on the topic. In order to demonstrate the application of mathematical methods to the biological sciences, the authors provide focused examples from the field of theoretical ecology, which serve as an accessible context for study while also demonstrating mathematical skills that are applicable to many other areas in the life sciences. The book's algorithms are illustrated using MATLAB®, but can also be replicated using other software packages, including R, Mathematica®, and Maple; however, the text does not require any single computer algebra package. Each chapter contains numerous exercises and problems that range in difficulty, from the basic to more challenging, to assist readers with building their problem-solving skills. Selected solutions are included at the back of the book, and a related Web site features supplemental material for further study. Extensively class-tested to ensure an easy-to-follow format, Mathematical Methods in Biology is an excellent book for mathematics and biology courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals working in the fields of biology, ecology, and biomathematics. |
| calculus for biology and medicine: Mathematics for the Life Sciences Erin N. Bodine, Suzanne Lenhart, Louis J. Gross, 2014-08-17 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 |
| calculus for biology and medicine: Mathematical Models in the Biosciences II Michael Frame, 2021-10-12 Volume Two of an award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences This is the second of a two-part series exploring essential concepts of calculus in the context of biological systems. Building on the essential ideas and theories of basic calculus taught in Mathematical Models in the Biosciences I, this book focuses on epidemiological models, mathematical foundations of virus and antiviral dynamics, ion channel models and cardiac arrhythmias, vector calculus and applications, and evolutionary models of disease. It also develops differential equations and stochastic models of many biomedical processes, as well as virus dynamics, the Clancy-Rudy model to determine the genetic basis of cardiac arrhythmias, and a sketch of some systems biology. Based on the author’s calculus class at Yale, the book makes concepts of calculus less abstract and more relatable for science majors and premedical students. |
| calculus for biology and medicine: Stochastic Dynamics for Systems Biology Christian Mazza, Michel Benaim, 2016-04-19 Stochastic Dynamics for Systems Biology is one of the first books to provide a systematic study of the many stochastic models used in systems biology. The book shows how the mathematical models are used as technical tools for simulating biological processes and how the models lead to conceptual insights on the functioning of the cellular processing |
| calculus for biology and medicine: An Introduction to Continuous-Time Stochastic Processes Vincenzo Capasso, David Bakstein, 2008-01-03 This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. Balancing theory and applications, the authors use stochastic methods and concrete examples to model real-world problems from engineering, biomathematics, biotechnology, and finance. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. The book will be of interest to students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, physics, and engineering. |
| calculus for biology and medicine: Mathematical Models in the Biosciences I Michael Frame, 2021-06-22 An award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences This is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers essential ideas and theories of basic calculus and probability while providing examples of how they apply to subjects like chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations, and nerve impulses. Based on the author’s calculus class at Yale University, the book makes concepts of calculus more relatable for science majors and premedical students. |
| calculus for biology and medicine: Calcium Phosphates in Oral Biology and Medicine Racquel Zapanta LeGeros, 1991 |
| calculus for biology and medicine: Aspects of Mathematical Modelling Roger J. Hosking, Ezio Venturino, 2008-03-02 The construction of mathematical models is an essential scientific activity. Mathematics is associated with developments in science and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in other fields. This book demonstrates the application of mathematics to research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management. |
| calculus for biology and medicine: Physical Biology of the Cell Rob Phillips, Jane Kondev, Julie Theriot, Hernan Garcia, 2012-10-29 Physical Biology of the Cell is a textbook for a first course in physical biology or biophysics for undergraduate or graduate students. It maps the huge and complex landscape of cell and molecular biology from the distinct perspective of physical biology. As a key organizing principle, the proximity of topics is based on the physical concepts that |
| calculus for biology and medicine: Mathematical Modeling in Systems Biology Brian P. Ingalls, 2022-06-07 An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis. |
| calculus for biology and medicine: Algebraic and Discrete Mathematical Methods for Modern Biology Raina Robeva, 2015-05-09 Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the modern biology skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. - Examines significant questions in modern biology and their mathematical treatments - Presents important mathematical concepts and tools in the context of essential biology - Features material of interest to students in both mathematics and biology - Presents chapters in modular format so coverage need not follow the Table of Contents - Introduces projects appropriate for undergraduate research - Utilizes freely accessible software for visualization, simulation, and analysis in modern biology - Requires no calculus as a prerequisite - Provides a complete Solutions Manual - Features a companion website with supplementary resources |
| calculus for biology and medicine: Mathematics in Population Biology Horst R. Thieme, 2018-06-05 The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples. Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. The theme of stage structure in an age-dependent context is developed in Part II, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. In Part III, the author considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues here in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies. Each section concludes with exercises, some with solutions, and suggestions for further study. The level of mathematics is relatively modest; a toolbox provides a summary of required results in differential equations, integration, and integral equations. In addition, a selection of Maple worksheets is provided. The book provides an authoritative tour through a dazzling ensemble of topics and is both an ideal introduction to the subject and reference for researchers. |
| calculus for biology and medicine: Mathematical Modeling of Biological Processes Avner Friedman, Chiu-Yen Kao, 2014-09-19 This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis. |
| calculus for biology and medicine: Stochastic Models for Fractional Calculus Mark M. Meerschaert, Alla Sikorskii, 2019-10-21 Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Many interesting problems in this area remain open. This book will guide the motivated reader to understand the essential background needed to read and unerstand current research papers, and to gain the insights and techniques needed to begin making their own contributions to this rapidly growing field. |
| calculus for biology and medicine: Essential Mathematical Biology Nicholas F. Britton, 2012-12-06 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. |
| calculus for biology and medicine: Likelihood and Bayesian Inference Leonhard Held, Daniel Sabanés Bové, 2020-03-31 This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications. |
| calculus for biology and medicine: Fractals in Biology and Medicine Gabriele A. Losa, Theo F. Nonnenmacher, Ewald R. Weibel, 1994 In March 2000 leading scientists gathered at the Centro Seminariale Monte Verità, Ascona, Switzerland, for the Third International Symposium on Fractals 2000 in Biology and Medicine. This interdisciplinary conference provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This volume highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes. |
| calculus for biology and medicine: Fractional Calculus and Waves in Linear Viscoelasticity Francesco Mainardi, 2010 This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types. It is intended to serve as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature given in the huge general bibliography. This book is likely to be of interest to applied scientists and engineers. |
| calculus for biology and medicine: The Calculus of Variations and Functional Analysis L. P. Lebedev, Michael J. Cloud, 2003 This volume is aimed at those who are concerned about Chinese medicine - how it works, what its current state is and, most important, how to make full use of it. The audience therefore includes clinicians who want to serve their patients better and patients who are eager to supplement their own conventional treatment. The authors of the book belong to three different fields, modern medicine, Chinese medicine and pharmacology. They provide information from their areas of expertise and concern, attempting to make it comprehensive for users. The approach is macroscopic and philosophical; readers convinced of the philosophy are to seek specific assistance. |
| calculus for biology and medicine: Student Solutions Manual to Accompany Calculus for Biology and Medicine Claudia Neuhauser, 2004 |
| calculus for biology and medicine: The Molecules of Life Kuriyan, John, Konforti, Boyana, Wemmer, David, 2012-07-25 This textbook provides an integrated physical and biochemical foundation for undergraduate students majoring in biology or health sciences. It is particularly suitable for students planning to enter the pharmaceutical industry. This new generation of molecular biologists and biochemists will harness the tools and insights of physics and chemistry to exploit the emergence of genomics and systems-level information in biology, and will shape the future of medicine. |
| calculus for biology and medicine: Optimal Control Applied to Biological Models Suzanne Lenhart, John T. Workman, 2007-05-07 From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into t |
| calculus for biology and medicine: Calculus Stanley I. Grossman, 1977 Revised edition of a standard textbook for a three-semester (or four- to five-quarter) introduction to calculus. In addition to covering all the standard topics, it includes a number of features written to accomplish three goals: to make calculus easier through the use of examples, graphs, reviews, etc.; to help students appreciate the beauty of calculus through the use of applications in a wide variety of fields; and to make calculus interesting by discussing the historical development of the subject. Annotation copyright by Book News, Inc., Portland, OR |
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