Explorations of Mathematical Models in Biology with MATLAB

Author: Mazen Shahin
Publisher: John Wiley & Sons
ISBN: 1118548531
Format: PDF, Kindle
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Explore and analyze the solutions of mathematical models from diverse disciplines As biology increasingly depends on data, algorithms, and models, it has become necessary to use a computing language, such as the user-friendly MATLAB, to focus more on building and analyzing models as opposed to configuring tedious calculations. Explorations of Mathematical Models in Biology with MATLAB provides an introduction to model creation using MATLAB, followed by the translation, analysis, interpretation, and observation of the models. With an integrated and interdisciplinary approach that embeds mathematical modeling into biological applications, the book illustrates numerous applications of mathematical techniques within biology, ecology, and environmental sciences. Featuring a quantitative, computational, and mathematical approach, the book includes: Examples of real-world applications, such as population dynamics, genetics, drug administration, interacting species, and the spread of contagious diseases, to showcase the relevancy and wide applicability of abstract mathematical techniques Discussion of various mathematical concepts, such as Markov chains, matrix algebra, eigenvalues, eigenvectors, first-order linear difference equations, and nonlinear first-order difference equations Coverage of difference equations to model a wide range of real-life discrete time situations in diverse areas as well as discussions on matrices to model linear problems Solutions to selected exercises and additional MATLAB codes Explorations of Mathematical Models in Biology with MATLAB is an ideal textbook for upper-undergraduate courses in mathematical models in biology, theoretical ecology, bioeconomics, forensic science, applied mathematics, and environmental science. The book is also an excellent reference for biologists, ecologists, mathematicians, biomathematicians, and environmental and resource economists.

Explorations of Mathematical Models in Biology with Maple

Author: Mazen Shahin
Publisher: John Wiley & Sons
ISBN: 111803211X
Format: PDF, Mobi
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"With an emphasis on Maple applications to showcase graphical and numerical techniques, this book investigates and analyzes the behavior of solutions of mathematical models and also features interesting linear and nonlinear models from diverse disciplines, such as biology, ecology, and environment. It utilizes difference equations, matrix algebra, and Markov chains as the main mathematical tools. It is an ideal book for students of mathematical biology, theoretical ecology, bioeconomics, forensic science, applied mathematics, and environmental science"--

Dynamical Systems with Applications using MATLAB

Author: Stephen Lynch
Publisher: Springer
ISBN: 3319068202
Format: PDF, Kindle
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This textbook, now in its second edition, provides a broad introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLAB®, Simulink®, the Image Processing Toolbox® and the Symbolic Math toolbox®, including MuPAD. Features new to the second edition include · sections on series solutions of ordinary differential equations, perturbation methods, normal forms, Gröbner bases, and chaos synchronization; · chapters on image processing and binary oscillator computing; · hundreds of new illustrations, examples, and exercises with solutions; and · over eighty up-to-date MATLAB program files and Simulink model files available online. These files were voted MATLAB Central Pick of the Week in July 2013. The hands-on approach of Dynamical Systems with Applications using MATLAB, Second Edition, has minimal prerequisites, only requiring familiarity with ordinary differential equations. It will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and physics. Praise for the first edition Summing up, it can be said that this text allows the reader to have an easy and quick start to the huge field of dynamical systems theory. MATLAB/SIMULINK facilitate this approach under the aspect of learning by doing. —OR News/Operations Research Spectrum The MATLAB programs are kept as simple as possible and the author's experience has shown that this method of teaching using MATLAB works well with computer laboratory classes of small sizes.... I recommend ‘Dynamical Systems with Applications using MATLAB’ as a good handbook for a diverse readership: graduates and professionals in mathematics, physics, science and engineering. —Mathematica

Differential Equations with MATLAB

Author: Mark McKibben
Publisher: CRC Press
ISBN: 1466557087
Format: PDF, ePub, Docs
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A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance. The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics. The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors’ accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB® GUIs allows students to discover patterns and make conjectures.

Development of Innovative Drugs via Modeling with MATLAB

Author: Ronald Gieschke
Publisher: Springer Science & Business Media
ISBN: 3642397654
Format: PDF, Docs
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The development of innovative drugs is becoming more difficult while relying on empirical approaches. This inspired all major pharmaceutical companies to pursue alternative model-based paradigms. The key question is: How to find innovative compounds and, subsequently, appropriate dosage regimens? Written from the industry perspective and based on many years of experience, this book offers: - Concepts for creation of drug-disease models, introduced and supplemented with extensive MATLAB programs - Guidance for exploration and modification of these programs to enhance the understanding of key principles - Usage of differential equations to pharmacokinetic, pharmacodynamic and (patho-) physiologic problems thereby acknowledging their dynamic nature - A range of topics from single exponential decay to adaptive dosing, from single subject exploration to clinical trial simulation, and from empirical to mechanistic disease modeling. Students with an undergraduate mathematical background or equivalent education, interest in life sciences and skills in a high-level programming language such as MATLAB, are encouraged to engage in model-based pharmaceutical research and development.

An Introduction to Optimal Control Problems in Life Sciences and Economics

Author: Sebastian Aniţa
Publisher: Springer Science & Business Media
ISBN: 9780817680985
Format: PDF
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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.

Explorations in Monte Carlo Methods

Author: Ronald W. Shonkwiler
Publisher: Springer Science & Business Media
ISBN: 038787836X
Format: PDF, Mobi
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Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.

Numerical techniques for chemical and biological engineers using MATLAB

Author: S. S. E. H. Elnashaie
Publisher: Springer Verlag
ISBN:
Format: PDF, ePub
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This is a textbook for undergraduate students of chemical and biologicalengineering. It is also useful for graduate students and professional engineers and numerical analysts. All reactive chemical and biological processes are highly nonlinear allowing for multiple steady states. This book addresses the bifurcation characteristics of chemical and biological processes as the general case and treats systems with a unique steady state as special cases. It uses a system approach which is the most efficient for knowledge organization and transfer. The book develops mathematical models for many commercial processes utilizing the mass-, momentum-, and heat-balance equations coupled to the rates of the processes that take place within the boundaries of the system. The models are solved numerically through MATLAB codes with emphasis on the design and optimization of the chemical and biological industrial equipment and plants, such as single and batteries of CSTRs, porous and nonporous catalyst pellets and their effectiveness factors, tubular catalytic and noncatalytic reactors, fluidized bed catalytic reactors, coupled fluidized beds such as reactor-regenerator systems (industrial fluid catalytic cracking units),fluidized bed reformers for producing hydrogen or syngas, fermenters for fuel ethanol, simulation of the brain acetylcholine neurocycle, anaerobic digesters,co- and countercurrent absorption columns, and many more. The book also includes verification against industrial data. The book's CD contains nearly 100 MATLAB programs which are meant to teach the readers how to solve a variety of important chemical and biological engineering problems. The algorithms include solving transcendental and algebraic equations, with and without bifurcation; as well as initial and boundary value ordinary differential equations.Said Elnashaie is Professor of Chemical and Biological Engineering at the University of British Columbia. Frank Uhlig is Professor of Mathematics at Auburn University. Chadia Affane is a PH.D. candidate in Applied Mathematics at Auburn with a B.S.in Chemical Engineering.The active interaction of these authors has brought about this new and modern interdisciplinary book.

Einf hrung in die Geometrie und Topologie

Author: Werner Ballmann
Publisher: Springer-Verlag
ISBN: 3034809018
Format: PDF, ePub, Mobi
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Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.