Description
Taylor & Francis Ltd Mathematical Modeling Models Analysis And Applications 2014 Edition by Sandip Banerjee
Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential equations, namely ordinary, partial, delay, and stochastic. The book also contains a chapter on discrete modeling, consisting of differential equations, making it a complete textbook on this important skill needed for the study of science, engineering, and social sciences. More than just a textbook, this how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial, delayed, and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB (R) and Mathematica (R) are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project.Since mathematical modeling involves a diverse range of skills and tools, the author focuses on techniques that will be of particular interest to engineers, scientists, and others who use models of discrete and continuous systems. He gives students a foundation for understanding and using the mathematics that is the basis of computers, and therefore a foundation for success in engineering and science streams. About Mathematical ModelingWhat Is Mathematical Modeling?History of Mathematical ModelingLatest Development in Mathematical ModelingVarious Functional Forms in Mathematical ModelingMerits and Demerits in Mathematical ModelingMathematically Modeling Discrete ProcessDifference EquationsIntroduction to Discrete ModelsOne Dimensional Density Independent ModelsOne Dimensional Density Dependent ModelsStability AnalysisNonlinear Two-Dimensional Models: Stability and BifurcationContinuous Models Using Ordinary Differential EquationsIntroduction to Continuous ModelsFormation of Various Continuous ModelsSteady State SolutionsStability and LinearizationPhase Plane Diagrams of Linear SystemsStability CharacteristicsNull Cline ApproachPoincare Bendixson TheoryBifurcation and Limit CycleSpatial Models Using Partial Differential EquationsDiffusion Equations: Observations and ConsequencesDispersal Models Using DiffusionEffect of Density Dependent Dispersal on Population DynamicsModels for Age Dependent DispersalSteady State Solutions and Traveling WavesNon Linear Stability Analysis for Diffusion Reaction SystemBifurcation Analysis and Limit CyclesNumerical Solutions of Differential Equations with DiffusionPattern Developing Instability in Diffusion Reaction SystemsEffect of Cross DiffusionModeling with Delay Differential EquationsAn Introduction to Delay Differential EquationsVarious Mathematical Models with Time DelayDelay Induced Model for Tumor Immune Interaction (Single Discrete Delay)Stage Structure Predator Prey Models with Multiple Delays and Its Global StabilityModels with Distributed DelaysModeling with Stochastic Differential EquationsStochastic Process and Stochastic Differential Equations: a PreviewEffect of Additive Noise on a Logistic EquationStochastic Stability: Asymptotically Mean Square StableMean Square Stability of a Stochastic Model with Time DelaysNumerical Simulation of Stochastic Differential EquationsStochastic Metapopulation ModelsExamples and Exercises appear at the end of each chapter.