Description
Apple Academic Press Inc. Mathematical Modelling With Case Studies Using Maple And Matlab 3Ed 2016 Edition by B. Barnes, G..R. Fulford
Mathematical Modelling with Case Studies: Using Maple (TM) and MATLAB (R), Third Edition provides students with hands-on modelling skills for a wide variety of problems involving differential equations that describe rates of change. While the book focuses on growth and decay processes, interacting populations, and heating/cooling problems, the mathematical techniques presented can be applied to many other areas.The text carefully details the process of constructing a model, including the conversion of a seemingly complex problem into a much simpler one. It uses flow diagrams and word equations to aid in the model-building process and to develop the mathematical equations. Employing theoretical, graphical, and computational tools, the authors analyze the behavior of the models under changing conditions. The authors often examine a model numerically before solving it analytically. They also discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model. The highly recommended second edition was praised for its lucid writing style and numerous real-world examples. With updated Maple (TM) and MATLAB (R) code as well as new case studies and exercises, this third edition continues to give students a clear, practical understanding of the development and interpretation of mathematical models. Introduction to Mathematical ModelingMathematical models An overview of the book Some modeling approaches Modeling for decision makingCompartmental Models Introduction Exponential decay and radioactivity Case study: detecting art forgeries Case study: Pacific rats colonize New Zealand Lake pollution models Case study: Lake Burley Griffin Drug assimilation into the blood Case study: dull, dizzy, or dead? Cascades of compartments First-order linear DEs Equilibrium points and stability Case study: money, money, money makes the world go aroundModels of Single PopulationsExponential growth Density-dependent growth Limited growth with harvesting Case study: anchovy wipe-out Case study: how can 2 x 106 birds mean rare? Discrete population growth and chaos Time-delayed regulation Case study: Australian blowfliesNumerical Solution of Differential Equations Introduction Basic numerical schemes Computer implementation using Maple and MATLAB Instability DiscussionInteracting Population ModelsIntroduction An epidemic model for influenza Predators and prey Case study: Nile Perch catastrophe Competing species Case study: aggressive protection of lerps and nymphs Model of a battle Case study: rise and fall of civilizationsPhase-Plane Analysis Introduction Phase-plane analysis of epidemic model Analysis of a battle model Analysis of a predator-prey model Analysis of competing species models The predator-prey model revisited Case study: bacteria battle in the gutLinearization AnalysisIntroduction Linear theory Applications of linear theory Nonlinear theory Applications of nonlinear theorySome Extended Population ModelsIntroduction Case study: competition, predation, and diversity Extended predator-prey model Case study: lemming mass suicides? Case study: prickly pear meets its moth Case study: geese defy mathematical convention Case study: possums threaten New Zealand cowsFormulating Heat and Mass Transport ModelsIntroduction Some basic physical laws Model for a hot water heater Heat conduction and Fourier's law Heat conduction through a wall Radial heat conduction Heat finsDiffusionSolving Time-Dependent Heat ProblemsThe cooling coffee problem revisitedThe water heater problem revisited Case study: it's hot and stuffy in the attic Spontaneous combustion Case study: fish and chips explodeSolving Heat Conduction and Diffusion ProblemsBoundary condition problems Heat loss through a wall Case study: double glazing: what's it worth?Insulating a water pipe Cooling a computer chipCase Study: Tumor growthIntroduction to Partial Differential EquationsThe heat conduction equation Oscillating soil temperatures Case study: detecting land mines Lake pollution revisitedAppendix A: Differential EquationsAppendix B: Further Mathematics Appendix C: Notes on Maple and MATLABAppendix D: Units and Scaling Appendix E: Parameters Appendix F: Answers and HintsReferences IndexExercises appear at the end of each chapter.