Introduction to Mathematical Modeling Mathematical models An overview of the book Some modeling approaches Modeling for decision making Compartmental 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 around Models of Single Populations Exponential growth Density-dependent growth Limited growth with harvesting Case study: anchovy wipe-out Case study: how can 2 Ã-- 106 birds mean rare? Discrete population growth and chaos Time-delayed regulation Case study: Australian blowflies Numerical Solution of Differential Equations Introduction Basic numerical schemes Computer implementation using Maple and MATLAB Instability Discussion Interacting Population Models Introduction 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 civilizations Phase-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 gut Linearization Analysis Introduction Linear theory Applications of linear theory Nonlinear theory Applications of nonlinear theory Some Extended Population Models Introduction 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 cows Formulating Heat and Mass Transport Models Introduction 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 fins Diffusion Solving Time-Dependent Heat Problems The cooling coffee problem revisited The water heater problem revisited Case study: it''s hot and stuffy in the attic Spontaneous combustion Case study: fish and chips explode Solving Heat Conduction and Diffusion Problems Boundary condition problems Heat loss through a wall Case study: double glazing: what''s it worth? Insulating a water pipe Cooling a computer chip Case Study: Tumor growth Introduction to Partial Differential Equations The heat conduction equation Oscillating soil temperatures Case study: detecting land mines <BR>Case study: anchovy wipe-out Case study: how can 2 Ã-- 106 birds mean rare? Discrete population growth and chaos Time-delayed regulation Case study: Australian blowflies Numerical Solution of Differential Equations Introduction Basic numerical schemes Computer implementation using Maple and MATLAB Instability Discussion Interacting Population Models Introduction 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 civilizations Phase-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 gut Linearization Analysis Introduction Linear theory Applications of linear theory Nonlinear theory Applications of nonlinear theory Some Extended Population Models Introduction 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 cows Formulating Heat and Mass Transport Models Introduction 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 fins Diffusion Solving Time-Dependent Heat Problems The cooling coffee problem revisited The water heater problem revisited Case study: it''s hot and stuffy in the attic Spontaneous combustion Case study: fish and chips explode Solving Heat Conduction and Diffusion Problems Boundary condition problems Heat loss through a wall Case study: double glazing: what''s it worth? Insulating a water pipe Cooling a computer chip Case Study: Tumor growth Introduction to Partial Differential Equations The heat conduction equation Oscillating soil temperatures Case study: detecting land mines &-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 gut Linearization Analysis Introduction Linear theory Applications of linear theory Nonlinear theory Applications of nonlinear theory Some Extended Population Models Introduction 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 cows Formulating Heat and Mass Transport Models Introduction 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 fins Diffusion Solving Time-Dependent Heat Problems The cooling coffee problem revisited The water heater problem revisited Case study: it''s hot and stuffy in the attic Spontaneous combustion Case study: fish and chips explode Solving Heat Conduction and Diffusion Problems Boundary condition problems Heat loss through a wall Case study: double glazing: what''s it worth? Insulating a water pipe Cooling a computer chip Case Study: Tumor growth Introduction to Partial Differential Equations The heat conduction equation Oscillating soil temperatures Case study: detecting land mines &odels Introduction 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 fins Diffusion Solving Time-Dependent Heat Problems The cooling coffee problem revisited The water heater problem revisited Case study: it''s hot and stuffy in the attic Spontaneous combustion Case study: fish and chips explode Solving Heat Conduction and Diffusion Problems Boundary condition problems Heat loss through a wall Case study: double glazing: what''s it worth? Insulating a water pipe Cooling a computer chip Case Study: Tumor growth Introduction to Partial Differential Equations The heat conduction equation Oscillating soil temperatures Case study: detecting land mines &ifferential Equations The heat conduction equation Oscillating soil temperatures Case study: detecting land mines Lake pollution revisited Appendix A: Differential Equations Appendix B: Further Mathematics Appendix C: Notes on Maple and MATLAB Appendix D: Units and Scaling Appendix E: Parameters Appendix F: Answers and Hints References Index Exercises appear at the end of each chapter.