mathematical modelling with case studies solutions

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Barnes b., fulford g.r., get access to all of the answers and step-by-step video explanations to this book and 5,000+ more. try numerade free., introduction to mathematical modelling, compartmental models, models of single populations, numerical solution of differential equations, interacting population models, phase-plane analysis, linearisation analysis, some extended population models, formulating basic heat models, solving time dependent heat problems, solving heat conduction problems, introduction to partial differential equations.

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Mathematical Modelling with Case Studies: Using Maple™ and MATLAB®, 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.

  • Focuses on compartmental models, population models, and heat transfer problems
  • Uses compartment diagrams and word equations to help readers conceptualize the formulation of differential equations
  • Includes many case studies to provide a practical understanding of how the models are used in current research, such as environmental science, biology, and archaeology
  • Supplies Maple codes in the text and online so results can be reproduced exactly
  • Offers end-of-chapter problems for practicing with the formulation, analysis, and interpretation of differential equation models.  Solutions manual available for qualifying instructors.

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Mathematical modelling with case studies : a differential equations approach using Maple and MATLAB

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  • 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 A
  • 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 Basic Heat 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 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 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 Introduction to Partial Differential Equations The heat conduction equation Oscillating soil temperatures Case study: detecting land mines Lake pollution revisited Appendix A: Differential Equations Properties of differential equations Solution by inspection First-order separable equations First-order linear equations Homogeneous equations Inhomogeneous equations Appendix B: Further Mathematics Linear algebra Partial derivatives and Taylor expansions Review of complex numbers Hyperbolic functions Integration using partial fractions Appendix C: Notes on Maple and MATLAB Brief introduction to Maple Using Maple to solve DEs Brief introduction to MATLAB Appendix D: Units and Scaling Scaling differential equations SI Units References Index Exercises appear at the end of each chapter.
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Mathematical Modelling

Case Studies and Projects

  • Jim Caldwell 0 ,
  • Douglas K. S. Ng 1

City University of Hong Kong, Kowloon, Hong Kong, P.R. China

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Part of the book series: Texts in the Mathematical Sciences (TMS, volume 28)

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Table of contents (19 chapters)

Front matter, introduction, ordinary differential equations, deterministic model in contagious disease, electromagnetic forces in high field magnet coils, mass balance of a reactor in steady state, the free and forced vibration of an automobile, cantilever beam subjected to an end load, ode problems, partial differential equations, cylindrical and spherical solidification in heat transfer, elastic analysis of a square plate with circular holes, motion of fluid layers, mass balance of a reactor with time dependency, flow through porous media, pde problems, optimization, linear programming problem involving wine production, transportation problem involving breweries and hotels, profit from an engineering plant.

  • linear optimization
  • mathematics
  • optimization
  • programming

Jim Caldwell, Douglas K. S. Ng

Book Title : Mathematical Modelling

Book Subtitle : Case Studies and Projects

Editors : Jim Caldwell, Douglas K. S. Ng

Series Title : Texts in the Mathematical Sciences

DOI : https://doi.org/10.1007/1-4020-1993-9

Publisher : Springer Dordrecht

eBook Packages : Springer Book Archive

Copyright Information : Springer Science+Business Media Dordrecht 2004

Hardcover ISBN : 978-1-4020-1991-3 Published: 31 March 2004

Softcover ISBN : 978-90-481-6566-7 Published: 04 December 2010

eBook ISBN : 978-1-4020-1993-7 Published: 10 April 2006

Series ISSN : 0927-4529

Edition Number : 1

Number of Pages : XI, 253

Topics : Mathematical Modeling and Industrial Mathematics , Engineering, general , Classical Mechanics , Numeric Computing , Algorithms

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  2. Mathematical Modelling with Case Studies

    Mathematical Modelling with Case Studies: Using Maple and MATLAB, 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

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  6. Mathematical Modelling with Case Studies: A Differential Equation

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    Mathematical Modelling with Case Studies: Using Maple™ and MATLAB®, 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 ...

  9. Mathematical Modelling with Case Studies

    Mathematical Modelling with Case Studies: Using Maple™ and MATLAB ®, 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 ...

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    Its content is based on many editions from the successful series of Modelling Weeks organized by the European Consortium of Mathematics in Industry (ECMI). Each chapter addresses a particular problem, and is written in a didactic way, providing the description of the problem, the particular way of approaching it and the proposed solution, along ...

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    Mathematical Modelling with Case Studies: Using Maple and MATLAB, 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

  21. Mathematical Modelling: Case Studies and Projects

    Softcover ISBN 978-90-481-6566-7 Published: 04 December 2010. eBook ISBN 978-1-4020-1993-7 Published: 10 April 2006. Series ISSN 0927-4529. Edition Number 1. Number of Pages XI, 253. Topics Mathematical Modeling and Industrial Mathematics, Engineering, general, Classical Mechanics, Numeric Computing, Algorithms. Back to top.

  22. Mathematical Modeling 4th Edition Textbook Solutions

    Step-by-step solution. Step 1 of 5. (a) Find the amount of rebate will maximize the profit using five step method. Consider that the five step method for the mathematical modelling approach as follows: Step 1: Ask the question. Step 2: Select the modelling approach. Step 3: Formulate the model. Step 4: solve the model.