Practical Applied Mathematics - Modelling, Analysis, Approximation

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1、PracticalAppliedMathematicsModelling,Analysis,ApproximationSamHowisonOCIAMMathematicalInstituteOxfordUniversityOctober10,20032Contents1Introduction91.1Whatismodelling/whymodel?.................91.2Howtousethisbook.......................91.3acknowledgements.........................9I

2、Modellingtechniques112Thebasicsofmodelling132.1Introduction............................132.2Whatdowemeanbyamodel?.................142.3Principlesofmodelling......................162.3.1Example:inviscidfluidmechanics............172.3.2Example:viscousfluids..................182.4Conserv

3、ationlaws.........................212.5Conclusion.............................223Unitsanddimensions253.1Introduction............................253.2Unitsanddimensions.......................253.2.1Example:heatflow....................273.3Electricfieldsandelectrostatics................

4、.284Dimensionalanalysis394.1Nondimensionalisation......................394.1.1Example:advection-diffusion..............394.1.2Example:thedampedpendulum............434.1.3Example:beamsandstrings...............454.2TheNavier–Stokesequations...................474.2.1Waterinthebathtub...

5、................504.3Buckingham’sPi-theorem....................5134CONTENTS4.4Onwards..............................535Casestudy:hairmodellingandcablelaying615.1TheEuler–Bernoullimodelforabeam.............615.2Hairmodelling..........................635.3Cable-laying..................

6、..........645.4Modellingandanalysis......................655.4.1Boundaryconditions...................675.4.2Effectiveforcesandnondimensionalisation.......676Casestudy:thethermistor1736.1Thermistors............................736.1.1Asimplemodel......................736.2Nondimensiona

7、lisation......................756.3Athermistorinacircuit.....................776.3.1Theone-dimensionalmodel...............787Casestudy:electrostaticpainting837.1Electrostaticpainting.......................837.2Fieldequations..........................847.3Boundaryconditions..........

8、.............867.4N