โ Scribed by J. Caldwell, Douglas K.S.
No coin nor oath required. For personal study only.
Unlike a traditional textbook, this book deals completely with Case Studies and Projects. The Case Studies and Projects involve Mathematical and Computational Methods from the three key areas of ODEs, PDEs and Optimization. The leading author, Dr Caldwell, has had extensive experience of Mathematical Modelling throughout his career in both university teaching and industry and was instructor for a team of three Hong Kong mathematics undergraduate students, one of which was Mr Ng, the second author, who won the first place award, Meritorious, in the 2000 Netease Cup China Undergraduate Mathematical Contest in Modelling (CUMCM). Mathematical Modelling is most effectively taught using a Case Study approach. An important aspect of the book is the use of scientific computer software packages such as MAPLE for symbolic algebraic manipulations, MATLAB for numerical simulation and LINDO for linear programming.
Table of Contents......Page 8
Preface......Page 10
Introduction......Page 14
Part I Ordinary Differential Equations......Page 18
Case Study A1: Deterministic Model in Contagious Disease......Page 20
Case Study A2: Electromagnetic Forces in High Field Magnet Coils......Page 38
Project B1: Mass Balance of a Reactor in Steady State......Page 52
Project B2: The Free and Forced Vibration of an Automobile......Page 68
Project B3: Cantilever Beam Subjected to an End Load......Page 80
ODE Problems......Page 98
Part II Partial Differential Equations......Page 104
Case Study A3: Cylindrical and Spherical Solidification in Heat Transfer......Page 106
Case Study A4: Elastic Analysis of a Square Plate with Circular Holes......Page 124
Project B4: Motion of Fluid Layers......Page 140
Project B5: Mass Balance of a Reactor with Time Dependency......Page 150
Project B6: Flow through Porous Media......Page 160
PDE Problems......Page 174
Part III Optimization......Page 184
Case Study A5: Linear Programming Problem Involving Wine Production......Page 186
Case Study A6: Transportation Problem Involving Breweries and Hotels......Page 198
Project B7: Profit from an Engineering Plant......Page 218
Project B8: Optimization of Manufacture of Personal Computers......Page 228
Project B9: Air Freight Transportation Problem......Page 242
Optimization Problems......Page 252
C......Page 260
F......Page 261
M......Page 262
S......Page 263
V......Page 264
Y......Page 265
๐ SIMILAR VOLUMES
Textbook is intended to build on and enhance students' modelling skills using a combination of case studies and projects. For senior undergraduates/postgraduates.
Textbook is intended to build on and enhance students' modelling skills using a combination of case studies and projects. For senior undergraduates/postgraduates.
<p>Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power a
<p>Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power a