Ebook: Mathematical Modelling: Case Studies and Projects
- Tags: Mathematical Modeling and Industrial Mathematics, Engineering general, Mechanics, Numeric Computing, Algorithms
- Series: Texts in the Mathematical Sciences 28
- Year: 2004
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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 and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is available through greater use of mathematical modelling and computer simulation. In particular, developments in computer algebra, symbolic manipulation packages and user friendly software packages for large scale problems, all have important implications in both the teaching of mathematical modelling and, more importantly, its use in the solution of real world problems. Many textbooks have been published which cover the art and techniques of modelling as well as specific mathematical modelling techniques in specialist areas within science and business. In most of these books the mathematical material tends to be rather tailor made to fit in with a one or two semester course for teaching students at the undergraduate or postgraduate level, usually the former. This textbook is quite different in that it is intended to build on and enhance students’ modelling skills using a combination of case studies and projects.
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.
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.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-3
Front Matter....Pages 5-5
Deterministic Model in Contagious Disease....Pages 5-24
Electromagnetic Forces in High Field Magnet Coils....Pages 25-37
Mass Balance of a Reactor in Steady State....Pages 39-54
The Free and Forced Vibration of an Automobile....Pages 55-66
Cantilever Beam Subjected to an End Load....Pages 67-84
ODE Problems....Pages 85-90
Front Matter....Pages 91-91
Cylindrical and Spherical Solidification in Heat Transfer....Pages 93-109
Elastic Analysis of a Square Plate with Circular Holes....Pages 111-125
Motion of Fluid Layers....Pages 127-136
Mass Balance of a Reactor with Time Dependency....Pages 137-146
Flow Through Porous Media....Pages 147-159
PDE Problems....Pages 161-169
Front Matter....Pages 171-171
Linear Programming Problem Involving Wine Production....Pages 173-183
Transportation Problem Involving Breweries and Hotels....Pages 185-204
Profit from an Engineering Plant....Pages 205-213
Optimization of Manufacture of Personal Computers....Pages 215-227
Air Freight Transportation Problem....Pages 229-238
Optimization Problems....Pages 239-246
Back Matter....Pages 247-253
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.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-3
Front Matter....Pages 5-5
Deterministic Model in Contagious Disease....Pages 5-24
Electromagnetic Forces in High Field Magnet Coils....Pages 25-37
Mass Balance of a Reactor in Steady State....Pages 39-54
The Free and Forced Vibration of an Automobile....Pages 55-66
Cantilever Beam Subjected to an End Load....Pages 67-84
ODE Problems....Pages 85-90
Front Matter....Pages 91-91
Cylindrical and Spherical Solidification in Heat Transfer....Pages 93-109
Elastic Analysis of a Square Plate with Circular Holes....Pages 111-125
Motion of Fluid Layers....Pages 127-136
Mass Balance of a Reactor with Time Dependency....Pages 137-146
Flow Through Porous Media....Pages 147-159
PDE Problems....Pages 161-169
Front Matter....Pages 171-171
Linear Programming Problem Involving Wine Production....Pages 173-183
Transportation Problem Involving Breweries and Hotels....Pages 185-204
Profit from an Engineering Plant....Pages 205-213
Optimization of Manufacture of Personal Computers....Pages 215-227
Air Freight Transportation Problem....Pages 229-238
Optimization Problems....Pages 239-246
Back Matter....Pages 247-253
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