Mathematical Modelling: Case Studies and Projects
Springer Science & Business Media, Mar 31, 2004 - Mathematics - 253 pages
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.
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A B C D Supply allocated analysis analytical solution approximation beam BEASY boundary conditions boundary element method Breweries Hotels calculated Caldwell cargo cell chemical coil Computer Algorithms considered constraints cost Crank-Nicolson method damping deflection differential equation enhanced model enthalpy Figure finite difference finite difference methods finite element finite element method geometry gives h h h hole infection Interpretation and Conclusions involves ITERATIONS L.P. problem linear programming linear programming problem mathematical model MATLAB maximize maximum Model Formulation Model Validation node number of removals Numerical Methods numerical results numerical solution objective function obtained Optimal solution parameters plane strain porous media production profit Project B1 reactor References and Bibliography Section shadow prices simplex method solved spherical solidification Stefan problem stone method stress supplies 5 units tableau temperature Thomas algorithm transportation problem units to hotel values variables velocity zero µ µ µ