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The focus in this text is on mathematical modelling stimulated by contemporary industrial problems involving heat conduction and mass diffusion. These include continuous metal casting, laser drilling, spontaneous combustion of industrial waste, water filtration and crop irrigation. The industrial problems prove to be an excellent setting for the introduction and reinforcement of modelling skills, equation solving techniques, qualitative understanding of partial differential equations and their dynamical properties. Mathematical topics include setting up partial differential equations and boundary conditions, dimensional analysis, scaling, perturbation expansions, boundary valuer problems, Fourier series, symmetry reductions, Stefan problems and bifurcations. For students of mathematics, engineering, or any other related discipline, this will be a great introduction to modelling the real world.
Table of contents:
1. Preliminaries; 2. Case study: continuous casting; 3. Case study: water filtration; 4. Case study: laser drilling; 5. Case study: factory fires; 6. Case study: irrigation; 7. Conclusions.
The focus in this undergraduate text is on mathematical modelling stimulated by contemporary industrial problems involving heat conduction and mass diffusion. These problems prove to be an excellent setting for the introduction and reinforcement of modelling skills, equation solving techniques, qualitative understanding of partial differential equations and their dynamical properties.
An undergraduate text focussing on mathematical modelling stimulated by contemporary industrial problems.
Table of contents:
1. Preliminaries; 2. Case study: continuous casting; 3. Case study: water filtration; 4. Case study: laser drilling; 5. Case study: factory fires; 6. Case study: irrigation; 7. Conclusions.
The focus in this undergraduate text is on mathematical modelling stimulated by contemporary industrial problems involving heat conduction and mass diffusion. These problems prove to be an excellent setting for the introduction and reinforcement of modelling skills, equation solving techniques, qualitative understanding of partial differential equations and their dynamical properties.
An undergraduate text focussing on mathematical modelling stimulated by contemporary industrial problems.