Ebook: Topics in Industrial Mathematics: Case Studies and Related Mathematical Methods

Industrial Mathematics is a relatively recent discipline. It is concerned primarily with transforming technical, organizational and economic problems posed by indus­ try into mathematical problems; "solving" these problems byapproximative methods of analytical and/or numerical nature; and finally reinterpreting the results in terms of the original problems. In short, industrial mathematics is modelling and scientific computing of industrial problems. Industrial mathematicians are bridge-builders: they build bridges from the field of mathematics to the practical world; to do that they need to know about both sides, the problems from the companies and ideas and methods from mathematics. As mathematicians, they have to be generalists. If you enter the world of indus­ try, you never know which kind of problems you will encounter, and which kind of mathematical concepts and methods you will need to solve them. Hence, to be a good "industrial mathematician" you need to know a good deal of mathematics as well as ideas already common in engineering and modern mathematics with tremen­ dous potential for application. Mathematical concepts like wavelets, pseudorandom numbers, inverse problems, multigrid etc., introduced during the last 20 years have recently started entering the world of real applications. Industrial mathematics consists of modelling, discretization, analysis and visu­ alization. To make a good model, to transform the industrial problem into a math­ ematical one such that you can trust the prediction of the model is no easy task.

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This book is devoted to some analytical and numerical methods for analyzing industrial problems related to emerging technologies such as digital image processing, material sciences and financial derivatives affecting banking and financial institutions. Case studies are based on industrial projects given by reputable industrial organizations of Europe to the Institute of Industrial and Business Mathematics, Kaiserslautern, Germany. Mathematical methods presented in the book which are most reliable for understanding current industrial problems include Iterative Optimization Algorithms, Galerkin's Method, Finite Element Method, Boundary Element Method, Quasi-Monte Carlo Method, Wavelet Analysis, and Fractal Analysis. The Black-Scholes model of Option Pricing, which was awarded the 1997 Nobel Prize in Economics, is presented in the book. In addition, basic concepts related to modeling are incorporated in the book.
Audience: The book is appropriate for a course in Industrial Mathematics for upper-level undergraduate or beginning graduate-level students of mathematics or any branch of engineering.

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This book is devoted to some analytical and numerical methods for analyzing industrial problems related to emerging technologies such as digital image processing, material sciences and financial derivatives affecting banking and financial institutions. Case studies are based on industrial projects given by reputable industrial organizations of Europe to the Institute of Industrial and Business Mathematics, Kaiserslautern, Germany. Mathematical methods presented in the book which are most reliable for understanding current industrial problems include Iterative Optimization Algorithms, Galerkin's Method, Finite Element Method, Boundary Element Method, Quasi-Monte Carlo Method, Wavelet Analysis, and Fractal Analysis. The Black-Scholes model of Option Pricing, which was awarded the 1997 Nobel Prize in Economics, is presented in the book. In addition, basic concepts related to modeling are incorporated in the book.
Audience: The book is appropriate for a course in Industrial Mathematics for upper-level undergraduate or beginning graduate-level students of mathematics or any branch of engineering.
Content:
Front Matter....Pages i-xiii
Case Studies at Kaiserslautern....Pages 1-52
Algorithms for Optimization....Pages 53-77
Maxwell’s Equations, Finite and Boundary Element Methods....Pages 79-152
Monte Carlo Methods....Pages 153-180
Image Processing and Fourier — Wavelet Methods....Pages 181-264
Models of Hysteresis and Applications....Pages 265-285
Appendix....Pages 287-344
Back Matter....Pages 345-377

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This book is devoted to some analytical and numerical methods for analyzing industrial problems related to emerging technologies such as digital image processing, material sciences and financial derivatives affecting banking and financial institutions. Case studies are based on industrial projects given by reputable industrial organizations of Europe to the Institute of Industrial and Business Mathematics, Kaiserslautern, Germany. Mathematical methods presented in the book which are most reliable for understanding current industrial problems include Iterative Optimization Algorithms, Galerkin's Method, Finite Element Method, Boundary Element Method, Quasi-Monte Carlo Method, Wavelet Analysis, and Fractal Analysis. The Black-Scholes model of Option Pricing, which was awarded the 1997 Nobel Prize in Economics, is presented in the book. In addition, basic concepts related to modeling are incorporated in the book.
Audience: The book is appropriate for a course in Industrial Mathematics for upper-level undergraduate or beginning graduate-level students of mathematics or any branch of engineering.
Content:
Front Matter....Pages i-xiii
Case Studies at Kaiserslautern....Pages 1-52
Algorithms for Optimization....Pages 53-77
Maxwell’s Equations, Finite and Boundary Element Methods....Pages 79-152
Monte Carlo Methods....Pages 153-180
Image Processing and Fourier — Wavelet Methods....Pages 181-264
Models of Hysteresis and Applications....Pages 265-285
Appendix....Pages 287-344
Back Matter....Pages 345-377
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