Industrial Mathematics

A Course in Solving Real-World Problems

Häftad, Engelska, 1994

929 kr

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Are calculus and ""post"" calculus (such as differential equations) playing an important role in research and development done in industry? Are these mathematical tools indispensable for improving industrial products such as automobiles, airplanes, televisions, and cameras? Do they play a role in understanding air pollution, predicting weather and stock market trends, and building better computers and communication systems? This book was written to convince the reader, by examples, that the answer to all the above questions is YES!Industrial mathematics is a fast growing field within the mathematical sciences. It is characterized by the origin of the problems that it engages; they all come from industry: research and development, finances, and communications. The common feature running through this enterprise is the goal of gaining a better understanding of industrial models and processes through mathematical ideas and computations. The authors of this book have undertaken the approach of presenting real industrial problems and their mathematical modeling as a motivation for developing mathematical methods that are needed for solving the problems.Each chapter presents and studies, by mathematical analysis and computations, one important problem that arises in today's industry. This book introduces the reader to many new ideas and methods from ordinary and partial differential equations, integral equations, and control theory. It brings the excitement of real industrial problems into the undergraduate mathematical curriculum.The problems selected are accessible to students who have taken the first two-year basic calculus sequence. A working knowledge of Fortran, Pascal, or C language is required.

Produktinformation

Utgivningsdatum1994-08-31
Mått152 x 229 x undefined mm
Vikt238 g
FormatHäftad
SpråkEngelska
Antal sidor149
FörlagSociety for Industrial & Applied Mathematics,U.S.
ISBN9780898713244

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IntroductionPreface to the StudentChapter 1: Crystal Precipitation. The Road Ahead-Some Helpful Hints to the StudentBackgroundThe ModelSome Facts About Differential Equations (BASIC)Picard's Method of Successive Approximations (BASIC)Non-rectangular Regions (BASIC)The Euler Method (or Method of Polygons) (BASIC)Crystals of Single SizeRemark on Theorems 1.8.3 - 1.8.5Reminder on Newton's MethodThe Runge-Kutta Method (BASIC)Discussion and Motivation (BASIC)Crystals of Several SizesSummaryReferencesChapter 2: Air Quality Modeling. BackgroundThe ModelThe Advection EquationNumerical MethodsThe General Advection EquationEnters DiffusionThe von Neumann Stability CriterionStability, Consistency and ConvergenceSummaryReferencesChapter 3: Electron Beam Lithography. BackgroundThe Mathematical ModelThe Heat EquationThe Proximity EffectThe Use of Fourier SeriesThe Inclusion of Backward ScatteringComputational ExperimentsSummability of Fourier SeriesSummaryReferencesAppendix: Proof of Féjer's TheoremChapter 4: Development of Color Film Negative. The ProcessThe Mathematical ModelThe Bulk Reaction ProblemAnalysis of the SolutionLate Development of FilmImplicit Methods for Solving the (4.12)-(4.16) NumericallySummaryReferencesAppendix: Proof of the Strong Maximum PrincipleChapter 5: How Does a Catalytic Converter Function?. BackgroundThe ModelThe Control ProblemA Simplified ModelThe Calculus of VariationsThe Euler-Lagrange EquationThe Simplified Control ProblemDetermining the Optimal ControlSummaryReferencesChapter 6: The Photocopy Machine. BackgroundThe Photocopy MachineThe Electric ImageModeling the Electric ImageSolving Poisson's Equations NumericallyTransmission ConditionsComputing the Electric ImageA Simple Method for Solving the Equations (6.18) (6.17)SummaryReferencesChapter 7: The Photocopy Machine (Continued). The Visible ImageImpossibility of a Precise ImageSummaryReferencesIndex.

'This is REAL. It has a different spirit. It gives students the distinct feeling that they could go into industry and actually work on problems like those in this book. The standard teaching of 'here is the mathematics, use it to solve this problem' has been replaced with 'here is a problem, use mathematics to solve it.' This book refreshes the interest of students in mathematics and motivates them to learn more of it. It helps them understand the nature and the importance of mathematics in real world applications.' Oscar Bruno, Assistant Professor of Mathematics, Georgia Institute of Technology