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Friedman A., Littman W. — Industrial Mathematics: A Course in Solving Real-World Problems
Friedman A., Littman W. — Industrial Mathematics: A Course in Solving Real-World Problems

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Название: Industrial Mathematics: A Course in Solving Real-World Problems

Авторы: Friedman A., Littman W.

Аннотация:

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.



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 151

Добавлена в каталог: 03.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Advection      27
Advection diffusion equation      29 36 45
Advection equation      29 30 35 45
Air quality modeling      27
Backward heat problem      53 57
Brachistochrone      92 93 95
Calculus of variations      92 100
Catalytic converter      87 88 102
Cauchy problem      52
Characteristics, method of      31 35 36 45
Color film negative      69
Color film negative, development of      69
Comparison theorem      75
Continuity equation      29
Control function      90
Control problem      90 92 95
Cost function      90 102
Coupler      70 71 77 78
Coupler, dye-forming      70
Coupler, inhibitor-forming      70
Crystal      2 6
Crystal precipitation      1 3 5
Diffusion      29 72
Diffusion equation      see "Advection diffusion equation"
Diffusion matrix      30 72
Dirichlet problem      128 129
Drift      72
Edge enhancement      132
Electric image      105 107 122
Electric image, computing      117
Electric image, modeling      108
Electron beam lithography      47
Emulsion      2 3 69
Euler equation      95
Euler method      12 14 18—20 22
Euler — Lagrange equation      93 95
Fejer's theorem      60 61 63
Fejer's theorem, proof of      63
Film, late development of      77
Finite differences      32 102 112 113 115 117
Finite differences, conditionally stable      44
Finite differences, consistent      37
Finite differences, convergent      33 37
Finite differences, explicit      33
Finite differences, implicit      44
Finite differences, stable      33 37
Finite differences, unconditionally stable      44
Finite differences, unstable      34
Fourier series      54 55 58 59 61 64
Fourier series, summability of      59
Free boundary problem      127 132
Gibbs — Thomson equation      5
Graininess      3
Heat equation      50 53 56 61
Inhibitor      71
Interstitial silver ions      70
Kink site      70
Latent image site      70
Lax equivalency theorem      44
Lax — Wendroff scheme      40 45
Maximum principle      74 75 78 114 118 129
Maximum principle, strong      76—78
Maximum principle, strong, one-dimensional      83
Maximum principle, strong, proof of the      83
Maximum principle, weak      53
Newton's method      16
Numerical methods      2 10 25 32 98
Ostwald ripening      3—5
Oxidized developer      71 73 77
Photocopy machine      105 123
Picard's method      10 20
Problem, ill posed      57
Problem, well posed      57
Reduced developer      70 71
Reflection principle      128
Runge — Kutta method      18 20 22
Scattering, backward      48 50 58 61
Scattering, forward      48 50 61
Toner      107
Transmission conditions      116
Visible image      105 107 123 125 128 132
von Neumann stability      37
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