Industrial Mathematics

Introduction Preface to the Student Chapter 1: Crystal Precipitation. The Road Ahead-Some Helpful Hints to the Student Background The Model Some 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 Size Remark on Theorems 1.8.3 - 1.8.5 Reminder on Newton's Method The Runge-Kutta Method (BASIC) Discussion and Motivation (BASIC) Crystals of Several Sizes Summary References Chapter 2: Air Quality Modeling. Background The Model The Advection Equation Numerical Methods The General Advection Equation Enters Diffusion The von Neumann Stability Criterion Stability, Consistency and Convergence Summary References Chapter 3: Electron Beam Lithography. Background The Mathematical Model The Heat Equation The Proximity Effect The Use of Fourier Series The Inclusion of Backward Scattering Computational Experiments Summability of Fourier Series Summary References Appendix: Proof of Fejer's Theorem Chapter 4: Development of Color Film Negative. The Process The Mathematical Model The Bulk Reaction Problem Analysis of the Solution Late Development of Film Implicit Methods for Solving the (4.12)-(4.16) Numerically Summary References Appendix: Proof of the Strong Maximum Principle Chapter 5: How Does a Catalytic Converter Function?. Background The Model The Control Problem A Simplified Model The Calculus of Variations The Euler-Lagrange Equation The Simplified Control Problem Determining the Optimal Control Summary References Chapter 6: The Photocopy Machine. Background The Photocopy Machine The Electric Image Modeling the Electric Image Solving Poisson's Equations Numerically Transmission Conditions Computing the Electric Image A Simple Method for Solving the Equations (6.18) (6.17) Summary References Chapter 7: The Photocopy Machine (Continued). The Visible Image Impossibility of a Precise Image Summary References Index.