Mathematical modeling for industry, science, and government

Description

(NOTE: Each chapter concludes with Exercises.) 1. Statistical Reasoning. Random Variables. Uniform Distributions. Gaussian Distributions. The Binomial Distribution. The Poisson Distribution. Taguchi Quality Control. 2. Monte Carlo Methods. Computing Integrals. Mean Time between Failure. Servicing Requests. The Newsboy Problem (reprise). 3. Data Acquisition and Manipulation. The z-transform. Linear Recursions. Filters. Stability. Polar and Bode Plots. Aliasing. Closing the Loop. Why Decibels? 4. The Discrete Fourier Transform. Real Time Processing. Properties of the DFT. Filter Design. The Fast Fourier Transform. Image Processing. 5. Linear Programming. Optimization. The Diet Problem. The Simplex Algorithm. 6. Regression. Best Fit to Discrete Data. Norms on Rn. Hilbert Space. Gram's Theorem on Regression. 7. Cost Benefit Analysis. Present Value. Life-Cycle Savings. 8. Microeconomics. Supply and Demand. Revenue, Cost, and Profit. Elasticity of Demand. Duopolistic Competition. Theory of Production. Leontiev Input/Output. 9. Ordinary Differential Equations. Separation of Variables. Mechanics. Linear ODEs with Constant Coefficients. Systems. 10. Frequency-Domain Methods. The Frequency Domain. Generalized Signals. Plants in Cascade. Surge Impedance. Stability. Filters. Feedback and Root Locus. Nyquist Analysis. Control. 11. Partial Differential Equations. Lumped versus Distributed. The Big Six PDEs. Separation of Variables. Unbounded Spatial Domains. Periodic Steady State. Other Distributed Models. 12. Divided Differences. Euler's Method. Systems. PDEs. Runge-Kutta Method. 13. Galerkin's Method. Galerkin's Requirement. Eigenvalue Problems. Steady Problems. Transient Problems. Finite Elements. Why So Effective? 14. Splines. Why Cubics? m-Splines. Cubic Splines. 15. Report Writing. The Formal Technical Report. The Memo. The Progress Report. The Executive Summary. The Problem Statement. Overhead Projector Presentations. Approaching a Writing Task. Style. Writer's Checklist. References. Index