Topics in Engineering Mathematics: Modeling and Methods

by A.H. van der Burgh (Editor), J Simonis (Editor)

Overview

This volume presents a selection of expository papers on various topics in engineering mathematics. The papers concern model problems relating to, amongst others, the automobile and shipping industries, transportation networks and wave propagation. Among the methods treated are numerical methods, such as the finite element method and Newton's method, Karmarkar's interior point method and generalizations, and recurrence and induction in computer science.
This volume will be of great interest to applied mathematicians, physicists and engineers interested in recent developments in engineering mathematics.
The papers are written with an emphasis on exposition and should be accessible to all members of scientific community interested in modeling and solving real-life problems.

Product Details

ISBN-13:	9789401048002
Publisher:	Springer Netherlands
Publication date:	10/23/2012
Series:	Mathematics and Its Applications , #81
Edition description:	1992
Pages:	265
Product dimensions:	6.30(w) x 9.45(h) x 0.02(d)

Table of Contents

A kaleidoscopic excursion into numerical calculations of differential equations.- 1. Introduction.- 2. Logistic equation.- 3. Harmonic oscillator.- 4. Wave equations.- 5. Epilogue.- An introduction to the Finite Element Method.- 1. Introduction.- 2. An elementary example.- 3. The 2-dimensional Poisson equation.- 4. Final remarks.- Coupling of sound and structural vibrations.- 1. Introduction.- 2. Governing equations and analysis.- 3. Numerical results and discussion.- Mathematical modeling and dimensional analysis.- 1. Introduction.- 2. Mathematical Modeling.- 3. Dimensional Analysis.- 4. Four-wheel steering.- About difference equations, algebras and discrete events.- 1. Difference equations.- 2. Changing the algebra.- 3 Example on production.- 4. Some graph theory and the spectral theory of matrices.- 5. A shastic extension.- 6. Counter versus dater description.- 7. The Z-transform.- 8. Conclusions.- Acoustical detection of obstructions in a pipe with a temperature gradient.- 1. Introduction.- 2. The problem.- 3. The model.- 4. Solution.- 5. Results.- 6. Conclusions.- Interior point approach to linear programming: theory, algorithms and parametric analysis.- 1. Introduction.- 2. Central approach to the theory of LP.- 3. A polynomial-time path-following algorithm.- 4. Parametric analysis.- Some reflections on Newton’s Method.- 1. Introduction and motivation.- 2. Rational Newton Flows.- 3. Structural Stability.- 4. Newton Graphs.- 5. Characterization of Newton Graphs.- 6. Open problems.- Recurrence and induction in Computer Science.- 1. Introduction.- 2. Strings of Symbols.- 3. Gray codes and recursiveness.- 4. Recursive algorithms.