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Mathematics in Chemical Engineering

  1. Bruce A. Finlayson1,
  2. Lorenz T. Biegler2,
  3. Ignacio E. Grossmann2

Published Online: 15 DEC 2006

DOI: 10.1002/14356007.b01_01.pub2

Ullmann's Encyclopedia of Industrial Chemistry

Ullmann's Encyclopedia of Industrial Chemistry

How to Cite

Finlayson, B. A., Biegler, L. T. and Grossmann, I. E. 2006. Mathematics in Chemical Engineering. Ullmann's Encyclopedia of Industrial Chemistry. .

Author Information

  1. 1

    Department of Chemical Engineering, University of Washington, Seattle, Washington, United States

  2. 2

    Carnegie Mellon University, Pittsburgh, Pennsylvania, United States

Publication History

  1. Published Online: 15 DEC 2006

This is not the most recent version of the article. View current version (30 SEP 2015)

Abstract

The article contains sections titled:

1.Solution of Equations
1.1.Matrix Properties
1.2.Linear Algebraic Equations
1.3.Nonlinear Algebraic Equations
1.4.Linear Difference Equations
1.5.Eigenvalues
2.Approximation and Integration
2.1.Introduction
2.2.Global Polynomial Approximation
2.3.Piecewise Approximation
2.4.Quadrature
2.5.Least Squares
2.6.Fourier Transforms of Discrete Data
2.7.Two-Dimensional Interpolation and Quadrature
3.Complex Variables
3.1.Introduction to the Complex Plane
3.2.Elementary Functions
3.3.Analytic Functions of a Complex Variable
3.4.Integration in the Complex Plane
3.5.Other Results
4.Integral Transforms
4.1.Fourier Transforms
4.2.Laplace Transforms
4.3.Solution of Partial Differential Equations by Using Transforms
5.Vector Analysis
6.Ordinary Differential Equations as Initial Value Problems
6.1.Solution by Quadrature
6.2.Explicit Methods
6.3.Implicit Methods
6.4.Stiffness
6.5.Differential - Algebraic Systems
6.6.Computer Software
6.7.Stability, Bifurcations, Limit Cycles
6.8.Sensitivity Analysis
6.9.Molecular Dynamics
7.Ordinary Differential Equations as Boundary Value Problems
7.1.Solution by Quadrature
7.2.Initial Value Methods
7.3.Finite Difference Method
7.4.Orthogonal Collocation
7.5.Orthogonal Collocation on Finite Elements
7.6.Galerkin Finite Element Method
7.7.Cubic B-Splines
7.8.Adaptive Mesh Strategies
7.9.Comparison
7.10.Singular Problems and Infinite Domains
8.Partial Differential Equations
8.1.Classification of Equations
8.2.Hyperbolic Equations
8.3.Parabolic Equations in One Dimension
8.4.Elliptic Equations
8.5.Parabolic Equations in Two or Three Dimensions
8.6.Special Methods for Fluid Mechanics
8.7.Computer Software
9.Integral Equations
9.1.Classification
9.2.Numerical Methods for Volterra Equations of the Second Kind
9.3.Numerical Methods for Fredholm, Urysohn, and Hammerstein Equations of the Second Kind
9.4.Numerical Methods for Eigenvalue Problems
9.5.Green's Functions
9.6.Boundary Integral Equations and Boundary Element Method
10.Optimization
10.1.Introduction
10.2.Gradient Based Nonlinear Programming
10.3.Optimization Methods without Derivatives
10.4.Global Optimization
10.5.Mixed Integer Programming
10.6.Dynamic Optimization
10.7.Development of Optimization Models
11.Probability and Statistics
11.1.Concepts
11.2.Sampling and Statistical Decisions
11.3.Error Analysis in Experiments
11.4.Factorial Design of Experiments and Analysis of Variance
12.Multivariable Calculus Applied to Thermodynamics
12.1.State Functions
12.2.Applications to Thermodynamics
12.3.Partial Derivatives of All Thermodynamic Functions