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Numerical Analysis for Chemical Engineers
Taechul Lee (tclee@prosys.korea.ac.kr)
Contents
Modeling, Computers, and Error Analysis
Mathematical Modeling and Engineering Problem-Solving
A Simple Mathematical Model
Computers and Software
The Software Development Process
Algorithm Design
Program Composition
Quality Control
Approximations and Round-Off Errors
Significant Figures
Accuracy and Precision
Error Definitions
Truncation Errors and the Taylor Series
The Taylor Series
Using the Taylor Series to Estimate Truncation Errors
Numerical Differentiation
Roots of Equations
Backeting Methods
Graphical Methods
The Bisection Method
The False-Position Method
Open Methods
Simple Fixed-point Iteration
The Newton-Raphson Method
The Secant Method
Multiple Roots
Systems of Nonlinear Equations
Roots of Polynomials
Polynomials in Engineering and Science
Computing with Polynomials
Conventional Methods
Root Location with Libraries and Packages
Engineering Applications: Roots of Equations
Linear Algebraic and Equations
Gauss Elimination
Solving Small Numbers of Equations
Naive Gauss Elimination
Pitfalls of Elimination Methods
Techniques for Improving Solutions
Complex Systems
Nonlinear Systems of Equations
Gauss-Jordan
LU Decomposition and Matrix Inversion
LU Decomposition
The Matrix Inverse
Error Analysis and System Condition
Special Matrices and Gauss-Seidel
Special Matrices
Gauss-Seidel
Linear Algebraic Equation with Libraries and Packages
Engineering Applications: Linear Algebraic Equations
Optimization
One-dimensional Unconstrained Optimization
Golden-Section Search
Quadratic Interpolation
Newton's Method
Multidimensional Unconstrained Optimization
Direct Methods
Gradient Methods
Contrained Optimization
Linear Programming
Optimization with Packages
Engineering Applications: Optimization
Curve Fitting
Least-Squares Regression
Linear Regression
General Linear Least-Squares
Nonlinear Regression
Interpolation
Newton's Divided-Difference Interpolating Polynomials
Lagrange Interpolating Polynomial
Spline Interpolation
Fourier Approximation
Curve Fitting with Sinusoidal Functions
Fourier Integral and Transform
Discrete Fourier Transform (DFT)
Fast Fourier Transform (FFT)
The Power Spectrum
Curve Fitting with Libraries and Packagies
Engineering Applications: Curve Fitting
Numerical Differentiation and Integration
Newton-Cotes Integration of Equations
The Trapezoidal rule
Simpson's rule
Intergrations of Equations
Romberg integration
Gauss Quadrature
Improper integrals
Numerical Differentiation
High-accuracy differentiation formulas
Richardson extrapolation
Derivatives of unequally spaced data
Numerical integration/differentiation formulas with libraties and packages
Engineering Applications: Numerical Integration and Differentiation
Ordinary Differential Equations
Runge-Kutta Methods
Euler's Method
Improvement of Euler's Method
Runge-Kutta Method
Systems of Equations
Adaptive Runge-Kutta Method
Stiffness and Multistep Methods
Stiffness
Multistep Methods
Boundary-Value and Engenvalue Problems
General Methods of Boundary-Value Problems
ODEs and Eigenvalues with Libraries and Packages
Engineering Applications: Ordinary Differential Equations
Partial Differential Equations
Finite Difference: Elliptic Equations
The Laplace Equations
Solution Techniques
Boundary Conditions
The Control Volume Approach
Finite Difference: Parabolic Equations
The Heat Conduction Equation
Explicit Methods
A Simple Implicit Method
The Crank-Nicholson Method
Finite Element Method
Calculus of variation
Example: The shortest distance between two points
The Rayleigh-Ritz Method
The Collocation and Galerkin Method
Finite elements for ordinary-differential equations
Engineering Applications: Partial Differential Equations
Using Matlab
설치
Matlab 기초
배열
Customization
Summary
제어문
if, else, and elseif
switch
while
for
break
Summary
함수만들기
Matlab에서 그림 그리기
plot 명령어
고급 plot 명령어
그림을 그리는 다른 명령어들
예제
Linear Equation
Using Fortran
설치 및 사용법
MS Window에서 작동하는 포트란
Unix 머신에서 작동하는 포트란
Summary
데이터와 입출력
기본적 구성
기본적 데이터 타입
입력과 출력에 관해
Redirection
Dimension
데이터 초기화
Summary
제어문
STOP문
GOTO문
PAUSE문
CONTINUE문
CALL문
RETURN문
IF문
DO문
Summary
부프로그램
FUNCTION
SUBROUTINE
부프로그램 컴파일
라이브러리 만들기
EXTERNAL 문 사용하기
IMSL 사용하기
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Taechul Lee
2001-11-29
