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Contents
Contents
Ceng 375 Numerical Computations
Cem Özdogan
Date:
27 December 2011
Contents
List of Tables
List of Figures
First Meeting
Lecture Information
Overview
Text Book
Grading Criteria & Policies
Numerical Analysis/Computations
Introduction to MATLAB
Help
Assignment Statements
Relational Operators
Loops & Conditionals
Functions
Matrices & Arrays
Graphics
Numeric vs Symbolic Computation
Preliminaries
Analysis vs Numerical Analysis
Computers and Numerical Analysis
An Illustrative Example
Some disasters attributable to bad numerical computing
Kinds of Errors in Numerical Procedures
Parallel and Distributed Computing
Speed -up and Efficiency
Measuring the Efficiency of Numerical Procedures
Taylor Series
Polynomials
Lab. Study: Preliminaries
Solving Nonlinear Equations
Interval Halving (Bisection)
Linear Interpolation Methods
The Secant Method
Linear Interpolation (False Position)
Newton's Method
Hands-on-Solving Nonlinear Equations with MATLAB I
Newton's Method, Continued
Muller's Method
Fixed-point Iteration;
Method
Other Rearrangements
Order of Convergence
Multiple Roots
The fzero function
Nonlinear Systems
Solving a System by Iteration
Hands-on-Solving Nonlinear Equations with MATLAB II
Solving Sets of Equations
Matrices and Vectors
Some Special Matrices and Their Properties
Using Computer Algebra Systems
Elimination Methods
Gaussian Elimination
The Gauss-Jordan Method
Hands-on-Solving Sets of Equations with MATLAB I
Assignment 1 - Solving Nonlinear Equations; Due to December 5, 2011
Using the LU Matrix for Multiple Right-Hand Sides
The Inverse of a Matrix and Matrix Pathology
Pathological Systems
Redundant Systems
Ill-Conditioned Systems
Norms
Matrix Norms
Iterative Methods
Jacobi Method
Gauss-Seidel Iteration
Hands-on- Solving Sets of Equations with MATLAB II
Assignment 2 - Solving Sets of Linear Equations - Due to December 25, 2011
Interpolation and Curve Fitting
Interpolating Polynomials
Interpolation versus Curve Fitting
Fitting a Polynomial to Data
Lagrangian Polynomials
Neville's Method
Hands-on-Interpolation and Curve Fitting with MATLAB I
Divided Differences
Spline Curves
The Equation for a Cubic Spline
Least-Squares Approximations
Hands-on-Interpolation and Curve Fitting with MATLAB II
Nonlinear Data, Curve Fitting
Least-Squares Polynomials
Use of Orthogonal Polynomials
Hands-on-Interpolation and Curve Fitting with MATLAB III
Approximation of Functions
Chebyshev Polynomials and Chebyshev Series
Chebyshev Polynomials
Economizing a Power Series
Chebyshev Series
Hands-on-Chebyshev Polynomials; Approximation of Functions with MATLAB I
Fourier Series
Fourier Series for Periods Other Than
Fourier Series for Nonperiodic Functions and Half-Range Expansions
Summary
Hands-on-Fourier Series; Approximation of Functions with MATLAB II
Assignment 3 - Interpolation and Curve Fitting; Due to January 07, 2012
Numerical Differentiation and Integration with a Computer
Differentiation with a Computer
Numerical Integration - The Trapezoidal Rule
The Trapezoidal Rule
The Composite Trapezoidal Rule
Hands-on-Numerical Differentiation and Integration with MATLAB
Vita
About this document ...
Cem Ozdogan 2011-12-27
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