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Ceng 375 Numerical Computations

Cem Özdogan

Date: 28 December 2004

• Contents
• List of Tables
• List of Figures
• Introduction to MATLAB
• Preliminaries
  • Analysis vs Numerical Analysis
  • Computers and Numerical Analysis
  • An Illustrative Example
  • Kinds of Errors in Numerical Procedures
  • Parallel and Distributed Computing
    • Speed -up and Efficiency
  • Measuring the Efficiency of Numerical Procedures
    • Taylor Series
    • Polynomials
  • Preliminaries with MATLAB
  
  
• Solving Nonlinear Equations
  • Interval Halving (Bisection)
  • Linear Interpolation Methods
    • The Secant Method
    • Linear Interpolation (False Position)
  • Newton's Method
    • Complex Roots
  • Solving Nonlinear Equations with MATLAB I
  • Muller's Method
  • Fixed-point Iteration; Method
    • Other Rearrangements
    • Order of Convergence
  • Multiple Roots
  • Nonlinear Systems
    • Solving a System by Iteration
  • 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
    • 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
    • Sparse Matrices and Banded Matrices
  • Parallel Processing
  • Solving Sets of Equations with MATLAB
  
  
• Interpolation and Curve Fitting
  • Interpolating Polynomials
    • Fitting a Polynomial to Data
    • Lagrangian Polynomials
    • Neville's Method
  • Divided Differences
  • Interpolation and Curve Fitting with MATLAB I
  • Spline Curves
    • The Equation for a Cubic Spline
  • Least-Squares Approximations
    • Nonlinear Data
    • Least-Squares Polynomials
    • Use of Orthogonal Polynomials
  • Interpolation and Curve Fitting with MATLAB II
  
  
• Approximation of Functions
  • Chebyshev Polynomials and Chebyshev Series
    • Chebyshev Polynomials
    • Economizing a Power Series
    • Chebyshev Series
  • Approximation of Functions with MATLAB I
  • Fourier Series
    • Fourier Series for Periods Other Than
    • Fourier Series for Nonperiodic Functions and Half-Range Expansions
    • Summary
  • Approximation of Functions with MATLAB II
  
  
• Numerical Differentiation and Integration
  • Differentiation with a Computer
    • Extrapolation Techniques
  • Numerical Integration - The Trapezoidal Rule
    • The Trapezoidal Rule
    • The Composite Trapezoidal Rule
  • Numerical Differentiation and Integration with MATLAB I
  
  
• vita
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