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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
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