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NUMERICAL METHODS ?????????????????

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NUMERICAL METHODS Suthida Chaichomchuen std_at_kmitnb.ac.th COURSE DESCRIPTION ... – PowerPoint PPT presentation

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Title: NUMERICAL METHODS ?????????????????


1
NUMERICAL METHODS?????????????????
  • Suthida Chaichomchuen
  • std_at_kmitnb.ac.th

2
COURSE DESCRIPTION
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3
GENERAL OBJECTIVE
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4
BEHAVIORAL OBJECTIVES
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5
BEHAVIORAL OBJECTIVES
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6
BEHAVIORAL OBJECTIVES
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7
BRIEF CONTEXT
  • Major Sources of Errors in Numerical Methods
  • Truncation Error
  • Round-off Error
  • Numbers on Computer

8
BRIEF CONTEXT
  • Polynomial Interpolation
  • Linear Interpolation
  • Lagrange Interpolation Formula
  • Newton Forward and Backward Interpolations on
    Equispaced Points
  • Newton Interpolation on Nonuniformly Spaced Points

9
BRIEF CONTEXT
  • Polynomial Interpolation
  • Interpolation with Chebychev Roots
  • Hermite Interpolation Polynomials
  • Two-Dimensional Interpolation
  • Extrapolation

10
BRIEF CONTEXT
  • Solution of Nonlinear Equations
  • Bisection Method
  • False Position Method and Modified False Position
    Method
  • Newtons Method

11
BRIEF CONTEXT
  • Solution of Nonlinear Equations
  • Secant Method
  • Successive Substitution Method
  • Bairstows Method

12
BRIEF CONTEXT
  • Numerical Integration
  • Trapezoidal Rule
  • Simpsons 1/3 Rule
  • Simpsons 3/8 Rule
  • Newton-Cotes Formulas

13
BRIEF CONTEXT
  • Numerical Integration
  • Gauss Quadratures
  • Numerical Integration with Infinite Limits or
    Singularities
  • Numerical Integration in a Two-Dimensional Domain

14
BRIEF CONTEXT
  • Numerical Differentiation
  • Using Taylor Expansion
  • A Generic Algorithm to Derive a Difference
    Approximation
  • Using Difference Operators
  • Using Differentiation of Newton Interpolation
    Polynomials
  • Difference Approximations of Partial Derivatives

15
BRIEF CONTEXT
  • Numerical Linear Algebra
  • Gauss and Gauss-Jordan Elimination for Simple
    Ideal Problems
  • Pivoting and Standard Gauss Elimination
  • Unsolvable Problems
  • Matrices and Vectors

16
BRIEF CONTEXT
  • Numerical Linear Algebra
  • Inversion of a Matrix
  • LU Decomposition
  • Determinant
  • Ill-Conditioned Problems
  • Solution of M Equations with N Unknowns

17
BRIEF CONTEXT
  • Computations of Matrix Eigenvalues
  • Eigenvalues
  • Eigenvectors

18
REFERENCE BOOKS
  • Applied Numerical Methods in C
  • Numerical Methods for Engineers
  • ??????????????????????????????????

19
MARKS
  • Final Exam. 40
  • Mid-term Exam. 30
  • Test/Quiz Exam. 15
  • Homework 10
  • Participation 5

20
GRADE
T-SCORE
21
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