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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
• 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