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

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

• Suthida Chaichomchuen
• std_at_kmitnb.ac.th

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COURSE DESCRIPTION
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GENERAL OBJECTIVE
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BEHAVIORAL OBJECTIVES

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BEHAVIORAL OBJECTIVES

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BEHAVIORAL OBJECTIVES

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BRIEF CONTEXT

• Major Sources of Errors in Numerical Methods
• Truncation Error
• Round-off Error
• Numbers on Computer

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BRIEF CONTEXT

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

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BRIEF CONTEXT

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

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BRIEF CONTEXT

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

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BRIEF CONTEXT

• Solution of Nonlinear Equations
• Secant Method
• Successive Substitution Method
• Bairstows Method

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BRIEF CONTEXT

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

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BRIEF CONTEXT

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

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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

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BRIEF CONTEXT

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

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BRIEF CONTEXT

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

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BRIEF CONTEXT

• Computations of Matrix Eigenvalues
• Eigenvalues
• Eigenvectors

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REFERENCE BOOKS

• Applied Numerical Methods in C
• Numerical Methods for Engineers
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MARKS

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

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GRADE
T-SCORE
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