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MATH 230: Numerical Methods ( Spring 2009)

Course Topics

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· Introduction to programming with MATLAB

· Root Finding (Chapter 2)

• Bisection method (2.1)
• Fixed-point iteration (2.2)
• Performance of Convergence
• Newton's method, Secant method (2.3)

· Interpolation (Chapter 3)

• Interpolation and the Lagrange (interpolating) polynomial (3.1)
• Divided differences and Newton's interpolatory divided-difference formula (3.2)

· Least Squares Data Fitting (Chapter 8)

• Least squares data fitting--data fitting, normal equation (8.1)

· Numerical Differentiation and Integration (Chapter 4)

• Numerical differentiation--forward, backward, and central finite differences (4.1)
• Elements of numerical integration (4.3)
• Composite rules (4.4)
• Gaussian quadrature -- Gaussian node points, weights (4.7)

· Solution of Ordinary Differential Equations (Chapter 5)

• Euler's method (5.2)

· Solving Linear Systems (Chapters 6 & 7)

• Gauss elimination--multipliers, Gauss elimination, back substitution, pivoting (6.1 - 6.2)
• LU factorization--LU, forward substitution (6.5)
• Iterative methods--matrix splitting, Jacobi method, Gauss-Seidel method, SOR method (7.3)

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Last Revised: 12 January 2009

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