Math 471 - Course Syllabus

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List of Topics

• Introduction; floating point arithmetic; catastrophic cancellation; chopping and rounding errors.
• Solution of Nonlinear equations; bisection, secant and Newton's methods; fixed-point interation; Muller's method, Golden section search.
• Computational linear algebra; elimination methods; LU decomposition; norms and errors, indirect (iteration) methods; nonlinear systems.
• Interpolation and curve fitting; Legrange and Newton interpolation; splines; least squares.
• Numerical integration; Newton-Cotes rules; Simpson's rule; Gaussian quadrature.
• Numerical solution of ordinary differential equations; Euler's method; Runge-Kutta method; multi-step methods; systems of ODEs; boundary value problems.

Text:

Gerald and Wheatley, Applied Numerical Analysis , 6 ed., 1998.

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