Math 471 - Course Syllabus

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.
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.

Gerald and Wheatley, Applied Numerical Analysis , 5 ed., 1994.