MthSc 860
Spring 2007
Review for Exam 2

V. Nonlinear Equations (Heath Ch. 5)
        Iterative Methods
                Convergence rate
                Termination criteria
		Bisection
        	Fixed-Point Iteration 
        	Newton's Method		
		Secant Method		
		Inverse Quadratic Interpolation
                Systems of Nonlinear Equations
			Fixed-Point Iteration
			Newton's Method
		
VII. Interpolation (Heath Ch. 7)
	Polynomial Interpolation
		Vandermonde (monomial) approach
			Nested multiplication
		Lagrange Form
		Newton Form
			Nested multiplication
			Divided Differences
		Accuracy
		
	Piecewise Polynomial Interpolation
		Continuous pw linear, quadratic, cubic
		Splines
			General definition
			Cubic
				Endpoint conditions
					
VIII. Numerical Integration (Heath Ch. 8)
	Newton-Cotes
		Midpoint, Trapezoid, Simpson's 
		Accuracy
		Polonomial Degree
		Open vs. closed
			
	Gaussian Quadrature
		Gauss-Legendre
           	Weighted Integrals
			
	Composite Quadrature Rules
		Error (convergence rates)
			
	Adaptive Quadrature
		Using Matlab quad routine