This page contains some links to pages with material relevant to the numerical analysis course. You will also find links to Mathematica notebooks which you can download and modify for further exploration.

• Selected homework solutions from the textbook and other homework solutions.
• Tests and their solutions.
• Current semester syllabus
• Students wondering why accurate and efficient numerical computing is important may want to read about some notable failures of numerical software.
• Users new to Mathematica may want to study a brief tutorial introduction to the software. Download this tutorial to a temporary folder or your desktop and open it with Mathematica.
• Taylor polynomial approximations of functions. Notebook: TaylorsTheorem.nb.
• Loss of precision in numerical calculations. Notebook: LossOfPrecision.nb.
• Exaggerated examples of round-off errors which occur when performing computer arithmetic. Notebook: rounding.nb.
• Behavior of a stable algorithm. Notebook: Stable.nb.
• Bisection Method of root finding. Notebook: Bisection.nb.
• Fixed Point Method of root finding. Notebook: FixedPoint.nb.
• Newton's Method of root finding. Notebook: Newton.nb.
• Secant Method of root finding. Notebook: Secant.nb.
• RegulaFalsi Method of root finding (method of false position). Notebook: RegulaFalsi.nb.
• Roots of multiplicity greater than one can cause Netwon's Method to slow its rate of convergence. Notebook: Multiplicity.nb.
• Aitken's Del-squared method can deliver derivative-free quadratic convergence. Notebook: Aitken.nb.
• Slides for a brief introduction to Lagrange Interpolating Polynomials.
• Lagrange polynomial interpolation of functions and data. Notebook: LagrangeInterpolation.nb.
• Newton's interpolatory divided difference scheme for polynomial interpolation of functions and data. Notebook: DividedDifference.nb.
• Slides for a brief introduction to cubic splines. Notebook: CubicSpline.nb.
• Slides for a brief introduction to numerical differentiation.
• Numerical approximations to first and second derivatives of functions. Notebook: Derivatives.nb.
• Improving approximations to derivatives using Richardson's extrapolation method. Notebook: Richardson.nb.
• Slides for a brief introduction to numerical integration.
• Slides for a brief introduction to composite numerical integration.
• A basic introduction to Simpson's Rule for approximating definite integrals. Notebook: SimpsonsRule.nb.
• A basic introduction to the Trapezoidal Rule for approximating definite integrals. Notebook: TrapezoidalRule.nb.
• Higher order accuracy NewtonCotes formulas for approximating definite integrals. Notebook: NewtonCotes.nb.
• Higher order accuracy composite Simpson's, Trapezoidal, and Midpoint formulas for approximating definite integrals. Notebook: CompositeIntegration.nb.
• An adaptive stepsize quadrature algorithm based on Simpson's Rule. Notebook: AdaptiveQuadrature.nb.
• Slides for a brief introduction to Gaussian Quadrature.
• The Gaussian Quadrature method for approximating definite integrals. Notebook: GaussianQuadrature.nb.
• Numerically approximating double integrals. Notebook: DoubleIntegrals.nb.
• Slides for a brief introduction to Gaussian Elimination.
• Solving linear systems of equations using variations on the method of Gaussian elimination. Notebook: GaussianElimination.nb.
• Computing the inverse of a matrix using various pivoting strategies. Notebook: MatrixInversion.nb.
• Computing the LU factorization of a matrix with and without row swapping. Notebook: LUDecomposition.nb.
• Finding the eigenvalues and eigenvectors of a matrix. Notebook: Eigensystems.nb.
• Approximating the solutions to linear systems using iterative linear techniques. Notebook: IterativeLinear.nb.
• An introduction to the preconditioned conjugate gradient method for approximating the solutions to linear systems. Notebook: ConjugateGradient.nb. A well-known technical report on the conjugate gradient method for solving linear systems is also available. (You may need a Postscript previewer to read this document, download one here.
• Calculating coefficients for the least squares fitting of data collected as ordered pairs. Notebook: LeastSquares.nb.
• Calculating coefficients of orthogonal polynomials used to approximate continuous functions. Notebook: OrthogonalPolynomials.nb.
• Slides for a brief introduction to Rational approximation of continuous functions.
• Using rational functions to approximate continuous functions. Notebook: RationalApproximation.nb.