Department of Mathematics University of Pennsylvania, 2002. - 124 pages.Differential and Difference Equations. Introduction. Linear equations with constant coefficients. Difference equations. Computing with difference equations. Stability theory. Stability theory of difference equations. The Numerical Solution of Differential Equations. Euler's method. Software notes. Systems and equations of higher order. How to document a program. The midpoint and trapezoidal rules. Comparison of the methods. Predictor-corrector methods. Truncation error and step size. Controlling the step size. Case study: Rocket to the moon. Maple programs for the trapezoidal rule. Example: Computing the cosine function. Example: The moon rocket in one dimension. The big leagues. Lagrange and Adams formulas. Numerical linear algebra. Vector spaces and linear mappings. Linear systems. Building blocks for the linear equation solver. How big is zero? Operation count. To unscramble the eggs. Eigenvalues and eigenvectors of matrices. The orthogonal matrices of Jacobi. Convergence of the Jacobi method. Corbato's idea and the implementation of the Jacobi algorithm. Getting it together. Remarks.
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