Math 225: Scientific Computing II

Math 225: Scientific Computing II (Spring 2004)

Instructor

Description

This course will develop the theoretical basis and computational techniques for: (i) the approximation of functions - interpolation, extrapolation, splines and orthogonal bases, (ii) the numerical differentiation and integration, and (iii) the solution of ordinary differential equations - both initial value problems and boundary value problems. Error analysis and formulation of convergent mathematical schemes will be used to derive stable, reliable, efficient, and accurate numerical methods for large classes of problems.

Scientific Computing II develops indispensable computation tools for research in many areas of applied mathematics, especially those in which differential equations are used to represent physical, chemical, biological, or social processes. Examples of such areas include fluid dynamics, industrial processes, and mathematical physiology.

This course is a prerequisite for Math 226 and 227: Numerical Partial Differential Equations, parts I & II.

Prerequisites

Scientific Computing I (Math 224) and undergraduate-level background in ODEs (at the level of Math 111 or 131).

Textbooks

Numerical Mathematics by Quateroni, Sacco and Saleri, 2000 (Chapters 8-12).
Scientific Computing by John Trangenstein (22 August 2000) (Chapters 9-12).

Reference books

An Introduction to Numerical Analysis, Second Edition, by Kendall E. Atkinson

Course web page

For more information go to John Trangenstein's Math 225 web page.

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