Difference between revisions of "Math 410: Intro to Numerical Methods"
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Revision as of 16:13, 3 April 2013
Contents
Catalog Information
Title
Introduction to Numerical Methods.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F
Prerequisite
Description
Root finding, interpolation, curve fitting, numerical differentiation and integration, multiple integrals, direct solvers for linear systems, least squares, rational approximations, Fourier and other orthogonal methods. [This official course description appears to differ with current standard practice, in that iterative solvers of linear systems are taught in this course, while "Fourier and other orthogonal methods" are postponed until Math 411.]
Desired Learning Outcomes
Prerequisites
Students are required to have had multivariable calculus.
Minimal learning outcomes
Students should be able to describe, derive, and implement the numerical methods listed below. They should be able to explain the advantages and disadvantages of each method. They should understand error analysis and be able to make practical decisions based on the outcomes of that analysis.
 Numerical solution of equations of one variable
 Bisection method
 Secant method
 Fixedpoint iteration
 Newton's method
 Error analysis
 Polynomial equations
 Interpolation
 Lagrange interpolation
 Divideddifference methods
 Hermite interpolation
 Cubic spline interpolation
 Numerical differentiation
 Derivation of formulas
 Backwarddifference
 Forwarddifference
 Centereddifference
 Error analysis
 Richardson's extrapolation
 Derivation of formulas
 Numerical integration
 NewtonCotes formulas
 Composite integration
 Adaptive quadrature
 Gaussian quadrature
 Multiple integrals
 Error analysis
 Numerical solution of linear systems
 Direct methods
 Gaussian elimination
 Pivoting strategies
 Factorization methods
 Gaussian elimination
 Iterative methods
 Jacobi iteration
 GaussSeidel iteration
 Relaxation methods
 Direct methods
Textbooks
Possible textbooks for this course include (but are not limited to):
 Richard L. Burde and J. Douglas Faires, Numerical Analysis (9th Edition), Brooks Cole, 2010.
Additional topics
Courses for which this course is prerequisite
Math 410 is the introductory numerical analysis course and is a prerequisite for the other 3 numerical analysis courses: Math 411, 510, and 511. It is also a prerequisite for Math 480.