# Difference between revisions of "Math 410: Intro to Numerical Methods"

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## Catalog Information

### Title

Introduction to Numerical Methods.

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### 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.

## Desired Learning Outcomes

### Prerequisites

Students are required to have had multivariable calculus.

### Minimal learning outcomes

1. Numerical solution of equations of one variable
• Bisection method
• Secant method
• Fixed-point iteration
• Newton's method
• Error analysis
• Polynomial equations
2. Interpolation
• Lagrange interpolation
• Divided-difference methods
• Hermite interpolation
• Cubic spline interpolation
3. Numerical differentiation
• Richardson's extrapolation
4. Numerical integration
• Newton-Cotes formulas
• Composite integration
• Adaptive quadrature
• Gaussian quadrature
• Multiple integrals
5. Numerical solution of linear systems
• Direct methods
• Gaussian elimination
• Pivoting strategies
• Factorization methods
• Iterative methods
• Jacobi iteration
• Gauss-Seidel iteration
• Relaxation methods

### 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.