MA473 NUMERICAL ANALYSIS (4 Cr.)

COURSE DESCRIPTION

Prerequisite:  MA 211 (Introduction to Matrix Theory and Linear Algebra) and either MA 265 (Calculus III) or MA 361 (Differential Equations)

Course Description
Notions and definitions of numerical analysis and computations of numerical methods applied to systems of linear algebraic equations, nonlinear equations, polynomial equations, integration, ordinary and partial differential equations, and integral equations.

Course Outline

1. Digital Computation
2. Applications of Taylor's Theorem
   1. Taylor's theorem with remainder
   2. Rectangle rule
   3. Difference quotients
   4. Simpson's rule
   5. Newton's rule
   6. Single step methods for ordinary differential equations
   7. Richardson extrapolation
   8. Pade
3. Theory of Interpolation
   1. Lagrange
   2. Hermite
   3. Piecewise polynomial
   4. Error of interpolation
4. Applications of Interpolation
   1. Integration rules
   2. Gaussian quadrature
   3. Multi-point
   4. Multi-step methods for ordinary differential equations
   5. Lease squares
5. Gaussian Elimination
   1. Formal reduction to triangular form
   2. Pivoting
   3. Scaling and uncertainty
   4. The full algorithm

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