Instructor: Gerard Richter
   (richter@cs.rutgers.edu, 732-445-2001 x2097)
   314 Core Building
   office hrs: Monday 1:30-2:30 pm, Thursday 1:30-2:30 pm, or by appointment
 

Teaching assistant: Zhennan Yan
   (zhennany@cs.rutgers.edu, 732-445-2001 x9785)   
   Hill 405
   office hours: Tuesday 2-3 pm, or by arrangement  

...recitation starts SECOND week of classes

Text: (recommended, but not required)  K. Atkinson & W. Han, Elementary Numerical Analysis, 3rd edition, Wiley
   on reserve in SERC reading room

Prerequisites:  CALC1, CALC2, Math 250 (linear algebra), ability to program in a high level language

Programs will be written in MATLAB language - Matlab tutorial + links to other references

Grading:

• written homework, computer programs ~ 20-25%
• midterm ~ 30%
• final exam ~ 45%

Outline of topics...

• Floating point numbers and roundoff error (Chap. 1-2 of text)
• Solution of nonlinear algebraic equations (Chap. 3)
• bisection method, fixed point iteration, secant method, Newton's method
• linear and quadratic convergence
• roots of polynomials
• Solution of linear algebraic systems (Chap. 6)
• Gaussian elimination, partial pivoting
• matrix inversion
• LU decomposition
• error analysis
• iterative methods
• PageRank
• Least squares approximation (Chap. 7.1)
• Polynomial interpolation (Chap. 4)
• Lagrange and Newton forms of interpolating polynomial
• error term
• interpolation of derivatives
• piecewise polynomial interpolation, splines
• Numerical differentiation and integration (Chap. 5)
• derivation of quadrature formulas and their error terms
• composite formulas
• adaptive quadrature
• Gaussian quadrature
• derivation of numerical differentiation formulas, error terms
• Numerical solution of ordinary differential equations (Chap. 8)
• introduction to ordinary differential equations
• basic numerical methods, e.g., Euler's method
• higher order equations, systems