Numerical Analysis I
Course Content and Outline
and Computers. What is Numerical Analysis.
Errors. Floating-Point Arithmetic. Floating-Point Arithmetic (continued);
data types and structures, arithmetic operations, functions, input and output,
interface programming, graphics;
Equations. The secant method. Newton's method and Fixed-Point Iterations.
Errors and Convergence. Roots of Polynomials. Multiple Roots; Golden Section
Search. Solving Sets of Equations.
Review of Linear
Algebra. Elimination Methods. The LU decomposition. The cost of elimination.
Improve the stability by pivoting. Norms and Condition Numbers. Iterative
methods for linear systems.
eigenvalues and eigenvectors (power method, Rayleigh quotient and Gerschgorin's
Curve Fitting. Lagrange and Neville Interpolation. Divided Differences. Least
Squares Approximation. Errors and Complexity. Approximation of Functions.
Chebyshev polynomials. Padé approximations.
Differentiation and Numerical Integration. Interpolation for Derivatives and
Integrals. Extrapolation and Newton-Cotes integration formulas. Composite Rules
and Romberg Integration. Gaussian Quadrature.
MODE OF DELIVERY
Lecture and discussion
- Reading and problem assignments
- Whiteboard and Markers
- Flip Charts
- LCD Projectors
- CDs,DVDs and Tapes