Contents of the Course Unit |
This course covers the Round-off Errors and Computer Arithmetic: Binary Machine Numbers, Decimal Machine Numbers, Rate of Convergence,The Bisection Method; Fixed-Point Iteration The Newton's Method; The Secant Method,The Method of False Position; Error Analysis for Iterative Methods; Accelerating Convergence,Interpolation and the Lagrange Polynomial,Data Approximation and Neville's Method,Divided Differences: Forward, Backward and Centered Differences Numerical Differentiation: Three and Five Point Formulas Numerical Integration,Numerical Differentiation: Second Derivative Midpoint Formula; Round-Off Error Instability,Numerical Integration: the Trapezoidal and Simpson's Rule , Romberg Integration, Adaptive Quadrature Methods, Gaussian Quadrature,Numerical Integration: Open and Closed Newton-Cotes Formulas,Numerical Integration: Composite Numerical Integration and Round-Off Error Stability. |