Numerical Analysis
- Sources of error, representation of real numbers in the machine, rounding and truncation
- Absolute and relative rounding and truncation errors, function calculation errors
- Finding roots of nonlinear functions and systems, determining the limits of roots
- Bisection method, displacement method, fixed point method, Newtons method and its improvement, chord method
- Convergence of the methods discussed and their order of convergence, solving nonlinear systems with Newtons method
- Interpolation, Lagrange interpolation, Newtons divided differences and Newtons interpolation, interpolation error
- Least squares approximation
- Numerical integration, midpoint integration rule, trapezoidal integration rule
- Simpsons integration rule, Gaussian integration formulas, degree of accuracy of integration formulas
- Numerical solution of initial value ordinary differential equations, Euler method
- Higher-order Taylor methods, Runge-Kutta methods
- Numerical solution of systems of ordinary differential equations, numerical solution of higher order ordinary differential equations
- Solving linear systems, Gaussian elimination method with axis selection
- Jacobi and Gauss-Seidel iterative methods and their convergence