Aim of this course is to give complex analyse and fundamental methods to solve numerical problems in mathematics, computer science,  physical sciences and engineering. Topics included are as follows: Definitions: Error types, Taylor series and truncation error and rounding numbers.  Numerical solution of nonlinear equations; Bracketing methods, Bisection and False position, Iterative methods: Fixed point and Newton method. Numerical methods for solution of linear systems, Iterative methods and LU decomposition methods.  Interpolation and polynomial approximation, Lagrange polynomials, Least square lines, curve fitting and spline functions (linear and quadratic). Evaluate derivatives by numerical analysis, numerical differentiation, finite difference formulas. Evaluate integrals by numerical analysis, numerical integration, Simpson's rules and Trapezoidal rules. Complex numbers, complex functions, derivative and integral of complex functions.