Types of errors (relative, Absolute, inherent, round off, truncation), significant digits and numerical instability, flow chart.
Use any Computational tools to Analysis the Numerical Solutions.
Functions of operators, difference operators and the derivative operators, identities.
Linear homogeneous and non homogeneous difference equations.
Solution of Non-linear Equations
Numerical methods for finding the roots of transcendental and polynomial equations (Secant, Newton – Raphson Chebyshev and Graeffe's root squaring methods), rate of convergence and stability of an iterative method.
Solution of Linear Equations
Numerical methods for finding the solutions of system of linear equations (Gauss-Elimination, Gauss-Jordan Elimination, triangularization, Cholesky, Jacobi and Gauss – Seidel).
Interpolation &- Curve Fitting
Lagrange's, Newton, Hermit, Spline, least squares approximation. (Linear and non-linear curves).
Numerical Integration & Differentiation
Computation of integrals using simple Trapezoidal rule, 1/3th Simpson's rule, 3/8th Simpson's rule, Composite Simpson's and Trapezoidal rules, computation of solutions of differential equations using ( Euler method, Euler modified method, Runge Kutta method of order 4). Numerical Solutions of Partial differential Equations, Optimization problem (Simplex Method). Steepest Ascent and Steepest Descent Methods.
Advance Engineering Mathematics Erwin Kreyszig Seven
Numerical Methods for Engineering Chapra 1988
Applied Numerical Analysis Gerald 1999