Types of errors, Propagation of errors, Correct and Significant digits, Examples and exercises.
Solution of System of Linear Equations
Exact methods: LU-decomposition, Gauss-elimination methods without and with partial pivoting. Iterative methods: Gauss-Jacobi and Gauss-Seidal methods, Matrix norm, Condition number and Ill-conditioning, Examples and Exercises.
Eigen values and Eigen vectors
Largest and Smallest eigen values and eigen vectors by power method, Examples and Exercises.
Roots of Non-linear Equations
Bisection, Regula Falsi, Newton–Raphson methods, Direct Iterative method with convergence criterion, Extension of Newton-Raphson and Iterative methods for two variables, Examples and Exercises.
Finite Differences and Divided Differences
Operators, Difference table, Propagation of errors, Divided differences with properties, Examples and Exercises.
Interpolation Formulae: Newton’s forward, backward, Stirling’s and Bessel’s formulae, Newton’s divided difference and Lagrange’s formulae, Errors in various interpolation formulae. Inverse Interpolation: Successive approximation and Lagrange’s method, Examples and Exercises.
Various formulae for first and second derivative with errors, Examples and Exercises.
Newton-Cotes formulae, General quadrature formula for equidistant ordinates, Trapezoidal, Simpson’s 1/3 and 3/8 rules with their geometrical interpretations and errors, Romberg integration and Gaussian quadrature formulae, Examples and Exercises.
Numerical solution of ODE
Picard, Taylor series, Modified-Euler, Fourth order Runge-Kutta methods with errors, Examples and Exercises.
James Scarborough, Numerical Mathematical Analysis, Oxford & IBH Publishing Co. Pvt. Ltd (1950), ISBN 10: 0009780021, ISBN-13:978-0009780021.
M. K. Jain, SRK Iyengar and R.K. Jain, Numerical Methods For Scientific & Engg 5e, New Age International (P) Ltd (2008), ISBN-13:978-8122420012.