Review of Errors: Accuracy and Precision, round-off error and truncation error. (Sec. 2.2-2.4)
Roots of Transcendental and Polynomial Equations: Bisection method, Iteration methods based on first degree equation, Rate of convergence, System of nonlinear equations. (Sec. 4.2, 4.3, 5.1-5.3, 5.5)
Review of Matrix Algebra: Systems of Equations, Eigenvalues and Eigen vectors.
Solution of System of Linear Algebraic Equations: Gauss Elimination and Gauss Jordan Methods. Iteration Methods. Eigenvalues and Eigenvectors: Jacobi Method for symmetric matrices and Power Method for arbitrary matrices. (Sec. 8.2, 8.7, 10.2, 22.2)
Interpolation and Approximation: Lagrange and Newton interpolation for unequal intervals, Finite difference operators, Interpolating polynomials using finite differences. (Sec. 13.1 – 13.4, 13.6)
Review of Ordinary Differential Equations:
Solutions of Ordinary Differential Equations: Initial value problems - Single step methods - Taylor Series Method, Second , Third and Fourth order Runge Kutta Methods. (Sec.20.1 – 20.3, 21.2)
Lab-Implementation of these methods: MATLAB or EXCEL or Free and Open Source Software (FOSS) tools like R-programming and Scilab.