Error analysis, Types of error, Sources of error, Norms of vectors and matrices, Computer arithmetic, Condition number of a matrix, Significant digits and loss of significant digits, Floating point arithmetic, Binary and decimal representation, Single and double precision

Interpolation: Newton forward and backward difference formula for interpolation, Central difference interpolation formulae, Lagrange’s interpolation, Error in interpolation, Linear least square approximation, Interpolation versus least square approximation, Relevant engineering case studies

Derivation of numerical differentiation of first order and second order derivatives using two points, three points, and five points formulas along with its application in engineering, Relevant case studies

Numerical integration: Trapezoidal rule, Simpson’s rules, Composite Trapezoidal Simpson Rules and Romberg integration, Applications of numerical in engineering, Relevant case studies

Solution of system of linear algebraic equations, Gauss elimination method

LU factorization, Tridiagonal solver

Applications of these methods in engineering disciplines, Relevant case studies

Numerical Solution of nonlinear equations: Bisection method, Newton’s method, Secant method, Convergence analysis of these methods

Newton’s method for system of nonlinear equations

Solution of system of linear equations by Jacobi, Gauss Seidel and SOR methods, Applications of these methods in engineering disciplines, Relevant case studies

Euler’s method and its variations, Taylor’s higher order methods, Error analysis, Consistency, stability and convergence

Runge-Kutta methods of order 2, 3, and 4, Stiff ODEs, Consistency, stability and convergence

Linear multistep methods, Numerical solution of system of ODEs

Numerical solution of BVPs by Finite Difference Method

Applications in engineering: Some relevant case studies

Eigenvalues and Eigenvectors of matrix: power method,

Inverse power method, Shifted inverse power method.

Applications of eigenvalues in engineering disciplines.

Unconstrained Optimization,

Golden search ratio, Lagrange Multipliers,

Method of steepest descent

Applications of optimization in engineering disciplines