Engineering Tutorials

M-801-A-NUMERICAL ANALYSIS AND OPTIMIZATION

System of linear algebraic equations and Eigen value problems: elimination method, Gauss method, Gauss-Jordan method; Eigen values and Eigen vectors, bounds on Eigen values, Jacobi methods for symmetric matrices, householder’s method for symmetric matrices.

Interpolation and approximation: interpolation problem, linear interpolation, Lagrange interpolation, Newton interpolation, interpolation with equidistant points, spline interpolation, least square approximation

Numerical differentiation and integration: differentiation of continuous functions, forward difference quotient, central difference quotient, error analysis; derivatives from differences table, higher-order derivatives, Richardson extrapolation techniques, Newton-Cotes method, trapezoidal rule, Simpson’s rule, higher order rules, Romberg integration. Numerical solution of ordinary differential equations: Taylor’s series method, Euler and modified Euler method, Runge-Kutta methods, Milne’s method, Adam-Bashforth-Moultan method.

Optimization: basic concept of optimization, classification of optimization, optimization techniques, engineering applications of optimization. Classical optimization techniques: unconstrained optimization single-variable optimization, multivariable optimization, multivariable optimization, multivariable optimization with equality constraints: solution by direct search method, solution by Lagrange-multipliers method, multivariable optimization with inequality constraints, Kuhn-Tucker conditions

Non-linear optimization: general non-linear programming problem, classification of non-linear programming problem, unconstrained optimization techniques: direct search method, gradient method. Constrained optimization techniques: separable programming, quadratic programming

Dynamic programming: Multistage decision process: representation of a multistage decision process, coversion of nonserial system to a serial system, types of multistage decision problems, principle of optimality, computational procedure in dynamic programming, linear programming as a case of dynamic programming, application of dynamic programming.

Text Books:

1. Engineering Optimization, by SS Rao; New Age International Ltd.
2. Numerical Method, by E. Balaguruswamy; Tata McGraw Hill.
3. Numerical methods for Scientific & Engineering Computation, by MK Jain, SRK Iyengar and RK Jain; New Age International Ltd.

Reference Books:

1. Operations Research, by Taha H Hamidi; Prentice Hall of India, New Delhi
2. Operations Research, by Philips, Revindran, Solgebery; Wiley ISE
3. Applied Numerical Analysis, by Curtis F Gerald & Patrick G Whealley; Pearson Education Ltd.
4. Introductory Methods of Numerical Analysis, by SS Sastry; Prentice Hall of India, New Delhi

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