CBCGS [2017 - current]

CBGS [2013 - 2016]

Old [2000 - 2012]

## University of Mumbai Semester 4 (SE Second Year) Numerical Methods and Optimization Techniques Revised Syllabus

University of Mumbai Semester 4 (SE Second Year) Numerical Methods and Optimization Techniques and their Unit wise marks distribution

### Units and Topics

## Syllabus

100 Module 1

- Error Analysis: Types, estimation, error propagation.

200 Module 2

- Roots of equation: Bracketing Methods- The bisection method, the false-position method, Open methods-The Newton-Raphson method, The secant method, Systems of Nonlinear EquationsNewton Raphson method.
- Application for the design of an electric circuit.
- Linear Algebraic Equations: LU Decomposition, Solution of currents and voltages in Resistor circuits.

300 Module 3

- Curve Fitting: Interpolation with Newton’s divided- difference interpolating polynomials, Lagrange interpolating polynomials, Coefficients of interpolating polynomials, Inverse interpolation, curve fitting with sinusoidal functions.

400 Module 4

- Solution of ordinary differential equation: Predictor –corrector methods, Milne’s method, Adams-Bashforth method, solution of simultaneous first order & second order differential equations by Picard’s and Runge-Kutta methods.
- Simulating transient current for an electric circuit.

500 Module 5

- One dimensional unconstrained Optimization: Golden-section search, quadratic interpolation, Newton’s method.

600 Module 6

- Constrained Optimization: Introduction of L.P.P., Formulation of the L.P.P., Canonical and Standard forms of L.P.P., solution of L.P.P. by Graphical Method, Introduction to Simplex Method, General Linear Programming Problem, Procedure of simplex method.
- Non-linear programming: Introduction, Single variable optimization, Multivariable optimization with equality constraint-Lagrange’s method, Multivariable optimization with non-equality constraint- Kuhn-Tucker conditions

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