BE Electrical Engineering Semester 4 (SE Second Year)University of Mumbai
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# Numerical Methods and Optimization Techniques Semester 4 (SE Second Year) BE Electrical Engineering University of Mumbai Topics and Syllabus

SubjectNumerical Methods and Optimization Techniques
CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]

## Topics with syllabus and resources

100.00 Module 1
• Error Analysis: Types, estimation, error propagation.
200.00 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.
300.00 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.
400.00 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.
500.00 Module 5
• One dimensional unconstrained Optimization: Golden-section search, quadratic interpolation, Newton’s method.
600.00 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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