Introduction – Formulation of optimization problems – Linear programming – duality - Non- linear programming – unconstrained optimization: optimality conditions, range elimination methods, gradient method, quasi-newton method, conjugate gradient method – Constrained optimization: Lagrange multiplier theorem, Kuhn Tucker condition, penalty function methods, projected gradient methods, Quadratic programming, sequential quadratic programming – Non-traditional optimization techniques for single and multi-objective optimization – Applications in Engineering.

Machine learning basics: capacity, overfitting and under fitting, hyper parameters and validation sets, bias & variance; PAC model; Rademacher complexity; growth function; VC- dimension; fundamental concepts of artificial neural networks; single layer perceptron classifier; multi-layer feed forward networks; single layer feed-back networks; associative memories; introductory concepts of reinforcement learning, Markhov decision process.

Introduction – approximate solutions to governing differential equations (GDE) – finite element formulations starting from GDE – finite element formulations based on stationarity of a functional – one-dimensional finite element analysis; shape functions, types of elements and applications – two and three-dimensional finite elements – numerical integration – applications to structural mechanics and fluid flow.

Review of basic equations of elasticity – state of stress at a point – analysis of strain, constitutive relations – generalized Hook’s law – formulation of boundary value problems – solution of 2D problems – energy methods in elasticity – bending, shear and torsion – thin walled beams – applications.