Mathematical review and computer arithmetic – numbers and errors; Nonlinear equations; Direct methods for linear systems; Iterative methods for linear systems; Eigenvalues and eigenvectors power method, inverse power method, QR method; Approximation theory – norms, orthogonalization, polynomial approximation, piecewise polynomial approximation, trigonometric approximation,rational approximation, wavelet bases; Numerical differentiation; Numerical integration – Romberg integration, Gauss quadrature, Adaptive quadrature; Numerical ordinary differential equations - single step and multi-step m

Introduction to international law; Space law – UNCOPUOS and its sub-committees and treaty formulation, definition and delimitation of outer space; Sources of space law – UN treaties, principles and resolutions, and domestic space legislations; Other international agencies relevant to space law; Legal aspects of space activities – state responsibility for space activities, debris mitigation; Legal and policty aspects of space applications – SATCOM policy, remote sensing data policy, position and navigation services, legal issues in satellite based services; Space Law relating to commercial s

Introduction - foundations of individual behavior and processes: personality, perception, workplace values, attitudes and emotions, learning, employee motivation, stress management – Group processes: foundations of group behavior, understanding work teams, communication, decision making and employee involvement, leadership, power and politics, conflict and negotiation – Organizational Processes: organization structure and design, organizational culture, organizational change and de- velopment.

Design process: identification of needs and requirements, conceptual solutions, preliminary design,detailing, manufacturing considerations, prototyping and testing.

Machine elements selection/design: shafts, couplings, pulleys and cables, clutches, screws, gears, cams, springs, structural elements, structural joints, sliding contact bearings, lubrication, rolling element bearings.

Basic acoustic principles – acoustic terminology and definitions – plane and spherical wave propagation – theories of monopole, dipole and quadrapole sound sources – sound transmission and absorption – sound transmission through ducts – structure borne sound – sound radiation and structural response – introduction to noise control.

Equations of Motion: rigid body dynamics, coordinate transformation, Euler angle & quaternion formulation – Dynamics of Generic Fixed Wing Aircraft: 6-DoF equations of motion, linearized equations of motion, linearised longitudinal & lateral equations, aerodynamic derivatives – LTI system basics – Stability of Uncontrolled Motion: linearized longitudinal & lateral dynamics, modes of motion – Response to Control Inputs: transfer function, step response & frequency response characteristics – Feedback Control: stability augmentation, PID control, root-locus technique for contro

Review of vibration of structural elements – one-dimensional motion in elastic media – discrete Fourier transform – spectral finite element method – standing waves – flexural waves in beams and plates – torsional waves in shafts – guided waves – structural health monitoring using wave propagation.

Basic equations – Hierarchy of mathematical models – Mathematical nature of flow equations and boundary conditions – Finite difference and finite volume methods – Analysis of Schemes: Numerical errors, stability, numerical dissipation – Grid generation – Wave equation – Numerical Solution of Compressible Euler Equation: Discontinuities and entropy, mathematical properties of Euler equation – Reconstruction-evolution – Upwind methods – Boundary conditions – Numerical solution of compressible Navier-Stokes equations – Turbulence Modeling: RANS, LES, DNS – Higher-order methods – Uncertainty in