Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors. Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, evaluation of definite and improper integrals, partial derivatives, total derivative, maxima and minima, gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals. Theorems of Stokes, Gauss and Green.
Differential Calculus: First order linear and nonlinear equations, higher order linear ODEs with constant coefficients, Cauchy and Euler equations, initial and boundary value problems, Laplace transforms. Partial differential equations and separation of variables methods.
Numerical methods: Numerical solution of linear and nonlinear algebraic equations, integration by trapezoidal and Simpson rule, single and multi-step methods for differential equations.
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Atmosphere: Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts.
Airplane performance: Pressure altitude; equivalent, calibrated, indicated air speeds; Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator. Drag polar; take off and landing; steady climb & descent,-absolute and service ceiling; cruise, cruise climb, endurance or loiter; load factor, turning flight, V-n diagram; Winds: head, tail & cross winds.
Static stability: Angle of attack, sideslip; roll, pitch & yaw controls; longitudinal stick fixed & free stability, horizontal tail position and size; directional stability, vertical tail position and size; dihedral stability. Wing dihedral, sweep & position; hinge moments, stick forces.
Dynamic stability: Euler angles; Equations of motion; aerodynamic forces and moments, stability & control derivatives; decoupling of longitudinal and lat-directional dynamics; longitudinal modes; lateral-directional modes.
Central force motion, determination of trajectory and orbital period in simple cases. Orbit transfer, in-plane and out-of-plane. Elements of rocket motor performance.
Basic Fluid Mechanics: Incompressible irrotational flow, Helmholtz and Kelvin theorem, singularities and superposition, viscous flows, boundary layer on a flat plate.
Airfoils and wings: Classification of airfoils, aerodynamic characteristics, high lift devices, ***** Joukowski theorem; lift generation; thin airfoil theory; wing theory; induced drag; qualitative treatment of low aspect ratio wings.
Viscous Flows: Flow separation, introduction to turbulence, transition, structure of a turbulent boundary layer.
Compressible Flows: Dynamics & Thermodynamics of I-D flow, isentropic flow, normal shock, oblique shock, Prandtl-Meyer flow, flow in nozzles and diffusers, inviscid flow in a c-d nozzle, flow in diffusers. subsonic and supersonic airfoils, compressibility effects on lift and drag, critical and drag divergence Mach number, wave drag.
Wind Tunnel Testing: Measurement and visualisation techniques.
Stress and Strain: Equations of equilibrium, constitutive law, strain-displacement relationship, compatibility equations, plane stress and strain, Airy's stress function.
Flight Vehicle Structures: Characteristics of aircraft structures and materials, torsion, bending and flexural shear. Flexural shear flow in thin-walled sections. Buckling. Failure theories. Loads on aircraft.
Structural Dynamics: Free and forced vibration of discrete systems. Damping and resonance. Dynamics of continuous systems.
Thermodynamics of Aircraft Gas Turbine engines, thrust and thrust augmentation.
Turbomachinery: Axial compressors and turbines, centrifugal pumps and compressors.
Aerothermodynamics of non rotating propulsion components: Intakes, combustor and nozzle. Thermodynamics of ramjets and scramjets. Elements of rocket propulsion.
Mathematical Logic: Propositional Logic; First Order Logic.
Probability: Conditional Probability; Mean, Median, Mode and Standard Deviation; Random Variables; Distributions; uniform, normal, exponential, Poisson, Binomial.
Set Theory & Algebra: Sets; Relations; Functions; Groups; Partial Orders; Lattice; Boolean Algebra.
Combinatorics: Permutations; Combinations; Counting; Summation; generating functions; recurrence relations; asymptotics.
Graph Theory: Connectivity; spanning trees; Cut vertices & edges; covering; matching; independent sets; Colouring; Planarity; Isomorphism.
Linear Algebra: Algebra of matrices, determinants, systems of linear equations, Eigen values and Eigen vectors.
Numerical Methods: LU decomposition for systems of linear equations; numerical solutions of non-linear algebraic equations by Secant, Bisection and Newton-Raphson Methods; Numerical integration by trapezoidal and Simpson’s rules.
Calculus: Limit, Continuity & differentiability, Mean value Theorems, Theorems of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives, maxima & minima.
FORMAL LANGUAGES AND AUTOMATA
Regular Languages: finite automata, regular expressions, regular grammar.
Context free languages: push down automata, context free grammars
Digital Logic: Logic functions, minimization, design and synthesis of combinatorial and sequential circuits, number representation and computer arithmetic (fixed and floating point)
Computer organization: Machine instructions and addressing modes, ALU and data path, hardwired and microprogrammed control, memory interface, I/O interface (interrupt and DMA mode), serial communication interface, instruction pipelining, cache, main and secondary storage
Data structures and Algorithms: the notion of abstract data types, stack, queue, list, set, string, tree, binary search tree, heap, graph, tree and graph traversals, connected components, spanning trees, shortest paths, hashing, sorting, searching, design techniques (greedy, dynamic, divide and conquer, Algorithm design by induction), asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, Basic concepts of complexity classes – P, NP, NP-hard, NP-complete.
Programming Methodology: Scope, binding, parameter passing, recursion, C programming – data types and declarations, assignment and control flow statements, 1-d and 2-d arrays, functions, pointers, concepts of object-oriented programming - classes, objects, inheritance, polymorphism, operator overloading.
Operating Systems (in the context of Unix): classical concepts (concurrency, synchronization, deadlock), processes, threads and interprocess communication, CPU scheduling, memory management, file systems, I/O systems, protection and security, shell programming.
Information Systems and Software Engineering: information gathering, requirement and feasibility analysis, data flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project, design, coding, testing, implementation, maintenance.
Databases: E-R diagrams, relational model, database design, integrity constraints, normal forms, query languages (SQL), file structures (sequential, indexed), b-trees, transaction and concurrency control.
Data Communication and Networks: ISO/OSI stack, transmission media, data encoding, multiplexing, flow and error control, LAN technologies (Ethernet, token ring), network devices – switches, gateways, routers, ICMP, application layer protocols – SMTP, POP3, HTTP, DNS, FTP, Telnet, network security – basic concepts of public key and private key cryptography, digital signature, firewalls
Web technologies: Proxy, HTML, XML, basic concepts of cgi-bin programming.