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[QUOTE=ijt.Ranjani;315766][B][U]Organisation [/U][/B]: Guru Jambheshwar University of Science & Technology
[B][U]Announcement [/U][/B]: Syllabus
[B][U]Entrance Exam [/U][/B]: PhD Entrance Test

[B][U]Home Page [/U][/B]: [URL]http://www.gjust.ac.in/index.php[/URL]
[B][U]Syllabus Here [/U][/B]: [URL]http://www.gjust.ac.in/exam/esyllabus.html[/URL]

[B][U]PhD Entrance Test Syllabus [/U][/B]:
[B][U]Computer Science & Engineering [/U][/B]:
[B]1. Digital Logic, Computer Organization and Architecture [/B]: 
Logic functions, Minimization, Design and synthesis of combinational and sequential circuits; Number representation and computer arithmetic (fixed and floating point). Machine instructions and addressing modes, ALU and data-path, CPU control design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and main memory, Secondary storage. Basics of microprocessors 8085, 8086.      (9 questions)

[B]2. Data Structures & Algorithms [/B]: 
Functions, Recursion, Parameter passing, Scope, Binding; Abstract data types, Arrays, Stacks, Queues, Linked Lists, Trees, Binary search trees, Binary heaps. Analysis, Asymptotic notation, Notions of space and time complexity, Worst and average case analysis;

Design : Greedy approach, Dynamic programming, Divide-and-conquer; Tree and graph traversals, Connected components, Spanning trees, Shortest paths; Hashing, Sorting, Searching. Asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, Basic concepts of complexity classes P, NP, NP-hard, and NP-complete. (9 questions)

[B]3. Object Oriented Programming & Languages Programming [/B]: 
Element of C, C++, Java -Tokens, Identifiers, Variable and constants, Data types, Control structure, Sequence selection and iteration, Structured data types in arrays, structure, union, string an pointers, Operator, O-O Programming concepts, Classes, Object, Inheritance, Polymorphism and overloading, Control Statement, Function parameter passing, Constructor and destructor, overloading inheritance temples , exception handling, templates.    (10 questions)

[B]4. Theory of Computation & Compiler Design [/B]: 
Regular languages and finite automata, Context free languages and Push-down automata, Recursively enumerable sets and Turing machines, Undecidability. Lexical analysis, Parsing, Syntax directed translation, Runtime environments, Intermediate and target code generation, Basics of code optimization.          (9 questions)

[B]5. Operating System [/B]: 
Processes, Threads, Inter-process communication, Concurrency, Synchronization, Deadlock, CPU scheduling, Memory management and virtual memory, File systems, I/O systems, Protection and security, Windows, Linux and Unix.      (9 questions)

[B]6. Databases [/B]: 
ER-model, Relational model (relational algebra, tuple calculus), Database design (integrity constraints, normal forms), Query languages (SQL), File structures (sequential files, indexing, B and B+ trees), Transactions and concurrency control, Data Ware Housing, Data Mining.

[b][u]Mathematical physics [/u][/b]:
[b][u]Vector spaces and matrices[/u][/b]: linear independence, bases, dimensionality, inner product, linear transformations, matrices, inverse, orthogonal and unitary matrices. Independent elements of a matrix, eigenvalues and eigenvectors, diagonalization, complete orthonormal sets of functions.

[b][u]Function of a complex variable[/u][/b]: Analytic functions, Cauchy-Reimann conditions, Elementary functions of Z, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor and Laurent series, Residues, Residue theorem, Jordon‘s lemma, Evaluation of real definite integrals.

[b][u]Second order linear ODE’s[/u][/b]: series solution (Frobenius’s method). The Wronskian and the second solution. Solution of Legendre, Bessel, Hermite and Lagaurre equations. Generating functions and recurrence relations.

Integral transforms, Laplace transform (LT), first and second shifting theorems, Inverse LT by partial fractions, L T of derivatives and integral of a function. Fourier series (FS) FS of arbitrary period, Half-wave expansions, partial sums; Fourier integral And transforms; F T of delta function.

[b][u]Text and Reference Books[/u][/b]:
T.L.Chow Mathematical Methods for Physicists
G. Arfken Mathematical Methods for Physics
A. W. Joshi Matrices and Tensors for Physicists
E. Ereyszig Advanced Engineering Mathematics
Mary L. Boas Mathematics for Physicists

[b][u]Classical Mechanics [/u][/b]:
Constraints and their classification, D’Alemberts principle, generalized coordinates, Lagrangian equation, and its applications, Hamilton’s principle and derivation of Lagrange’s equations from Hamilton’s principle, symmetries and conservation laws.

Reduction to equivalent one body problem , the equation of motion and first integrals, the equivalent one – dimensional problem and the classification of orbits, the differential equation for orbits, the Kepler’s problem(inverse square law), scattering in central force field.

The Euler’s angles, rate of change of a vector, the Coriolis force and its applications, Legendre transformation and Hamilton’s equation of motion, cyclic coordinates, the equations of canonical transformation, examples of canonical transformation, Poission’s brackets, Poission’s theorem.

Hamilton-Jacobi equation for Hamilton’s principal function, Harmonic Oscillator problem, stable and unstable equilibria, elementary idea of small oscillations, normal modes and coordinates , free vibrations of a linear triatomic molecule.

[b][u]Reference books [/u][/b]:
N.C.Rana and P.S.joag Classical mechanics, Tata McGraw-hill,1991
H.Goldstien Classical mechanics, Addison Wesley,1980
A.Sommerfeld Mechanics, (acadmic press,1952)
I. Perceival and D. Richards Introduction to dynamics, Cambridge Univ. Press,1982.
Kiran C.Gupta Classical Mechanics[/QUOTE]

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