Maxwell relations - adiabatic and isothermal compression
Phase equilibrium
Gibbs phase rule
The system of variable composition
Vant Hoffs equation
Applications of Gibbs - Duhem equation.
VITMEE Syllabus 2024 For Chemistry
Atomic Structure: Planck’s quantum theory - wave - particle duality
Heisenberg’s principle
VB and MO theories
VITMEE 2024 Syllabus for Civil Engineering
Engineering Mathematics : Linear Algebra - Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.
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, Stokes, Gauss and Green’s theorems.
Take a look at the full syllabus of VITMEE 2024 in the below link :
VITMEE Syllabus 2024 For Computer Science and Engineering, IT & Software Technology Syllabus :
Engineering Mathematics
Mathematical Logic - Syntax of First-Order Logic, Semantics of First-Order Logic, a Sequent Calculus, the Completeness Theorem, the Limitations of First-Order Logic.
Differential and Integral Calculus - Limit, Continuity, Differentiability, Leibniz theorem, Mean Value Theorems, Taylor’s theorem, Integrals, Improper integrals, Total Differentiation, Partial derivatives, Maxima and Minima, vector calculus, Linear differential equations.
Probability and Statistics - Probability, conditional probability, Bayes theorem, means, median, mode, moments, standard deviation. Random variables, Uniform, Binomial, Poisson, normal distributions, Correlation and regression, Sampling and Tests of significance.
Numerical Methods - Solutions to algebraic and transcendental equations(Bisection and Newton Raphson’ methods), simultaneous linear algebraic equations(Gauss elimination, Gauss seidal and relaxation), Interpolation methods (forward, backward and central), numerical integration (Trapezoidal, Simpson’s and Weddle’s) eigen values and eigen vectors, Numerical solutions to ordinary (Euler, modified Euler, Runga Kutta 4th order) and partial differential ( parabolic, elliptic and Hyperbolic) equations.
Linear Algebra and Transforms - Linear vector space, determinants, matrices, eigen values, eigen vectors, elements of complex analysis, Laplace transforms, Fourier analysis.
Theoretical Computer Science
Discrete Mathematics : Sets, relations and functions, algebra of matrices and determinants, algebraic structures, Boolean algebra and applications, order relations and structures, graph theory, logic and combinatorics
Theory of computation : Regular languages and finite automata, context free languages and Push down automata, recursively enumerable sets and Turing machines, undecidability.
Analysis of algorithms and computational complexity : Asymptotic analysis ( best , worst, average case) of time and space, Upper and lower bounds on the complexity of specific problems, NP-completeness, code and query tuning techniques, numerical analysis, power analysis & resiliency, intractable problems.
Computer Hardware
Electronics : Network analysis, semiconductor devices, bipolar transistors, FET’s, Power supplies, amplifier, Oscillators, Operational amplifiers, elements of digital electronics, logic circuits.
Digital logic : Number systems and codes, Gates, TTL circuits, Boolean algebra and Karnaugh maps, Arithmetic logic units, Flip flops, registers and counters, Memories, Combinational and sequential logic circuits .
Computer Architecture and organization : Machine instructions and addressing modes, ALU and data path, Register Transfer Language, hardware and micro programmed control, memory interface, RAM, ROM I/O interface ( Interrupt and DMA modes), serial communication interface, instruction pipelining, Cache, main and secondary memory storage, organization and structure of disk drives, RAID architectures Microprocessors: 8085, 8086, Interfacing and memory addressing.
Software systems
Data structures : Notion of abstract data types, stack, Queue, List, set, string, Tree, binary search trees, heap, graph.
Programming methodology : Introduction to programming, pointers, arrays, control structures, Iterational control structures, functions, recursion, testing, debugging, code review, structures, files.
Algorithms for problem solving : Tree and graph traversal, connected components, spanning trees, shortest paths, hashing, sorting, searching, design paradigms (Greed y, dynamic programming, divide and conquer).
Programming language processors : Compiler, Interpreter, assembler, Linker, Loader, Macro processors, phases of compilers, Lexical analysis, parsing, Top-down parsing and bottom up parsing, syntax directed translation, runtime environment, Symbol table, type checking, intermediate Code generation, Code optimization, code generation.
Operating Systems : Memory management, page faults, overlay, processor management, device management, dead locks, Process, thread and inter process communication, CPU scheduling, file systems, I/O systems, protection and security.
System & program development methodology : Software paradigms, principles of programming in any language, documentation, system analysis and design methodologies, User Interface Design (UID), software construction, software testing, software quality, Object Oriented Analysis and Design (OOAD) concepts.
Management Information systems : Aspects of Management and Information systems, decision support and operation support system, sys t ems approaches to MIS, computers and information system in business.
Databases management systems : Data, database and DBMS, Data dictionary/directory, schema, description of database structure, forms of DBMS systems, Hierarchical, network and RDBMS, DDL, DML , stored data structure language and query language, Recent trends in database management systems, Memory management techniques used in computers, query languages(SQL), file structures ( sequential files, indexing, B* trees) Transactions and concurrency control, Basic concepts of transaction processing , ACID properties of transactions, serializability of transactions, concurrency control, recovery, OLAP.
Computer networks & Data communications : Analog versus Digital communication, modems, multiplexers, and concentrators, serial versus parallel communication, simplex, duplex, and half duplex communication, synchronous and asynchronous communication, Error detection/correction methods, data link control protocols, balanced and unbalanced interfaces, communication media, ISO/OSI stack, Sliding window protocol, LAN Technologies (Ethernet, Token ring), TCP/UDP, IP, switches, gateways, and routers.
Web technologies : HTML, XML, Concepts of network and internet, WWW and HTTP, web server, web applications, load balancing and application server, web securities.
Computing Technologies : Client server computing, Logical layers in client server architecture, Two - tier versus Three-tier, Distributed computing, Middleware, Mobile Computing, Cloud Computing.
VITMEE Syllabus 2024 For Electronics and Communication Engineering Engineering Mathematics :
Linear Algebra : Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus : Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential equations : First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary Value problems, Partial Differential Equations and variable separable method.
Complex variables : Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue theorem, solution integrals.
Numerical Methods : Solutions of non-linear algebraic equations, single and multi- step methods for differential equations.
Transform Theory : Fourier transform, Laplace transform, Z - transform.
Network
Network graphs : Matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices. Solution methods; nodal and mesh analysis. Network theorems; superposition, Thevenin and Nortan’s, maximum power transfer, wye-delta transformation, steady state sinusoidal analysis using phasors, Fourier series, linear constant coefficient differential and difference equations; time domain analysis of simple RLC circuits. Laplace and Z transforms: frequency domain analysis of RLC circuits, convolution, 2-port network parameters, driving point and transfer functions, state equation for networks.
Analog Circuits : Characteristics and equivalent circuits (large and small signal) of diodes, BJT, JFETsand MOSFET simple diode circuits: clipping, clamping, rectifier, biasing and bias stability of transistor and FET amplifiers. Amplifiers: single and multi-s tage, differential, operational, feedback and power. Analysis of amplifiers; frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal oscillators: criterion for oscillation; single-transistor and op-amp configurations. Function generators and wave shaping circuits, Power supplies.
Digital Circuits : Boolean algebra; minimization of Boolean functions; logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinational circuits: arithmetic circuits, code converters, multiplexers and decoders. Sequential circuits: latches and flip-flops, counters and shift- registers. Comparators, timers, multivibrators. Sample and hold circuits, ADCs and DACs. Semiconductor memories. Microprocessor (8085): architecture, programming, memory and I/O interfacing
Control Systems : Basic control system components; block diagrammatic description, reduction of block diagrams, properties of systems: linearity, time-invariance, stability, causality. Open loop and closed loop (feedback) systems. Special properties of linear time-invariance (LTI) systems- transfer function, impulse response, poles, zeros, their significance and stability analysis of these systems. Signal flow graphs and their use in determining transfer functions of systems; transient and steady state analysis of LTI system and frequency response. Tools and techniques for LTI control system analysis: Root, loci, Routh - Hurwitz criterion, Bode and Nyquist plots; Control system compensators: elements of lead and lag compensations, elements of proportional-integral- Derivative (PID) control. State variable representation and solution of state equation for LTI systems.
Communication Systems : Fourier analysis of signals - amplitude, phase and power spectrum, auto-correlation and cross-correlation and their Fourier transforms. Signal transmission through linear time-invariant (LTI) systems, impulse response and frequency response, group delay phase delay. Analog modulation systems-amplitude and angle modulation and demodulation systems, spectral analysis of these operations, superhete rodyne receivers, elements of hardwares realizations of analog communication systems. Basic sampling theorems. Pulse code modulation (PCM), differential pulse code modulation (DPCM), delta modulation (DM). Digital modulation schemes: amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK). Multiplexing – time division and frequency division. Additive Gaussian noise; characterization using correlation, probability density function (PDF), power spectral density (PSD). Signal to- noise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM) for low noise conditions.
Electromagnetics : Elements of vector calculus: gradient, divergence and curl; Gauss and strokes theorems, maxwells equation: differential and integral forms. Wave equation. Poynting vector. Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth Transmission lines: Characteristic impedence; impedence transformation; smith chart; impedence matching pulse excitation. Wave guides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Antennas; Dipole antennas; antenna arrays; radiation pattern; reciprocity theorem, antenna gain.
