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# Gate Syllabus Cheat Sheet by [deleted]

Gate CSE, ECE, EEE syllbus

### ECE

 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. Prob­ability and Statis­tics: Sampling theorems, Condit­ional probab­ility, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distri­but­ions, Poisson, Normal and Binomial distri­bution, Correl­ation and regression analysis. Nume­rical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differ­ential equations. Tran­sform Theory: Fourier transform, Laplace transform, Z-tran­sform. GENERAL APTITU­DE(­GA): Verbal Ability: English grammar, sentence comple­tion, verbal analogies, word groups, instru­ctions, critical reasoning and verbal deduction. Elec­tronics and Commun­ication Engine­ering Netw­orks: 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 Norton's maximum power transfer, Wye-Delta transf­orm­ation. Steady state sinusoidal analysis using phasors. Linear constant coeffi­cient differ­ential equations; time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits. 2-port network parame­ters: driving point and transfer functions. State equations for networks. Elec­tronic Devices: Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon: diffusion current, drift current, mobility, and resist­ivity. Generation and recomb­ination of carriers. p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET, LED, p-I-n and avalanche photo diode, Basics of LASERs. Device techno­logy: integrated circuits fabric­ation process, oxidation, diffusion, ion implan­tation, photol­ith­ogr­aphy, n-tub, p-tub and twin-tub CMOS process. Analog Circui­ts: Small Signal Equivalent circuits of diodes, BJTs, MOSFETs and analog CMOS. Simple diode circuits, clipping, clamping, rectifier. Biasing and bias stability of transistor and FET amplif­iers. Amplif­iers: single-and multi-­stage, differ­ential and operat­ional, feedback, and power. 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, 555 Timers. Power supplies. Digital circui­ts: Boolean algebra, minimi­zation of Boolean functions; logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combin­atorial circuits: arithmetic circuits, code conver­ters, multip­lexers, decoders, PROMs and PLAs. Sequential circuits: latches and flip-f­lops, counters and shift-­reg­isters. Sample and hold circuits, ADCs, DACs. Semico­nductor memories. Microp­roc­ess­or(­8085): archit­ecture, progra­mming, memory and I/O interf­acing. Signals and Systems: Defini­tions and properties of Laplace transform, contin­uou­s-time and discre­te-time Fourier series, contin­uou­s-time and discre­te-time Fourier Transform, DFT and FFT, z-tran­sform. Sampling theorem. Linear Time-I­nva­riant (LTI) Systems: defini­tions and proper­ties; causality, stability, impulse response, convol­ution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay. Signal transm­ission through LTI systems. Control Systems: Basic control system compon­ents; block diagra­mmatic descri­ption, reduction of block diagrams. Open loop and closed loop (feedback) systems 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 control systems 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 compen­sation, elements of Propor­tio­nal­-In­teg­ral­-De­riv­ative (PID) control. State variable repres­ent­ation and solution of state equation of LTI control systems. Comm­uni­cat­ions: Random signals and noise: probab­ility, random variables, probab­ility density function, autoco­rre­lation, power spectral density. Analog commun­ication systems: amplitude and angle modulation and demodu­lation systems, spectral analysis of these operat­ions, superh­ete­rodyne receivers; elements of hardware, realiz­ations of analog commun­ication systems; signal­-to­-noise ratio (SNR) calcul­ations for amplitude modulation (AM) and frequency modulation (FM) for low noise condit­ions. Fundam­entals of inform­ation theory and channel capacity theorem. Digital commun­ication systems: pulse code modulation (PCM), differ­ential pulse code modulation (DPCM), digital modulation schemes: amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth consid­eration and probab­ility of error calcul­ations for these schemes. Basics of TDMA, FDMA and CDMA and GSM. Elec­tro­mag­net­ics: Elements of vector calculus: divergence and curl; Gauss' and Stokes' theorems, Maxwell's equations: 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 impedance; impedance transf­orm­ation; Smith chart; impedance matching; S parame­ters, pulse excita­tion. Wavegu­ides: modes in rectan­gular wavegu­ides; boundary condit­ions; cut-off freque­ncies; dispersion relations. Basics of propag­ation in dielectric waveguide and optical fibers. Basics of Antennas: Dipole antennas; radiation pattern; antenna gain.

### EE

 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. Prob­ability and Statis­tics: Sampling theorems, Condit­ional probab­ility, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distri­but­ions, Poisson, Normal and Binomial distri­bution, Correl­ation and regression analysis. Nume­rical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differ­ential equations. Tran­sform Theory: Fourier transform, Laplace transform, Z-tran­sform. GENERAL APTITU­DE(­GA): Verbal Ability: English grammar, sentence comple­tion, verbal analogies, word groups, instru­ctions, critical reasoning and verbal deduction. Elec­trical Engine­ering Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady­-state analysis, resonance, basic filter concepts; ideal current and voltage sources, Theven­in's, Norton's and Superp­osition and Maximum Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distri­but­ions; Ampere's and Biot-S­avart's laws; induct­ance; dielec­trics; capaci­tance. Signals and Systems: Repres­ent­ation of continuous and discre­te-time signals; shifting and scaling operat­ions; linear, time-i­nva­riant and causal systems; Fourier series repres­ent­ation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transf­orms. Elec­trical Machin­es: Single phase transf­ormer - equivalent circuit, phasor diagram, tests, regulation and effici­ency; three phase transf­ormers - connec­tions, parallel operation; auto-t­ran­sfo­rmer; energy conversion princi­ples; DC machines - types, windings, generator charac­ter­istics, armature reaction and commut­ation, starting and speed control of motors; three phase induction motors - princi­ples, types, perfor­mance charac­ter­istics, starting and speed control; single phase induction motors; synchr­onous machines - perfor­mance, regulation and parallel operation of genera­tors, motor starting, charac­ter­istics and applic­ations; servo and stepper motors. Power Systems: Basic power generation concepts; transm­ission line models and perfor­mance; cable perfor­mance, insula­tion; corona and radio interf­erence; distri­bution systems; per-unit quanti­ties; bus impedance and admittance matrices; load flow; voltage control; power factor correc­tion; economic operation; symmet­rical compon­ents; fault analysis; principles of over-c­urrent, differ­ential and distance protec­tion; solid state relays and digital protec­tion; circuit breakers; system stability concepts, swing curves and equal area criterion; HVDC transm­ission and FACTS concepts. Control Systems: Principles of feedback; transfer function; block diagrams; steady­-state errors; Routh and Niquist techni­ques; Bode plots; root loci; lag, lead and lead-lag compen­sation; state space model; state transition matrix, contro­lla­bility and observ­abi­lity. Elec­trical and Electronic Measur­eme­nts: Bridges and potent­iom­eters; PMMC, moving iron, dynamo­meter and induction type instru­ments; measur­ement of voltage, current, power, energy and power factor; instrument transf­ormers; digital voltmeters and multim­eters; phase, time and frequency measur­ement; Q-meters; oscill­osc­opes; potent­iom­etric recorders; error analysis. Analog and Digital Electr­oni­cs: Charac­ter­istics of diodes, BJT, FET; amplifiers - biasing, equivalent circuit and frequency response; oscill­ators and feedback amplif­iers; operat­ional amplifiers - charac­ter­istics and applic­ations; simple active filters; VCOs and timers; combin­ational and sequential logic circuits; multip­lexer; Schmitt trigger; multi-­vib­rators; sample and hold circuits; A/D and D/A conver­ters; 8-bit microp­roc­essor basics, archit­ecture, progra­mming and interf­acing. Power Electr­onics and Drives: Semico­nductor power diodes, transi­stors, thyris­tors, triacs, GTOs, MOSFETs and IGBTs - static charac­ter­istics and principles of operation; triggering circuits; phase control rectif­iers; bridge converters - fully controlled and half contro­lled; principles of choppers and inverters; basis concepts of adjustable speed dc and ac drives.

### CSE/IT

 Engi­neering Mathem­atics 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. GENERAL APTITU­DE(­GA): Verbal Ability: English grammar, sentence comple­tion, verbal analogies, word groups, instru­ctions, critical reasoning and verbal deduction. Computer Science and Inform­ation Technology Digital Logic : Logic functions, Minimi­zation, Design and synthesis of combin­ational and sequential circuits; Number repres­ent­ation and computer arithmetic (fixed and floating point). Computer Organi­zation and Archit­ect­ure: 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. Prog­ramming and Data Struct­ures: Progra­mming in C; Functions, Recursion, Parameter passing, Scope, Binding; Abstract data types, Arrays, Stacks, Queues, Linked Lists, Trees, Binary search trees, Binary heaps. Algo­rit­hms: 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, NP-com­plete. Theory of Comput­ati­on: Regular languages and finite automata, Context free languages and Push-down automata, Recurs­ively enumerable sets and Turing machines, Undeci­dab­ility. Compiler Design: Lexical analysis, Parsing, Syntax directed transl­ation, Runtime enviro­nments, Interm­ediate and target code genera­tion, Basics of code optimi­zation. Oper­ating System: Processes, Threads, Inter-­process commun­ica­tion, Concur­rency, Synchr­oni­zation, Deadlock, CPU schedu­ling, Memory management and virtual memory, File systems, I/O systems, Protection and security. Data­bas­es: 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. 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. Computer Networ­ks: ISO/OSI stack, LAN techno­logies (Ethernet, Token ring), Flow and error control techni­ques, Routing algori­thms, Congestion control, TCP/UDP and sockets, IP(v4), Applic­ation layer protocols (icmp, dns, smtp, pop, ftp, http); Basic concepts of hubs, switches, gateways, and routers. Network security basic concepts of public key and private key crypto­graphy, digital signature, firewalls. Web techno­log­ies: HTML, XML, basic concepts of client­-server computing.

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