Graduate Aptitude Test in Engineering 2014 (GATE 2014) : Syllabus for Mathematics (MA)

GRADUATE APTITUDE TEST IN ENGINEERING (GATE 2014) : MATHEMATICS (MA) SYLLABUS

GATE 2014 : Mathematics(MA) Syllabus 

Linear Algebra : Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.

Complex Analysis : Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.

Real Analysis : Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

Ordinary Differential Equations : First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients; method of Laplace transforms for solving ordinary differential equations, series solutions; Legendre and Bessel functions and their orthogonality.

Algebra : Normal subgroups and homomorphism theorems, automorphisms; Group actions, Sylow’s theorems and their applications; Euclidean domains, Principle ideal domains and unique factorization domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.

Functional Analysis : Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

Numerical Analysis : Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error of polynomial interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules, Gauss Legendrequadrature, method of undetermined parameters; least square polynomial approximation; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method, numerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler’s method, Runge-Kutta methods.

Partial Differential Equations : Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.
Mechanics : Virtual work, Lagrange’s equations for holonomic systems, Hamiltonian equations.

Topology : Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.
Probability and Statistics : Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests based on normal, X2 , t, F – distributions; Linear regression; Interval estimation.

Linear programming : Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex 
method, big-M and two phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, u -u method for solving transportation problems; Hungarian method for solving assignment problems.

Calculus of Variation and Integral Equations : Variation problems with fixed boundaries; sufficient conditions for extremum, linear integral equations of Fredholm and Volterra type, their iterative solutions.

Useful Links : GATE-2014

GATE 2014 : Eligibility
GATE 2014 : AEROSPACE ENGINEERING (AE) SYLLABUS
GATE 2014 : AGRICULTURAL ENGINEERING (AG)
GATE 2014 : Architecture and Planning (AR) Syllabus 
GATE 2014 : Bio-technology (BT) Syllabus 
GATE 2014 : Civil Engineering (CE) Syllabus 
GATE 2014 : Chemical Engineering (CH) Syllabus
GATE 2014 : Chemistry (CY) Syllabus
GATE 2014 : Computer Science and Information Technology (CS) Syllabus
GATE 2014 : Electrical Engineering (EE) Syllabus
GATE 2014 : Electronics and Communication Engineering (EC) Syllabus 
GATE 2014 (Graduate Aptitude Test in Engineering 2014) : Syllabus for Geology and Geophysics (GG)

GATE 2014 : HOW TO APPLY , Last date for Submission of Online Applications : 3rd October 2013.

GATE 2014 : HOW TO APPLY 

GATE 2014 Online Application Processing System (GOAPS) : An online interface is provided for most of applicant’s interaction with the GATE office. With this interface an applicant can

• Do Enrolment using “New User Register here”
• Fill the online application form
• Upload photograph and signature.
• Pay the application fee through net-banking or indicate your option for payment through bank challan (State Bank of India or Syndicate Bank).
• Check the Status of your application form: Received, Under Scrutiny, Accepted, Defect Status, Status after Rectification, Rejected with Valid Reasons, 
• Admit Card Ready for Download, etc.
• Contact the Zonal GATE office in case of any queries/problems.
• Download Admit Card.

Filling in Online Application : GATE 2014

GOAPS: GATE 2014 Online Application Processing System (GOAPS website) can be accessed from the website of the respective Zonal GATE Offices or from the website of the GATE 2014 Organizing Institute.
Enrolment : Aspirants enroll here by providing a valid email address, mobile number and a GOAPS password. 
GOAPS Password : This will be the password that you will be providing to the GOAPS during the Enrolment. You must remember this along with the GOAPS Enrolment ID to log in to GOAPS. Choose a password that cannot be guessed easily (it should NOT be your name, date of birth, or some string of numbers or letters like 12345, abcd, etc.), so as to ensure that the data you provide is not accessible to any person other than yourself. Length of the password should be 8 -15 characters. The following are not permitted:  \a, \b, \n, \r, \t, \\

GOAPS Enrolment ID : Upon registration, an email and SMS containing your GOAPS Enrolment ID will be sent to you. You need to remember this along with the 
GOAPS password for all GATE 2014 related communications/website operations.

Data Requirement for Online Application : GATE-2014

Before login to GOAPS using Enrolment ID and Password, Aspirants keep ready with following information ready:
=> Personal information (name, date of birth, your personal mobile number, parent’s          name, parent’s mobile number etc.)
=> Address for Communication (including PIN code)
=> Eligibility degree details (College address, PIN code of college)
=> GATE paper, choice of GATE Examination Cities
=> Good quality image of your photograph conforming to the requirements specified in         Photograph Requirements
=> Good quality image of your signature conforming to the requirements specified in           Signature Specifications.
=> Details of a valid ID Proof that you will carry to the examination hall.
=> Optional : Your Net banking login and password to make the application fee payment via online net banking mode. Alternately, you may wish to pay via the challan mode.
Application Filling : Fill in the necessary data in the online application form by carefully following instructions given there. You may edit the data at this stage if you require. Upload the required soft copy of photo and signature. Check the correctness of the photo and signature that are uploaded. If you are not satisfied, you may upload them again.
=> You will have to select one of the two payment options (details given below) while filling the online form.
=> The GOAPS allows you to enter data, “Save” partially filled form, “Logout”, and resume filling in by logging in again. You may address the error messages that may appear on saving the filled in data.
Before you make the payment, you have to carefully check for any errors or missing data.
Once you press “Submit & Proceed to Payment” button, no further changes to the application can be made.
After processing “Submit & Proceed to Payment” you will be taken to payment option where you may choose offline or via Netbanking option.
The download application form will contain two pages as mentioned below
Page 1: Instructions to the candidate and address slip where you need to send the hard copy
Page 2: The application form. Note that the bottom part may contain the certificate to be signed by the college Principal or may be left blank (depending on your eligibility status).
Those who opted offline payment: Optional page for candidates who select “bank challan” mode of payment (as against the net-banking). This page will contain 3 copies of the challan to be processed with the respective banks (SBI or Syndicate Bank).

Supporting Documents for GATE 2014

Eligibility Documents
SC/ST/PwD Certificate
PwD Category

Application Fee : GATE 2014

Male Candidates (General/OBC) : Rs 1500/-
Women Candidates of any category   :  Rs 750/-
Other Candidates (General/OBC)   :  Rs 1500/-
SC / ST / PwD Category Candidates :   Rs 750/-

Mailing Documents to GATE Office

The printed application form along with the supporting documents must be mailed by Speed Post or Registered Post to the Zonal Office,

The signed application form (with photograph affixed) with Principal’s certificate, if that is proof of your eligibility to appear in GATE 2014.
Other eligibility documents required to appear for GATE 2014 (e.g. degree certificate).
Category certificate for claiming discounted application fee.
GATE copy of challan duly stamped by the bank after payment of fees (you need not submit challan in case of payment by net banking).

GATE 2014 Help Desk

For any GATE 2014 related issues, kindly contact through phone, fax or email using the Phone Numbers & Email address given below
Phone: +91 3222 282093
            +91 3222 282094
            +91 3222 282091

Fax     : +91 3222 278243
E-mail: gate@adm.iitkgp.ernet.in

Useful Links for GATE 2014

GATE 2014 : Importnt dates
GATE 2014 : EXAMINATION SCHEDULE

GATE 2014 : Eligibility

GATE 2014 : AEROSPACE ENGINEERING (AE) SYLLABUS
GATE 2014 : AGRICULTURAL ENGINEERING (AG)
GATE 2014 : Architecture and Planning (AR) Syllabus 
GATE 2014 : Bio-technology (BT) Syllabus 
GATE 2014 : Civil Engineering (CE) Syllabus
GATE 2014 : Chemical Engineering (CH) Syllabus
GATE 2014 : Chemistry (CY) Syllabus 
GATE 2014 : Computer Science and Information Technology (CS) Syllabus
GATE 2014 : Electrical Engineering (EE) Syllabus
GATE 2014 : Electronics and Communication Engineering (EC) Syllabus 
GATE 2014 (Graduate Aptitude Test in Engineering 2014) : Syllabus for Geology and Geophysics (GG)

Hindustan Petroleum Corporation Ltd. (HPCL) : Job Opportunities as Graduate Engineers through GATE-2014

HINDUSTAN PETROLEUM CORPORATION LIMITED : RECRUITMENT OF ENGINEERS ON THE BASIS OF GATE- 2014 

Recruitment of Graduate Engineers through GATE-2014 : Hindustan Petroleum Corporation Ltd.

HPCL invites  bright and dynamic Engineering Graduates, in specified disciplines aspiring to join it’s team of world class professionals. Interested candidates are required to appear for GATE 2014 for their respective discipline.
Education Qualifications :
Bachelor’s degree in engineering / technology in the below mentioned disciplines with minimum 60% marks (aggregate marks of all semesters) in qualifying degree examination for General and OBC candidates, relaxed to 50% (aggregate marks of all semesters) for SC/ST/PWD candidates.
Candidates currently in final year of their engineering studies may  also  apply.
However, they must be in a position to submit their final mark sheet by 31st  August 2014. 
Age Limit : Maximum 25 years as on 30th June 2014 (Relaxation applicable)
Selection Process : 
Graduate Aptitude Test in Engineering (GATE- 2014)score of the candidates in the concerned disciplines. The graduate engineers from  the relevant  disciplines, desirous of taking up a career with Hindustan Petroleum are required to appear in GATE-2014 

Engineering discipline : (Corresponding GATE-2014 Paper )
Mechanical      :        Mechanical Engineering (ME)
Civil               :         Civil Engineering   (CE)
Electrical        :         Electrical Engineering  (EE)
Electronics &Telecommunication  : Electronics and Communication Engineering (EC)
Instrumentation      :    Instrumentation Engineering (IN)

On the basis of valid GATE-2014 marks, candidates who qualify in GATE 2014 in their respective discipline list of candidates will be drawn up a discipline wise, category wise for further selection process comprising of Group Discussion/Group Task and /or Personal Interview. 

How to apply : GATE 2014

GATE-2014 Online Examination is scheduled in the  month of Feb 2014.
For detailed information of GATE-2014 log on  www.gate.iitk.ac.in/gate2014  

The candidates will receive their GATE-2014 Registration number printed on their admit card. On receipt of GATE registration number, the candidates need to apply to Hindustan Petroleum on-line.
The relevant link will be made available from 05th Nov'2013 at the ‘Careers Opportunities  ’ link of Hindustan Petroleum Website www.hpclcareers.com or www.hindustanpetroleum.com

last date for receiving application online for HPCL :  07th January 2014.


Processing Fee (Non-refundable) :
Rs. 200 + applicable Banking charges towards processing fee is required to be paid by General &  OBC-NC  candidates while applying for HPCL.
No Processing fee is applicable for SC/ST & PWD candidates.

HOW TO APPLY : HPCL JOBS 

Apply online  only  on www.hpclcareers.com   or  through www.hindustanpetroleum.com

Online submission of the application will be allowed on the website upto 07.01.2014.
No other mean / mode of the application shall be accepted.
Online Application System will be open from  05.11.2013 to 2400 hrs. on 07.01.2014.

The payment of application fees will be accepted till 1700 hours on 11th Jan 2014.
However the online application for applying will be disabled after 2400 hours on 07.01.2014.
Steps for Applying: HPCL Jobs
1. Login to www.hindustanpetroleum.com and click on Career Opportunities.
Candidate should keep scan copy of Passport size photo (in jpg / gif format less than 500 kb)
2. Fill  in the online  form with all the relevant details carefully (details once submitted cannot be modified). Upload Scan copy of your latest passport size photograph.
Note: Candidates  completing their qualifying degree by 31st August, 2014, are required to specify the aggregate % marks upto last completed semester, in the box provided for % marks against the qualifying degree field, while filling the Online application form.
3. Click Submit. You will get a system generated important unique 12 Digit Application / Reference No. and will be required for all future references throughout the selection process. Take Printout of the Online Application Form and preserve it for future reference.
4. Choose the option for Payment of Application & Processing Fee as detailed  above For Payment  through challan at SBI and through Debit/ Credit card

Note: Candidates are “NOT” required to submit hard copy of application form to HPCL.

Candidates are advised to visit HPCL website- www.hindustanpetroleum.com or the careers page www.hpclcareers.com regularly for latest updates.

Important Dates  :  GATE 2014

Commencement of online application for GATE-2014    :   2nd September 2013
Last date of online application for GATE-2014       :    03rd October 2013

Commencement of online Registration of application for HPCL :  5th November 2013
Last  date  for  online  registration  of  application for HPCL :  07th January 2014

GATE-2014 Online Examination  Between  1st Feb' 2014 and 2nd March 2014

Download recruitment notification of HPCL
Latest Job Openings in Hindustan Petroleum Corporation Ltd.

NHPC Limited : Trainee Engineer (Civil/ Electrical/ Mechanical) Jobs 2013 through GATE-2014

NHPC Limited : Trainee Engineer (Civil/ Electrical/ Mechanical) Recruitment 2014 through GATE - 2014

NHPC Limited (A Government of India Enterprise), NHPC Office Complex, Sector-33, Faridabad-121003 (Haryana). : Job Opportunities 

NHPC Limited is India’s leading Company in Power Sector having excellence in Planning, Designing and Executing Hydro Projects and Operation and Maintenance of Hydro Power Stations. NHPC has also plans to diversify in Thermal, Wind and Solar etc in India and abroad.

NHPC Limited offers a challenging and rewarding career to young and dynamic graduates in the disciplines of Electrical, Civil and Mechanical Engineering.

1. Trainee Engineer (Civil) : 25 posts
Educational Qualifications : Full time regular Bachelor’s Degree in Engineering/ Technology /B.Sc.(Engineering). Degree in Civil Engineering from recognized Indian University/ Institute approved by AICTE with minimum 60% marks or equivalent grade.
Or
AMIE (Civil Engineering) with minimum 60% marks are also eligible.

2. Trainee Engineer (Electrical) : 130 posts

Educational Qualifications : Full  time  regular  Bachelor’s Degree in Engineering/ Technology/B.Sc.(Engineering).   Degree from recognized Indian University/ Institute approved by AICTE with minimum 60% marks or equivalent grade. Or AMIE with minimum 60% marks are also eligible.
Electrical Disciplines includes Electrical/Electrical & Electronics /Power Systems & High Voltage/ Power Engineering.
3. Trainee Engineer (Mechanical) : 25 posts
Educational Qualifications : Full  time  regular  Bachelor’s  Degree  in  Engineering/ Technology/ B.Sc.(Engineering).   Degree from recognized  Indian  University  /  Institute approved  by AICTE with minimum 60% marks or equivalent grade. Or
AMIE with minimum 60% marks are also eligible.
Mechanical Disciplines includes Mechanical/ Production/ Thermal/ Mechanical & Automation.

How to Apply : NHPC ltd. Jobs

Candidates interested in joining NHPC as Trainee Engineers in 2014 -15 are required to appear in GATE -2014. Interested candidates who have passed the eligibility qualification can apply online at NHPC Limited website  http://www.nhpcindia.com/career.htm after obtaining the registration number for GATE-2014.

IMPORTANT DATES OF GATE-2014

Commencement of online submission of GATE - 2014 Applications  :  2nd Sep' 2013
Last date for online submission of GATE 2014 Applications  :  3rd Oct' 2013
Last  date  for  receipt  of  hard  copy  of  online  GATE  Applications  at respective GATE Offices    :  10th October 2013
GATE Examination     :   Between 1st  February and 2nd March 2014
Announcement of GATE Results       :     28th March 2014
For information about GATE-2014 visit :  Click Here

IMPORTANT DATES TO APPLY IN NHPC

Online submission of applications commences : 7th January 2014
Last date for on-line submission of applications  :    21st January 2014
Last date for receipt of hard copy of online application along with documents  : 5th February 2014

Download NHPC ltd. Trainee Engineer notification 2014
Latest Job openings NHPC Limited 

Power Grid corporation of India ltd : Executive Trainee (Electrical) Recruitment with GATE 2014

POWER GRID CORPORATION OF INDIA LIMITED : RECRUITMENT FOR EXECUTIVE TRAINEES (ELECTRICAL)

Power Grid corporation  of India ltd : Executive Trainee (Electrical) – 19th Batch

POWERGRID, the Central Transmission Utility (CTU) of India and a Navratna Public   Sector Enterprise under the Ministry of Power, Govt. of India is engaged in power transmission business with the mandate for planning, co-ordination, supervision and control over complete inter-State transmission system and operation of National & Regional Power Grids.  
POWERGRID is looking for Bright, Committed and Energetic engineers to join its fold as EXECUTIVE TRAINEE in Electrical discipline.

UPPER AGE LIMIT   : 28 years as on 31.12.2013
ESSENTIAL QUALIFICATION : 

Full Time B.E./ B.Tech/ B.Sc (Engg) from recognized University/ Institute Electrical/ Electrical (Power)/ Electrical and Electronics/Power Systems Engineering Minimum 65% or Equivalent CGPA.

AMIE Electrical  Minimum 65% with both Sections A & B cleared by 31.03.2014
Final Year /Semester  students who expect their  results by 14.08.2014 are also eligible, provided they have obtained minimum 65% marks or equivalent CGPA in aggregate  of all semesters/years up to pre-final examination.
SELECTION PROCESS : Based on the marks obtained (Out of 100) by the eligible candidates in the EE paper of GATE 2014, followed by group discussion and personal interview of the candidates who qualify in the GATE paper and have been shortlisted category wise for the GD and interview. 
Candidates shall have the option for appearing the GD/ interview in Hindi or English.

Eligible candidates will have to appear for the Electrical Engineering (EE) paper of GATE - 2014.
Candidates  obtaining  a valid score (Marks out of 100) shall only be eligible for the  next stage of selection. The score is valid only if the candidate obtains more than or equal to the qualifying marks as fixed for the EE paper of GATE 2014

Qualifying Marks in GATE-2014 : 
The qualifying marks  for GATE Examination shall be as per the criteria adopted by the GATE-2014 examination conducting authority for different categories.

Please note that only  GATE-2014 score (Marks  out  of  100) is valid for this recruitment exercise. GATE - 2013 score or prior is not valid.

Online Registration for GATE-2014 shall commence on 2nd  September 2013.
For details on GATE -2014, please visit http://gate.iitkgp.ac.in/gate2014.

Note : A separate notification with details  regarding number of vacancies, important instructions regarding  submission of POWERGRID  online  application, date of interview etc. shall  be hosted on our website, from 7th  January 2014.

How to apply : Power Grid Corporation of India ltd Job Opportunities

Candidates have to register themselves online at POWERGRID website with details of their GATE -2014 Application No., GATE-2014 Registration Number and other required information, which will be made available  at CAREER section of www.powergridindia.com

IMPORTANT DATES : GATE - 2014

Commencement of Online submission of GATE Application  :     02 Sept' 2013
Last date for Online submission of GATE Application  :     03 Oct' 2013
Last date for receipt  of hard copy of Online GATE Application at respective GATE Offices     : 10 Oct 2013

IMPORTANT DATES : POWERGRID RECRUITMENT 2013 

Application Commencement of Online Submission of Application to POWERGRID (tentative) : first week of January 2014 
Last date for  Online submission of Application to POWERGRID (tentative) : second week of February 2014

POWER GRID CORPORATION OF INDIA LIMITED JOB OPPORTUNITIES
Download notification for Power Grid corporation
GATE 2014 Notification 
Examination Schedule: GATE 2014

Indian oil Corporation ltd IOCL) : Graduate Engineers Recruitment 2013 on the basis of GATE-2013 score

Indian oil Corporation ltd (IOCL): Recruitment of Graduate Engineers through GATE 2013.

Indian Oil Offers Unique Opportunity to 250 Graduate Engineers to Join As Assistant Officers/ Assistant Engineers on the basis of GATE-2013 score

IOCL looking for energetic and dedicated Graduate Engineers (Indian nationals only) from the following engineering disciplines for recruitment as Assistant Officers/ Assistant Engineers:
1. Civil  Engineering (excluding Construction/ Environmental/ Transportation Engineering)
2. Chemical Engineering (including Petrochemicals/ Polymer Engineering but excluding Oil/ Paint Technology/ Surfactant Technology/ Ceramics Engineering)
3. Electrical Engineering (including Electrical & Electronics engineering but excluding Electrical & Communication/ Telecommunication engineering)
4. Instrumentation  Engineering (Including  Electronics & Instrumentation engineering  but  excluding  Electronics & Communication engineering/ Telecommunication engineering)
5. Mechanical Engineering (excluding Automation/ Automobile/ Production/ Manufacturing/ Industrial Engineering)
6. Metallurgical Engineering                                                                                           

Educational qualifications : Bachelor’s Degree in Engineering/ Technology (BE/B.Tech or equivalent) in  the above mentioned disciplines (full time regular courses only) from recognized Indian Universities / Institutes.
General and OBC (non- creamy layer) categories, should have secured minimum 65% marks in qualifying degree examinations. It is relaxed to ‘pass’ for Scheduled Caste (SC)/ Scheduled Tribe (ST) /People With Disability (PWD) candidates.
Candidates pursuing/ completed M.Tech in any disciplines, other than mentioned above, for being eligible, must have completed (or are completing) BE/ B.Tech in one of the above mentioned disciplines and already taken GATE-2013 examination in the discipline of their B.Tech are eligible to apply.
Age Limit :
Maximum 26 years (relaxation applicable)
Selection Process : 
Graduate Aptitude Test in Engineers GATE-2013 score of the candidates in the advertise core disciplines.
Group Discussion / Group Task
Personal Interview for assessment of different facets of knowledge, skill, attitude and aptitude.

How to apply : Apply online only for IOCL

Candidates  must  have  a   valid  GATE-2013  Registration Number and Valid  Score from GATE-2013 examination.
Candidate should take a print out of completed  application, affix his/her recent passport size photograph, put his/ her signature at the space provided and keep with him/ her safely for future reference.
Fees : Candidates need not to pay any separate application fee to IOCL.

Last date for receiving the ONLINE applications   :  21st September, 2013 

Apply online for Assistant Officers/ Assistant Engineers recruitment in IOCL
Click here for Latest job openings Indian Oil Corporation ltd.
Click here to download recruitment notification Assistant Officers/ Assistant Engineers

GATE 2014 (Graduate Aptitude Test in Engineering 2014) : Syllabus for Geology and Geophysics (GG)

Graduate Aptitude Test in Engineering (GATE 2014) :Syllabus for Geology and Geophysics (GG).

GATE 2014 : Geology and Geophysics (GG) Syllabus 

PART – A :  COMMON TO GEOLOGY AND GEOPHYSICS

Earth and Planetary system, size, shape, internal structure and composition of the earth; atmosphere and greenhouse effect; isostasy; elements of seismology; physical properties of the interior of the earth; continents and continental processes; physical oceanography; geomagnetism and paleomagnetism, continental drift, plate tectonics.

Weathering; soil formation; action of river, wind, glacier and ocean; earthquakes, volcanism and orogeny. Basic structural geology, mineralogy and petrology. Geological time scale and geochronology; stratigraphic principles; major stratigraphic divisions of India. Engineering properties of rocks and soils. Ground water geology. Geological and geographical distribution of ore, coal and petroleum resources of India.

Introduction to remote sensing. Physical basis and applications of gravity, magnetic, electrical, electromagnetic, seismic and radiometric prospecting for oil, mineral and ground water; introductory well logging.

PART B – SECTION 1:  GEOLOGY

Crystalsymmetry, forms, twinning; crystal chemistry;  optical mineralogy, classification of minerals, diagnostic physical and optical properties of rock forming minerals.
Igneous rocks – classification, forms and textures, magmatic differentiation; phase diagrams and trace elements as monitors of magma evolutionary processes; mantle melting models and derivation and primary magmas.  Metamorphism; controlling factors, metamorphic facies, grade and basic types; metamorphism of pelitic, mafic and impure carbonate rocks; role of fluids in metamorphism; metamorphic P-T-t paths and their tectonic significance; Igneous and metamorphic provinces of India; structure and petrology of sedimentary rocks; sedimentary processes and environments, sedimentary facies, basin analysis; association of igneous, sedimentary and metamorphic rocks  with tectonic setting.

Stress, strain and material response; brittle and ductile deformation; primary and secondary structures; geometry and genesis of folds, faults, joints, unconformities; cleavage, schistosity and lineation; methods of projection, tectonites and their significance; shear zone; superposed folding; basement cover relationship.

Morphology, classification and geological significance of important invertebrates, vertebrates, microfossils and palaeoflora; stratigraphic principles and Indian stratigraphy.

Geomorphic processes and agents; development and evolution of landforms; slope and drainage; processes on deep oceanic and near-shore regions; quantitative and applied geomorphology.

Oremineralogy and optical properties of ore minerals; ore forming processes vis-à-vis ore-rock association (magmatic, hydrothermal, sedimentary and metamorphogenic ores);  ores and metamorphism; fluid inclusions as an ore genetic tool; prospecting and exploration of economic minerals; sampling, ore reserve estimation, geostatistics, mining methods.  Coal and petroleum geology; origin and distribution of mineral and fuel deposits in India; marine geology and ocean resources; ore dressing and mineral economics.

Cosmic abundance; meteorites; geochemical evolution of the earth; geochemical cycles; distribution of major, minor and trace elements; elements of geochemical thermodynamics, isotope geochemistry; geochemistry of waters including solution equilibria and water rock interaction.
Engineering properties of rocks and soils; rocks as construction materials; role of geology in the construction of engineering structures including dams, tunnels and excavation sites; natural hazards.  Ground water geology – exploration, well hydraulics and water quality.  Basic principles of remote sensing – energy sources and radiation principles, atmospheric absorption, interaction of energy with earth’s surface, air-photo interpretation, multispectral remote sensing in visible, infrared, thermal IR and microwave regions, digital processing of satellite images.  GIS – basic concepts, raster and vector mode operation.

PART B – SECTION 2:  GEOPHYSICS
The earth as a planet; different motions of the earth;  gravity field of the earth, Clairaut’s theorem, size and shape of earth; geochronology; seismology and interior of the earth;  variation of density, velocity, pressure, temperature, electrical and magnetic properties of the earth; earthquakes-causes and measurements, magnitude and intensity, focal mechanisms, earthquake quantification, source characteristics, seismotectonics and seismic hazards; digital seismographs, geomagnetic field, paleomagnetism; oceanic and continental lithosphere; plate tectonics; heat flow; upper and lower atmospheric phenomena.

Scalar and vector potential fields; Laplace, Maxwell and Helmholtz equations for solution of different types of boundary value problems in Cartesian, cylindrical and spherical polar coordinates; Green’s theorem; Image theory; integral equations in potential theory; Eikonal equation and Ray theory.  Basic concepts of forward and inverse problems of geophysics, Ill-posedness of inverse problems.
‘G’ and ‘g’ units of measurement, absolute and relative gravity measurements; Land, airborne, shipborne and bore-hole gravity surveys; various  corrections in gravity data reduction – free air, Bouguer and isostatic anomalies; density estimates of rocks; regional and residual gravity separation; principle of equivalent stratum; upward and downward continuation; wavelength filtering; preparation and analysis of gravity maps; gravity anomalies and their interpretation – anomalies due to geometrical and irregular shaped bodies, depth rules, calculation of mass.
Earth’s magnetic field – elements, origin and units of measurement, magnetic susceptibility of rocks and measurements, magnetometers, Land, airborne and marine magnetic surveys, corrections, preparation of magnetic maps, upward and downward continuation, magnetic anomalies-geometrical shaped bodies, depth estimates, Image processing concepts in processing of magnetic anomaly maps; Interpretation of processed magnetic anomaly data.
Conduction of electricity through rocks, electrical conductivities of metals, non-metals, rock forming minerals and different rocks, concepts of D.C. resistivity measurement, various electrode configurations for resistivity sounding and profiling, application of filter theory, Type-curves over multi-layered structures, Dar-Zarrouck parameters, reduction of layers, coefficient of anisotropy, interpretation of resistivity field data, equivalence and suppression, self potential and its origin, field measurement,  Induced polarization, time and frequency domain IP measurements; interpretation and applications of IP, ground-water exploration, environmental and engineering applications.
Basic concept of EM induction, Origin of electromagnetic field, elliptic polarization, methods of measurement for different source-receiver configuration, components in EM measurements.  Skin-depth, interpretation and applications; earth’s natural electromagnetic field, tellurics, magneto-tellurics; geomagnetic depth sounding principles, electromagnetic profiling, methods of measurement, processing of data and interpretation.  Geological applications including groundwater, mining and hydrocarbon exploration.

Seismic methods of prospecting; Elastic properties of earth materials; Reflection, refraction and CDP surveys; land and marine seismic sources, generation and propagation of elastic waves, velocity – depth models, geophones, hydrophones, recording instruments (DFS), digital formats, field layouts, seismic noises and noise profile analysis, optimum geophone grouping, noise cancellation by shot and geophone arrays, 2D and 3D seismic data acquisition, processing and interpretation; CDP stacking charts, binning, filtering, dip-moveout, static and dynamic corrections,  Digital seismic data processing, seismic deconvolution and migration methods,  attribute analysis, bright and dim spots, seismic stratigraphy, high resolution seismics, VSP, AVO.  Reservoir geophysics.

Geophysical signal processing, sampling theorem, aliasing, Nyquist frequency, Fourier series, periodic waveform,  Fourier and Hilbert transform, Z-transform and wavelet transform; power spectrum, delta function, auto correlation, cross correlation, convolution, deconvolution, principles of digital filters, windows, poles and zeros.

Principles and techniques of geophysical well-logging.  SP, resistivity, induction, gamma ray, neutron, density, sonic, temperature, dip meter, caliper, nuclear magnetic, cement bond logging, micro-logs.  Quantitative evaluation of formations from well logs; well hydraulics and application of geophysical methods for groundwater study;  application of bore hole geophysics in ground water, mineral and oil exploration.

Radioactive methods of prospecting and assaying of minerals (radioactive and non radioactive) deposits, half-life, decay constant, radioactive equilibrium, G M counter, scintillation detector, semiconductor devices, application of radiometric for exploration and radioactive waste disposal.

Geophysical inverse problems; non-uniqueness and stability of solutions; quasi-linear and non-linear methods including Tikhonov’s regularization method, Backus-Gilbert method, simulated annealing, genetic algorithms and artificial neural network.
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Graduate Aptitude Test in Engineering (GATE 2014) : Syllabus for Electrical Engineering (EE)

GATE 2014 (Graduate Aptitude Test in Engineering 2014 ) : Syllabus for Electrical Engineering (EE)

GATE 2014 :  Electrical Engineering (EE) Syllabus 

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.
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.

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Graduate Aptitude Test in Engineering 2014 (GATE 2014) : Syllabus for Electronics and Communication Engineering (EC)

GATE 2014 (Graduate Aptitude Test in Engineering 2014): Syllabus for Electronics and Communication Engineering (EC)

GATE 2014 : Electronics and Communication Engineering (EC) Syllabus 

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.
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.
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GATE 2014 : Civil Engineering (CE) Syllabus 
GATE 2014 : Chemical Engineering (CH) Syllabus 
GATE 2014 : Computer Science and Information Technology (CS) Syllabus 
GATE 2014 : Chemistry (CY) Syllabus