Analysis and Design of algorithms - Study Notes for GATE

Chapter 1 : Review

• Concept of algorithm
• Components of algorithms

Chapter 2 : Different perspectives of algorithm

• Numerical algorithm
• Review of searching algorithm
• Review of sorting algorithm
• Recursion v/s iteration

Chapter 3 : Graph theory and related data structure

• Introduction to graph theory
• Matrix representation
• Trees

Chapter 4 : Divide and Conquer

• Divide & Conquer : Binary search
• Max- Min Search & Merge sort
• Integer Multiplication

Chapter 5 : Greedy method

• Cassette filling
• Knapsack problem
• Job scheduling

Chapter 6 : Backtracking and Branch and Bound

• Backtracking
• Branch & Bound

Chapter 7 : Graph theoretic algorithms

• Shortest path
• Minimal spanning trees
• Techniques for Graphs

GATE syllabus for MECHANICAL ENGINEERING

ENGINEERING MATHEMATICS

1. Linear Algebra: Algebra of matrices, system of linear equations, eigen values and eigen vectors
   
2. Calculus: Taylor series, fourier series, partial derivatives, total derivatives, definite and improper integrals, multiple integrals
   
3. Vector Calculus: Gradient, divergence and curl, line and surface integrals, Green, Gauss, and Stokes theorem
   
4. Differential Equations: Linear ODE’s, First order non-linear ODE’s, initial and boundary value problems, Laplace Transform, PDE’s-laplace, wave and diffusion equations.
   
5. Numerical methods: Solution of system of linear equations, interpolation, numerical integration, newton-raphson method, runge-kutta method.
   
6. Probability and statics: Gaussian, Weibul distribution and their properties, method of least squares , regression analysis, analysis of variance.
   

APPLIED MECHANICS AND DESIGN

1. Engineering Mechanics: Equivalent force systems, free-body concepts, equations of equilibrium, trusses and frames, virtual work and minimum potential energy. Kinematics and dynamics of particles and rigid bodies, impulse and momentum , energy methods, central force motion.
   
2. Strength of Materials: Stress and strainm, Elastic constants, stress-strain relationship, Mohr’s circle, deflection of beams, bending and shear stress, shear force and bending moment diagrams, torsion of circular shafts, thin thick cylinders, Eulers theory of columns, strain energy methods, thermal stress.
   
3. Theory of machines: Analysis of plane mechanisms, dynamic analysis of slider-crank mechanism, planer cams and followers, grear tooth profiles, kinematics and design of gears, governors and flywheels, balancing of reciprocating and rotating masses.
   
4. Vibrations: Free and forced vibrations of single degree freedom systems, effect of damping, vibration isolation, resonance, critical speed shafts.
   
5. Design of Machine Elements: Desing for statics and dynamic loading, fatigue strength, failure theories, design of bolted, riveted and welded joints, design of shafts and keys, design of spur gears, brakes and clutches, rolling and sliding contact bearings , belt, ropes and chain drives.
   

THERMAL SCIENCE AND ENGINEERING

1. Fluid Mechanics: Fluid properties, fluid statics, manumetry, buoyancy, control-volume analysis of mass, momentum and energy, fluid acceleration, differential equation of continuity and momentum. Bernoulli's equation. Viscous flow of incompressible fluids; boundary layer, flow through pipes, head losses in pipes, bends etc.
   
2. Turbo machines: Velocity triangles Euler’s equation, specific speed, Pelton wheel, centrifugal pump, Francis and Kaplan turbines.
   
3. Heat-Transfer: Modes of heat transfer, one dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction, fins, dimensionless parameters in free and forced convective heat layer, effect of turbulence, radiative heat transfer, black and grey surface shape factors, networ analysis, heat exchanger performance, LMTD and NTU methods.
   
4. Thermodynamics: Zeroth, fact and second laws of thermodynamics, thermodynamic system and processes, irreversibility and availability, behavior of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes. Analysis of thermodynamics cycles related to energy conversion. Carnot, Rankine, Otto, Diesel, Brayton and Vapour compression cycle.
5. Steam engineering: Steam generators, Steam engines, steam turbines-impulse and reaction, velocity diagrams, compounding, reheat factor.
   
6. I.C. Engines: Requirements and suitability of fuels in IC engines, fuel ratings, fuel- air mixture requirements, normal combustion in SI and CI engines, engine performance calculations, components of gas turbine.
   
7. Reciprocating Air Compressor: Isothermal, adiabatic and polytropic compression, staging the compression process, inter cooling and aftercooling, minimum work requirement, volumetric efficiency. Centrifugal and axial flow compressors.
   
8. Refrigeration and air-conditioning: Refrigerant compressors, expansion devices, condensers and evaporators, properties of moist air, psychrometric chart, basic psychrometric processes.
   

MANUFACTURING AND INDUSTRIAL ENGINEERING

1. Engineering materials: Structure and properties of engineering materials and their applications, heat treatment.
   
2. Metal casting: Casting processes- pattern making, molds and cores, solidification, design of casting, casting defects.
   
3. Metal working: Stress-strain diagrams for ductile and brittle material, plastic deformation, mechanisms, fundamentals of hot and cold working processes-forging, extrusion, wire drawing, hseet metal working, punching, blanking, bending, deep drawing, coining and spinning.
   
4. Machining Processes and Machine Tool Operation: Mechanics of metal cutting, single and multipoint cutting tools, geometry and machining aspects, tool life, machinability, economics of machining, non- traditional machining processes.
   
5. Metrology and Inspection: Limits, fits and tolerances, linear and angular measurements, comparators, gauge design interferometry,form and finish measurement, measurement of screw threads, alignment and testing methods.
   
6. Tool Engineering: Principles of work holding, design of jigs and fixtures, design of press working tools.
   
7. Manufacturing Analysis: Part-print analysis, tolerance analysis in manufacturing and assembly, time and cost analysis.
   
8. Computer Integrated Manufacturing: Basic concepts of CAD, CAM , Group technology.
   
9. Work Study: Method study, work measurement time study, work sampling, job evaluation, merit rating.
   
10. Production planning and control: Forecasting models, aggregate production planning, master scheduling, materials requirements planning.
    
11. Inventory control: Deterministic and probabilistic models, safety stock inventory control systems.
    
12. Operations Research: Linear programming, simplex and duplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.

GATE question papers with answer keys

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Tips and Tricks for GATE 2013 Aspirants

1. Aim for taking GATE exam varies from candidate to candidate. Students from private engineering colleges try to get into M.Tech in order to have stamp of the better known institutions and for them reasonable percentile serves the purpose. On the other hand, students studying in well established institutes may aim to get into IIT or other equivalent institutions. For them very high percentile is essential.
2. Normally 3 to 4 months of serious study will be sufficient for the preparation.
3. Those students who are in final year have to schedule their studies as semester exam in winter and other engagements may absorb lot of time.
4. First of all make a proper strategy before starting preparation of the examination.
5. You have to choose the subject and study as per the syllabus mentioned in the GATE brochure.
6. Collect the Syllabus for the GATE exam.
7. Collect all the relevant books for the subject. This collection must include the books for Fundamental and basic concepts as well as for specific problems, guide book for GATE and previous year question papers.
8. Always try to go through the standard books which are easily available and in which you can easily understand the concepts. This will improve your learning ability.
9. Mean time you should be in touch with some GATE experienced persons for proper guidance.
10. Read syllabus and question papers carefully so that it will easy for you to make a proper approach.
11. Start preparing from the initial topics i.e. the basic ones and note down the basic concepts (definitions, unit, dimension etc.) as well as necessary theories, formulae etc.
12. Try to solve as many problems as possible from different book as well as try to find more and more tricks.
13. Try to apply your own logics and tricks in solving problems and note it down because it will save your time in the examination hall.
14. Conduct self tests based on various chapters. Continue the self tests and try to achieve a very good score.
15. Practice more and more problems and follow the same procedure for the rest of the chapters and subjects.
16. Finally, go for self tests based on whole syllabus and if necessary take help of others in conducting self-tests.
17. To do all these things one has to spend lots of time on studies and should be very sincere throughout the preparation.
18. One month before the examination you should start revising the course as many times as possible so that on the day before the exam you will be prepared enough to crack the exam.
19. In the revision stage concentrate more on the selected topics.
20. Always reach the examination centre 30 min before the start of the exam. It helps you to stay cool and calm during exam.
21. Keep all your necessary stationeries and admit card with you before going to the examination centre.
22. During exam try to attempt section A which is compulsory and that to Q1 carrying one mark each and those in Q2 carrying two marks each.
23. It’s very important to manage the time well during the exam. So manage the time well during the exam.
24. In the examination hall one should not get panickly upon receiving the question paper rather candidates should stay cool before the test so that they do not get confused while attempting the paper.
25. Time management is important but not at the cost of answering the paper accurately.
26. Always try to attempt only those questions in which you are pretty confident and you know the answer very well.
27. Read the questions carefully and apply proper logic before marking the answer.
28. Always avoid the negative marking.
29. Do not attempt unnecessary questions in which you are not confident because that may cost you much.
30. Do not try to get hold of the entire syllabus prescribed by GATE. A selective preparation would be a very helpful concept and should be learned accurately.
31. Memorization of any problem without a clear idea of the concept will be a futile exercise.
32. I feel that it is better to have flexible time plan before going to exam and have a balance of mind. It helps in avoiding the silly mistakes.
33. Results of qualified candidates in GATE will give All India Rank and indicate percentile score. For example, a percentile score of 99 means you are in the top 1% category of the candidates who appeared for GATE.
34. Candidates who get less than 70 percentile get no score card.
35. After publication of GATE results, students must apply to individual Institutes to get their application forms.
36. Institutes advertise M.Tech admissions in leading newspapers from 1st April till end July. However some Institutes do not advertise and therefore students have to get the forms themselves.
37. Admission in the Institute is based on GATE percentile.
38. The concerned Institute may conduct written test and/or interview for the purpose of admission.
39. During the pursuit of M.Tech, you are paid a scholarship of Rs. 5000 per month by the Government of India. This amount is enough for living expenses including purchase of books etc. the scholarship is paid for the entire period of M.Tech.