For CSE and IIT aspirants

Mathematics part 2

In Uncategorized on June 13, 2010 at 7:36 am

A major question that comes in the mind of an aspirant is whether she should go for selective or exhaustive preparation. I went for the exhaustive preparation, as most part of the syllabus was part of my graduation curriculum. But if time does not permit one can leave some topics from point of view of full 60 marks question. In this post I am giving topic wise preparation strategy.

Paper I

1. Linear Algebra Focus should on understanding the definition of various terms mentioned in the syllabus (like vector spaces, subspaces, linear dependence and so on). While answering questions explain all the steps.

2. Calculus Single variable calculus is not a problem for candidates. Refer to chapters (book I mentioned in the booklist) that deal with continuity and differentiability for 2 variables. For double and triple integration also refer to that book. The solved examples from that book are sufficient. The relevant chapters are:12,13,15,16,17,18. Theory is not important , just understand the techniques through solved examples.

3. Analytic Geometry Refer book by PN Chaterjee(Rajhans Publications). This book contains solved examples and all the questions are taken from this book.

4. Ordinary Differential Equations In this topic it is better to make a sheet of all the formulas and techniques. Practice all the solved questions of the book I have mentioned.

5. Dynamics and Statics Completing the Krishna Series books(do only topics mentioned in the syllabus) will be sufficient for attempting 60 marks question. Common Catenary, central orbits, constrained motion should be covered in depth(that is do all the solved examples).  For rest of the topics covering only few examples is sufficient.

6. Vector Analysis In this topic make the formula sheet. And practice previous year questions. Regularly practice the derivations asked in the exam.

Paper II

1. Algebra For the people who are totally new to this topic i would suggest that read the books i have mentioned 2-3 times. Then practice all the theorems and questions yourself 2-3 times.

2. Real Analysis Cover chapters: 2- The Real Numbers(till page 24), 3-Neighbourhoods and Limit Point of a set(till page 11),  4 Countability of Sets(first 12 theorems and examples given at the end) 5,6,7(Regarding Sequence and series) 8. Real Functions. Limit and Continuity, 9,10,11,12,13,15,16. For the topics underlined cover the theorems also. For rest of the chapters solved examples are enough.

3. Complex Analysis Cover this topic from any book. Practice this topic thoroughly.

4. Linear Programming Practice is important. Improve upon the speed and accuracy for this topic.

5. Partial Differential Equations Same as Ordinary Differential Equations.

6. Numerical Analysis and Computer Programming Make the formula sheet for all the methods. Cover error analysis for newton raphson, lagrange interpolation, numerical integration. Draw flow chart and algorithm for all the numerical methods. Practice them regularly. For other topics i had M Morris Mano(this is digital electronics book). One can refer to the internet if she does not find the leftover topics in book.

7. Mechanics and Fluid Dynamics For Mechanics focus on chapters of Lagrangian(cover it from Vol-II, Rigid Dyanamics-Krishna Series), Hamiltonian, Moment Of Inertia, D’Alembert’s principle. For Fluid Dynamics  cover topics mentioned in the syllabus. The book of MD Raisinghania covers syllabus from IAS exam perspective also.

My methodology was to first cover the topic from the books. Then practice previous year questions from that topic. I covered the topics in the order mentioned in the syllabus. However it does not matter much. After covering the entire syllabus I practiced last 3-4 year papers in exam like conditions.

Next i will be uploading some of my sample answers.

  1. Hi sir,

    I have one question how you check your Practice papers for general studies and electrical engg.

    Please comment..!!:)

    Thanks & Regards

  2. this is a very useful post… esp since u mentioned the chapters of the books… thanks alot for this…Could you please also mentioned the chapter wise content of Modern Algebra either in bhambri or hertstein.. thanks

    • @ajay: bhambri chapter 2,3,4,7,8,9 and herstein chapter 2(leave sylow theorems) and 3.

    • hello sir its great to see ur marks in maths. sir i am preparing for CDS exam and there is also a maths paper in it. pls can u help me in giving some tips and tricks to solve quick in exam. as u know the syllabus is vast can u suggest any topics who covers maximum questions
      pls reply soon

  3. also could u please tell how many revision you did of all the topics in total..

  4. and also did you solved all the unsolved problems given at the end of chapter or just solved the examples given..

    • @ajay: i did only solved examples. i did not get time for unsolved problems.

  5. THANK YOU very much Mr. Rajpurohit.This is excellent.Great points you have made in the topic-wise preparation.

    Very helpful indeed…thanx..


  6. hello prakash
    so nice of u, its really great!
    please tell are krishna n shantinarayan enough for analytic geometry or need to go for chaterjee.

    • @neelam: many aspirants have complaints that shanti narayan book does not have enough solved examples. i havent seen krishna series.

  7. how many days (approx) will it take to complete complex analysis and lin prog (seperately),if not studied earlier?

    • @neelam: it is a subjective matter. i may require only 2 days but some other candidate may take 2 weeks.

  8. hello prakash
    please check once the book mentioned for calculus- [Shanti Narayan – Course on Mathematical Analysis (S. Chand)] doesnot contain all topics like curve tracing, maxima minima…

    • @neelam: this book is for multivariable calculus only. chapter of partial derivative covers maxima and minima also. curve tracing is for single variable, refer any other book for it.

  9. hello sir,

    i am an ECE graduate aspiring for civil services..

    i just saw your discussions with supreet sir on his blog.Did you get that preparation strategy followed by revu sir? if yes, could you please share it with us.. and i would like to know your own strategy too..

    many thanks.

  10. hello prakash,
    please do suggest us a blueprint for overall preparation of Mains-2010(like time division for both optionals (especially mathematics) and gs, along with revision time, practice sessions… )from june to september.
    ‘would be a great help!

  11. Hello Prakash, what should be the strategy for preparing Abstract algebra for someone who is doing it for the first time.. considering no coaching or previous exposure to the subject… also which book is better to start hertstein or Fraleigh… thanks

    • @ajay: i know only about herstein and bhambri. both are good. i would suggest you to read it 2 times first and then practice them.

  12. Hello Sir,

    First of all Hearty Congratulations to you.
    It is people like you who make us strong and confident – almost everyone I consulted had the stand that Technical subjects have no good outcome in UPSC – You Jammed them all 🙂 – Hats off to your success. You are a big inspiration for us all.

    Was just curious, is there a need of coaching for IAS Maths ?
    I am a resident of Mumbai ans aim to Clear CSE 2012 – There are no good coaching institutes in Mumbai specially for mathematics !

    What is your take on that ?

    also for Modern Algebra I have got Krishna series book – could you mention which are important topics in Modern Algebra from Mains point of view ?

    • raghuveer: Need of coaching is a subjective matter. I did not take any.
      For Algebra I would suggest you to follow the books I have mentioned.

  13. Raghuveer am too from mumbai with same optional , shall we be friend

  14. @ Prakash sir – Thanks for your genuine advice
    @ Rohan – Sure Brother.
    let’s be in contact through mails –
    my e-mail id –

    do drop in a mail

  15. Hello Prakash, Is Direct Product and Finitely Generated abelian group in the syllabus for modern algebra. Also could you please upload the answers for atleast pure mathematics questions you attempted in the exam.

    • @ajay: no, they are not in the syllabus. i will be uploading answers soon.

  16. Hello Prakash,
    Do we have to attempt all parts of a question at one place or can they be done separately also?
    e.g. can it be done like Q. 1.a) first, then Q. 5) & then Q. 1.b),1.c) etc.on different pages

    • @sunpreet: all parts of the same question are to be done at same place. but their ordering does not matter. for eg, 1(b),1(c),1(a) is allowed.

  17. hello prakash
    please tell
    1-are sylow’s thms in syllabus?
    2-from unit-5 (fields)of herstien which topics need to be covered.

    3-for linear algebra what to study from herstien, especially from chapter-6 (linear transformations)?
    4-where to prepare the matrices part (second portion of the syllabus) of linear algebra from?

    5- D.(A×B)=A.(B×D)=B.(D×A)
    here D:del operator,
    A and B are vectors,
    is the statement correct?

    • @neelam:
      1-no, sylows theorem are not in the syllabus
      2-unit -5 is also not there.
      3-it is not necessary to study linear algebra from herstein-if you want to study only relevant topics
      4-refer to any book for matrices part-practice previous year papers
      5-statement is not correct- correct is div(A x B) = B.(curl A) – A.(curl B)

  18. hello prakash,
    actually i was asking (5) in view of
    [a b c]= A.(B×C)= C.(A×B)= B.(C×A).
    can the same be applied for [del A B]?
    or is it that since ‘del’ is an operator and the formula is for triple VECTOR product, so cant befitted here?

    • @neelam: you cant do like this. you have to apply the definition of del(it is an operator not vector) to show this.

  19. correction
    [A B C]= A.(B×C)= C.(A×B)= B.(C×A).

  20. automorphism, counting principle, another counting principle- are these needed for exam?

  21. hello prakash,
    so nice of u for the directions.

  22. hello prakash
    please tell
    1-can calculus and real analysis preparation be integrated?
    which should be prepared first then?

    2-is scientific calculator allowed for numerical analysis? if not, how to prepare then?

    • @neelam: yes they can be integrated. calculus should be prepared first. yes scientific calculator is allowed in the mains exam.

  23. hello prakash, in the complex analysis part, are conformal mapping and convergence of power series( including uniform convergence) in the syylabus.

    • @ajay: conformal mapping is not there. but convergence of power series is there.

  24. hello prakash,
    please specify chapters of the prescribed book for differential equations and partial diff equations.

    • @neelam: i have old edition. somebody has asked the same question in “about this blog” section, kindly go through that. else you can specify name of chapters in the book you have, i will tell which one to cover.

  25. many ppl suggest i.n . sneddon for PDE . whats ur opinion on that?

  26. hello prakash
    is double integration is to be done in numerical analysis?

  27. when asked to apply euler’s method whether to go for- euler/ improved form/ modified form? (in numerical analysis)

    • @neelam: i would have applied simple euler form as y(i+1) = y(i) + h*f[x(i),y(i)]

  28. hello prakash
    ‘ve gone thru the section. but plse tell partial diff equations chapter too.

    1>origin of partial diff equation..
    2>liner partial diff eq of order 1
    3>non-liner partial diffrential eq of order 1
    4>homogeneous liner partial diff eq(PDE) with constant coeff
    5>non-homogeneous liner partial diff eq(PDE) with constant coeff
    6>PDE reducible to eq with constant coeff
    7>PDE of ord 2 with variable coeff
    8>classification of PDE….Riemann Method
    9>Monge’s method
    10>transport Eqa..

    and hearty thanks to you for the directions, cos for me its like ,
    ‘m studying- struck with some doubt- come to this blog- get the answer.


    • @neelam: 1,2,4,6 are there. I am not sure about charpits method. Do canonical forms (might be in chapter 7). Some topics were given in Additional topic part like cauchy’s method of characteristics, canonical forms. Cover that also.

  29. Hi Prakash,
    Good Morning…This blog is indirectly guiding so many people..Very good initiative.
    1) Could you please start a new post for interaction of mathes,gs and Electrical engg aspirants?
    2) Could you please tell us(through a new post) what are your coming posts on this blog to help the aspirants?

    Thanks ,

  30. hello prakash
    where to get algorithms, flowcharts of various numerical methods’ from?
    are they given in jain n iynger?

    • @neelam: no, they are not given(although codes are given). i can upload them also.

  31. hello prakash
    which method to adopt for finding out torsion and curvature of a given curve-
    -directly applying formulae,
    -without formulae,in theoritical way?

  32. hello prakash
    please do upload then required algorithms and flowcharts, as soon as possible.

  33. Hi all,
    here i have created a group for the UPSC maths ….those who have taken maths as one of the optional paper ..are welcome for this group….in this group we can discuss with each other our doubts..and also we will follow prakash’s suggestions……

  34. hello prakash
    what to refer for laplace transformations?

    • @neelam: i had some potion of s.chand’s book. i dont know the author’s name.

  35. Hi prakash
    Can u post a similar strategy for physics?
    thanks in advance

    • @gokul: how can i post, if havent studied it?

      • hi prakash
        i am sorry, i thought yours were maths and physics….anyway cheers on your results….have a gr8 career ahead

  36. hello prakash
    inner automorphism, characteristic subgroups, conjugate elements, similar permutations, partition of an integer—these are topics of chap-4(automorphisms and conjugate elements) of bhambri, please tell how much needs to be covered?

    • @neelam: only one problem was asked in 2002( to show that group of order p-square is abelian). i covered these topics so as to be able to solve that. i did not cover partition of an integer, characteristic subgroup.

  37. hello prakash
    inner product, norm of a vector, orthonormal set are they in syllabus?

  38. and dual spaces?

  39. Is Charpit method for solving non-linear equations still in the syllabus? Prior to 2008 it was explicitly mentioned but now it has been revised.Furthermore, though Canonical form wasn’t mentioned in the unrevised syllabus yet they asked a question on it in 2008. So, what needs to be done in this case?
    Also suggest some book for boundary value problems.

    • @nikunj: non-linear equations itself is not there in the syllabus. better to file an rti in upsc to clarify if charpit is there or not.
      canonical for are there in the syllabus(2008 was revised syllabus). there is book by md raisinghania on bvp.

  40. hello prakash
    how to find out normal subgroups of a given group of n order, say 108, tell the sequence of logics involved. it is asked in many qstns in one way or the other.

    • @neelam: it is not in the syllabus. they are to be done by sylow’s theorem, i guess.

  41. sir i hv just started the preparation with math.with which topic sud i start?

  42. 2007- prove that there doesnt exist any simple group of order 48.

    my guess- if we can show any subgroup is there of order 24, we are done, since its index will be 2 hence it’ll be normal. but unable to get it. is there some other way…

    2006- let o(G)=108. show that there exist a normal subgroup of order 27 or 9.

    is it like earlier sylow’s thm were there in syllabus? cos i have no idea bout that.

  43. hello prakash
    please upload the algorithms and flowcharts from numerical analysis section as soon as possible.

  44. hello prakash
    taylor’s thm (all forms of remainder), maclaurin’s infinite series need to be done in Mean value thms part of real analysis?


  45. hi prakash,
    1. i have calculus of schuam series (speigel), would shanti narayan be still req to mop up the relevant CSE portions effectively?
    2. Dynamics by Raisinghania and Statics by lesser known golden publications ( bali )… would krishna series be req? Actually krishna publications is tough get hold off in banglore… please can you do me a favour and let me knw the titles of the books for krishna series?
    3. I have Numerical analysis by S.S.SASTRY and by Vashisht (krishna series), would Jain and Iyenger be still req?
    to my bad luck i found this blog after i had purchased the hitherto mentioned books :(….
    4.Assuming that i do get the books suggested by u, would it be ok to solve problems by multiple books for maths? or should we really be concentrating on a single author??

    • @manjunath: see, i havent gone through the books which you are reading. so it is not possible to suggest whether they are sufficient or not. you can yourself compare whether those books cover entire syllabus and questions are asked from them or not.

  46. I totally understand…thanks for your time, Prakash!

  47. Hello Prakash,

    This is Q 2(a) of Math Paper-II 2009:

    How many proper non-zero ideals does Z12 have? How many does Z12 + Z12 have?

    I think Z12 + Z12 = Z12, so the ideals of the two are same. Is that really so easy?
    Actually the Z12 + Z12 part has been alloted 10 marks in the 15 marks Q. So I have doubt.

    Please suggest..


    • @sunpreet: yes you are correct, perhaps you need to show why Z12+Z12 = Z12.

      • Hello Prakash,
        Sorry for troubling you again.

        This is Q 1 (b) of Math paper-II 2009:

        Determine the no. of homomorphism from Z(15) to Z(10).

        I thought it out like this.
        If f : Z15 to Z10 is homomorphism, then f(Z15) is isomorphic to Z15/(Ker f).
        Now, since o(Ker f) = 1 or 3 or 5 or 15, implies o(f(Z15)) = 1 or 3 or 5 or 15.
        Also f(Z15) is a subgroup of Z(10), o(f(Z15))= 1 or 2 or 5 or 10.
        Therefore o(f(Z15))= 1 or 5
        Now if o(f(Z15))= 1, then f is the zero homomorphism & f(Z15)=0.

        If o(f(Z15)) = 5, then please suggest how to know the no. of homomorphisms? Is there any theorem or result involved or do we have to write all the kernels of order 3, f(Z(15)) of orders 5 & design the mappings & hence know their number.

        Please clear the air.

        Thanks a lot

      • @sunpreet: i think the isomorphism theorem is valid for onto homomorphism only.
        to do this question, you need to know that by knowing f(1) you can identify f(n) = n f(1). All you need to find is f(1). Now o(f(1)) can be 1,2,5,10. Also o(f(1)) divides o(1) which is 15. So o(f(1)) = 1 or 5. Which means f(1) = Z OR Z+2. There are only TWO such homomorphism(verify that these mappings are indeed homomorphism).

    • its Z12(+)Z12, which is direct sum .its elements are of form (a,b) where a,b is in Z12.

  48. Hello sir,

    Please can you let me the topics to be covered under ‘ Boundary value and conditions of M.D.RAISINGHANIA’, u have mentioned tat in ur book list.
    I couldnt really guage which topics of the syllabus of CSE it covers ?

  49. Hi Prakash,
    One more doubt… Regarding Dynamics from Krishna Series, should we be covering only the portions strictly listed in the syllabus???
    1. Central Orbits ( only Central Forces to be covered or we need to cover the portion for elliptic,hyberbolic, parabolic orbits,apses, apsidal also to be covered as they are not mentioned in the portion)
    likewise for the below….
    2.Planetary Motion ( only Kepler laws )
    4. only Conservation of energy, Constrained motion from 4th chapter?
    5. only Motion of Projectiles from 5th chapter?
    and none from chapter 6,7and 8???

    Thanks for your patient replies…the above questionaire is just to clarify if we are on teh right track

    • @manjunath: while covering any book stick to the syllabus and also make sure that you are able to do all previous year questions. central forces means whole chapter including apses and different orbits. just go through exam questions to have an idea.

  50. Hi Prakash,
    Thanks a lot for your prompt replies.

    Regarding the previous question, I think o(f(1))=5 implies f(1)=2 or 4 or 6 or 8, all of which have orders 5 in Z10. So that way there would be 5 homomorphisms(including f(1)=1).

    Also f(Z15) would be the homomorphic image of Z15, so f would be onto homomorphism from Z15 to f(Z15), so isomorphism th. is valid.

    Please correct me if I am wrong.

    Do you know from which book these Abstract Algebra questions of Math paper-II, 2009 were asked. I could locate only Q. 1(a) & 2(b) in Khanna, Bhambhri & none of the other Q. in either of Khanna, Bhambhri or Herstein or Krishna Pub.

    Thanks a lot for your help. Sorry for pestering you again & again.

    • @sunpreet: yes you are correct in both the cases. i think you can find all of them in some form or the other in khanna and bhambhri book.

  51. there was a ques on integration; limits being: [0,2*pi]
    integrand was 1/(a + b*cos(x) + c*sin(x)).
    i tried solving using residue theorem, but didnt get correct result..
    could u plz explain. solving it simply does give the right answer..
    plz do reply

  52. hi prakash,
    well i got the solution using residue theorem.
    Have another doubt, for the optional ques pertaining to numerical analysis: what we need to do is numericals + algo + flow charts of all methods.
    apart from this do we also need to go thru basic programming??

  53. Dear friends, any idea about maths cut off for prelims for 2010? I understand its funny to ask this now, just 2-3 days before result. but any idea?

  54. Hi Prakash,
    Happy Independence Day

    This is Q.3 a) of Math Paper-II 2009.
    Show that Z[X] is a UFD that is not a PID. Is it possible to give example of a PID that is not UFD? (15 marks)

    Should we start from the scratch for proving Z[X] is a UFD or can we directly write that since Z is UFD, therefore Z[X] is UFD. And then cite the theorems to prove that it is PID too.


    • @sunpreet: i dont think there is any need of starting from scratch. you can cite the relevant theorems used.

  55. prakash plz clrify:
    if for linear programming problems we need to compute inverse of a matrix; then solving it manually(finding out cofactors) is desired or can it be done directly using calculator??

  56. **i meant linear algebra and linear programming

  57. Prakash- Newton divided differences , Gauss eliminations ke algorithms karne hain kya?

    @Sunpreet: where are u from? If from chandigarh or nearby we can study together.

  58. sir,
    has anybody other than you cleared this time with maths many people have cleared with mathematics this time

  59. @nitish
    yes i cleared with maths but scored a dismal 148 and 97.
    looking for drastic improvement in paper 2.

    sunpreet yaar you are quite far but we can discuss questions here i guess.

  60. in 2008 there was a ques on complex nos..
    one of the integrand was log(z-6).. when mod(z)=3 was the given contour..
    integral(log(z-6)), do we solve by parts and hence find the poles??

    • @arijit: you need to just check whether the given function is analytic or not.(only z=6 is a point of singularity which does not lie in |z| = 3)

  61. hi sir,
    i am a B-TECH student (NIT-B ,ELECTRICAL,3rd year).i want to take mathematics as my second optional.Altough i had compete in AIEEE but my school education was not so can you please guide me how should i start my preparation .should i first read NCERT for basics or i can start from reference book directly.

    • @akash: see competition is maths is very tough and it is better to go with humanities subject(as most of the successful engg candidates do)

  62. hello prakash please tell
    1-would you be able to upload algorithms and flowcharts of numerical analysis methods, i know from 30 onwards u r going to be occupied. so please tell how to get them?
    2-where did u cover error analysisi part from (for methods u mentioned in numerical anlysis)?

    • @neelam: i have written them on paper, i have given them to someone to upload. i refer jain & iyenger only for error parts also.

  63. Hi,
    I am following “Integratal Equation & Boundary Value Problems” by M.D.raisinghania….for the boundry value problem…But i couldnt able to find the relevent chapters in this book..could u plz tell me chapter names/nos that we need to read for the UPSC syllabus.

  64. Hi
    I did my b tech in electrical eng. from IIT Kgp…and luckly i passed UPSC prelims for this year…but my problem is i dont have any preparation for the mains…I am still in the process of deciding optional papers.One of the optional paper i have decided as Maths ( this is decided) and 2nd is still deciding..actually i have only 2 months and i was planing for Public Admin/Pali as the 2nd optinal paper…but everyone saying in 2 months time frame u wont b able to do much in these i dont have any option except choosing EE as 2nd optinal My b tech i have completd arnd 40% of syllabus…but i have to revise all the topics again…do u suggest i should go for Electrical Engineering for this next attempt i will choose some other paper based on my performence in Electrical.
    I asked this question here because i asked same thing earlier in other blog but u didnt reply till now….

  65. hello prakash
    thank u so much for the valuable guidance, ur blog is really a great help for those having mathematics n ee as optional, the way u guided us all thru this is commendable.
    hope u’ll be able to answer our queries further too, whenver get time.


  66. does it make a differnce to cover error analysis from jain n iynger or krishna series?

  67. hi prakash hope u r doing well i’ve two urgent doubts:
    1. log(z-6) has singularities in the interval (0,6); so [0,3] lies within the mod(z)=3.. so clarify..
    2. the solved algorithm that u’ve put up, have doubt regarding that:
    error u took as abs(x-x1); whereas i feel there have be two cases i.e.
    error must be abs(x-x0) and abs(x-x1) depending upon whether x0 is replaced or x1 by x..
    it shouldnt be abs(x-x1) in all cases, error is abs(new-old)…
    plz clarify as soon as possible..i’m stuck up..thanks a lot..

  68. also if say algo for newton-raphson method is asked do we have to elaborate convergence properties??

  69. Hello Sir,

    one of my optional is mathematics; could you tell me the maximum time in which one can finish the whole syllabus for mains, i am an average student;just to ensure i dont waste a lot of time. Can you please tell the marks weightage of each topic in paper 1 and paper 2.

    Thank you,

    • @angela: how can i comment on your preparation time? you can look at the previous year papers to calculate the weightage.

  70. in 2008 there was a ques on complex nos..
    one of the integrand was log(z-6).. when mod(z)=3 was the given contour..
    integral(log(z-6)), do we solve by parts and hence find the poles??
    log(z-6) has singularities in the interval (0,6); and [0,3] lies within the mod(z)=3.. cud u pls clarify..

  71. the krishna series book on STATICS doesnot cover friction ,work and potential energy.where to cover these topics from?

  72. last yr maths mains 2009..
    1) ques on temperature as fn of x,y,z paper1… i solved using partial differentiation… any other mthd??
    2) ques on iteration Q5 where alpha, beta are given as roots… wat do we assume x0 as?? i assumed as (a+b)/2

    • 1) this question is to be done using lagarange method of multipliers(i hope you are referring to that)
      2)is any assumption required?

  73. hello prakash, howz the training going on…
    please tell, is revised simplex method (chapter-5, krishna series) there in complex analysis.


  74. please tell chapters to be covered in linear programming among-
    1-mathematical preliminaries
    2-convex set n their properties
    3-simplex method
    4-resolution of degeneracy
    5-revised simplex method
    6-sesitivity analysis
    7-parametric lin prog
    8-integer prog

  75. Dear Sir,
    Can u plz specify the chapters of the A.R. VASISHTHA’S book of complex analysis which are to be done.

  76. hello prakash
    please tell, do we need to cover theorems in complex analysis.


  77. is there any other book for fluid dynamics.the book by raisinghania has not properly explained some chapters like equations of motion for inviscid fluid,images part in sources and sinks.

    also do we have to read vortex motion,navier-stokes eqn in detail,because no questions have been asked from these parts.

  78. Hello Sir,

    Where can one find solutions to the mains question papers for prev years ?

    I have doubts whether what im solving is correct or not.

    Like :
    In Mains 2008 – a qn from real analysis –

    T = {1/n,n belongs to N}U{1+3/2n,n belongs to N}U{6-1/3n,n belongs to N}

    Find derived set T’ of T.
    Find Supremum of T
    Find Greatest number of T

    My soln –
    Derived set : {0,1,6}
    Supremum : 6
    Greatest number : Does not exist.

    Please let me know whether i am correct.
    @others : do chip in your comments also

  79. hello sir.
    i need ur advise.i am preparing for cse and i want to opt maths as one of my optionals but sir
    everybody says mathematics is not a good choice for cse.i am in a big confusion.what should i do? material and guidance in maths are not easily available and solution of previous
    year questions papers are not available.
    sir plz guide me and tell where can i get solutions to the main question papers.
    plz plz reply.

  80. Hi,

    Just saw your blog. I am giving CSE 2014. So was thinking of taking Mathematics as my optional subject. I am studying Electrical Engineering from IIT Delhi, therefore there are many topics in the syllabus which i am familiar with. I wanted to ask you whether questions in CSE are as difficult as they are in JEE or more than that. Basically i want to know about the level of paper; how indepth my preparation should be?

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