Ramanasri. IAS/IFoS. Institute

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1 [Type text] Ramanasri IAS/IFoS Institute Mathematics Optional Brochure Reputed Institute for IAS/IFoS Exams Page 1

2 Syllabus for IAS Mathematics Optional PAPER I (1) Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; Row and column reduction, Echelon form, congruence s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigen values and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, Skew- Hermitian, orthogonal and unitary matrices and their eigen values. (2) Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, mean value theorem, Taylor s theorem with remainders, indeterminate forms, maxima Reputed Institute for IAS/IFoS Exams Page 2

3 and minima, asymptotes; Curve tracing; equations); Determination of complete Functions of two or three variables: limits, solution when one solution is known using continuity, partial derivatives, maxima and method of variation of parameters. Laplace minima, Lagrange s method of multipliers, and Inverse Laplace transforms and their Jacobian. Riemann s definition of definite properties; Laplace transforms of integrals; Indefinite integrals; Infinite and elementary functions. Application to initial improper integrals; Double and triple value problems for 2nd order linear integrals (evaluation techniques only); equations with constant coefficients. Areas, surface and volumes. (5) Dynamics & Statics: (3) Analytic Geometry: Rectilinear motion, simple harmonic Cartesian and polar coordinates in three motion, motion in a plane, projectiles; dimensions, second degree equations in constrained motion; Work and energy, three variables, reduction to canonical conservation of energy; Kepler s laws, orbits forms, straight lines, shortest distance under central forces. Equilibrium of a between two skew lines; Plane, sphere, system of particles; Work and potential cone, cylinder, paraboloid, ellipsoid, energy, friction; common catenary; hyperboloid of one and two sheets and their Principle of virtual work; Stability of properties. equilibrium, equilibrium of forces in three dimensions. (4) Ordinary Differential Equations: (6) Vector Analysis: Formulation of differential equations; Equations of first order and first degree, Scalar and vector fields, differentiation of integrating factor; Orthogonal trajectory; vector field of a scalar variable; Gradient, Equations of first order but not of first divergence and curl in Cartesian and degree, Clairaut s equation, singular cylindrical coordinates; Higher order solution. Second and higher order linear derivatives; Vector identities and vector equations with constant coefficients, equations. Application to geometry: Curves complementary function, particular integral in space, Curvature and torsion; Serretand general solution. Second order linear Frenet s formulae. Gauss and Stokes equations with variable coefficients, Euler- theorems, Green s identities. Cauchy equation (Homogeneous linear Reputed Institute for IAS/IFoS Exams Page 3

4 PAPER II (1) Modern Algebra: Groups, subgroups, cyclic groups, cosets, Lagrange s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley s theorem. Rings, sub rings and ideals, homeomorphisms of rings; Integral domains, principal Ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields. (2) Real Analysis: Analytic functions, Cauchy-Riemann equations, Cauchy s theorem, Cauchy s integral formula, power series representation of an analytic function, Taylor s series; Singularities; Laurent s series; Cauchy s residue theorem; Contour integration. (4) Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality. Transportation and assignment problems. Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series. Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals; Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima. (3) Complex Analysis: (5) Partial differential equations: Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasi linear partial differential equations of the first order, Cauchy s method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions. (6) Numerical Analysis & Computer Programming: Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Reputed Institute for IAS/IFoS Exams Page 4

5 Newton-Raphson methods; solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel (iterative) methods. Newton s (forward and backward) interpolation, Lagrange s interpolation. Numerical integration: Trapezoidal rule, Simpson s rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods. Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers. Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms. Representation of unsigned integers, signed integers and reals, double precision reals and long integers. Algorithms and flow charts for solving numerical analysis problems. (7) Mechanics and Fluid Dynamics: Generalized coordinates; D Alembert s principle and Lagrange s equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions. Equation of continuity; Euler s equation of motion for in viscid flow; Stream-lines, path of a particle; Potential flow; Twodimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier- Stokes Equation for a viscous fluid. IAS MATHS OPTIIONAL ANALYSIS Note: LA CAL AG ODE VA D&S MA RA CA LP PDE NA&CP M&FD Linear Algebra Calculus Analytical Geometry Ordinary Differential Equations Vector Analysis Dynamics & Statics Modern Algebra Real Analysis Complex Analysis Linear Programming Partial Differential Equations Numerical Analysis & Computer Programming Mechanics & Fluid Dynamics IAS-2013 Maths question & Topic wise Analysis Paper-I Section A Q. No Sub Q. No Topic Marks 1 1.a LA 10 1.b LA 10 1.c CAL 10 1.d AG 10 Reputed Institute for IAS/IFoS Exams Page 5

6 1.e AG 10 7.c D&S a (i) LA 10 2.a (ii) LA 8 2.b (i) LA 8 2.b (ii) LA 8 2.c (i) LA 8 2.c (ii) LA a CAL 20 3.b CAL 15 3.c CAL a AG 15 4.b AG 15 4.c AG 20 Section B 5 5.a ODE 10 5.b ODE 10 5.c D&S 10 5.d D&S 10 5.e VA a ODE 10 6.b ODE 10 6.c ODE 15 6.d ODE a D&S 20 7.b D&S a VA 10 8.b VA 10 8.c VA 15 8.d VA 15 Paper-II Section A Q. No Sub Q. No Topic Marks 1 1.a MA 10 1.b MA 10 1.c RA 10 1.d CA 10 1.e LP a MA 10 2.b MA 13 2.c RA 13 2.d RA a MA 15 3.b MA 15 3.c RA 10 3.d RA a LP 15 4.b CA 15 4.c LP 20 Reputed Institute for IAS/IFoS Exams Page 6

7 Section B 1.e AG a PDE 10 5.b PDE 10 5.c NA&CP 10 5.d M&FD 10 5.e M&FD a PDE 15 6.b PDE 15 6.c PDE a NA&CP 20 7.b NA&CP 15 7.c NA&CP a M&FD 15 8.b M&FD 15 8.c M&FD 20 IAS-2014 Maths question & Topic wise Analysis Paper-I Section A Q. No Sub Q. No Topic Marks 1 1.a LA 10 1.b LA 10 1.c CAL 10 1.d CAL a LA 15 2.b LA 10 2.c LA 10 2.d CAL a CAL 15 3.b CAL 20 3.c(i) LA 8 3.c (ii) LA a(i) AG 10 4.a(ii) AG 10 4.b AG 15 4.c AG 15 Section B 5 5.a ODE 10 5.b VA 10 5.c D&S 10 5.d D&S 10 5.e VA a ODE 10 6.b ODE 20 6.c VA a ODE 15 7.b D&S 15 7.c D&S 20 Reputed Institute for IAS/IFoS Exams Page 7

8 8 8.a ODE 15 5.d NA&CP 10 8.b D&S 15 8.c ODE 20 Paper-II Section A Q. No Sub Q. No Topic Marks 1 1.a MA 10 1.b RA 10 1.c CA 10 1.d CA 10 1.e LP a MA 15 2.b RA 15 2.c LP a MA 15 3.b RA 15 3.c RA a MA 15 4.b RA 15 4.c LP 20 Section B 5 5.a PDE 10 5.b NA&CP 10 5.c NA&CP 10 5.e M&FD a PDE 15 6.b NA&CP 15 6.c NA&CP a M&FD 15 7.b NA&CP 15 7.c M&FD a PDE 15 8.b NA&CP 15 8.c M&FD 20 IAS-2015 Maths question & Topic wise Analysis Paper-I Section A Q. No Sub Q. No Topic Marks 1 1.a LA 10 1.b LA 10 1.c CAL 10 1.d CAL 10 1.e AG a LA 12 Reputed Institute for IAS/IFoS Exams Page 8

9 2.b CAL 13 7.b D&S 13 2.c LA 12 2.d AG a LA 12 3.b CAL 13 3.c AG 13 3.d CAL a CAL 13 4.b LA 12 4.c AG 13 4.d CAL 12 Section B 5 5.a ODE 10 5.b ODE 10 5.c D&S 10 5.d D&S 10 5.e VA a ODE 12 6.b D&S 13 6.c ODE 12 6.d D&S a ODE 12 7.c VA 12 7.d ODE a D&S 12 8.b D&S 13 8.c VA 12 8.d ODE 13 Paper-II Section A Q. No Sub Q. No Topic Marks 1 1.a MA 10 1.b MA 10 1.c RA 10 1.d CA 10 1.e LP a MA 15 2.b RA 15 2.c CA a CA 15 3.b RA 15 3.c LP a MA 15 Reputed Institute for IAS/IFoS Exams Page 9

10 4.b RA 15 Section A 4.c LP 20 Section B 5 5.a PDE 10 5.b PDE 10 5.c NA&CP 10 5.d M&FD 10 5.e M&FD a PDE 15 6.b M&FD 15 6.c NA&CP a PDE 15 7.b NA&CP 15 7.c M&FD a PDE 15 8.b NA&CP 15 8.c M&FD 20 Q. No Sub Q. No Topic Marks 1 1.a LA 10 (4+6) 1.b LA 10 (7+3) 1.c CAL 10 1.d AG 10 1.e AG a LA 16 (10+6) 2.b LA 16 (8+8) 2.c LA a CAL 20 3.b CAL 15 3.c CAL a AG 10 4.b AG 10 4.c CAL 15 4.d AG 15 Section B IAS-2016 Maths question & Topic wise Analysis Paper-I 5 5.a ODE 10 5.b VA 10 5.c ODE 10 5.d ODE 10 Reputed Institute for IAS/IFoS Exams Page 10

11 5.e D&S 10 2.a RA a ODE 10 6.b ODE 15 6.c ODE 15 6.d ODE a D&S 15 7.b D&S 15 7.c D&S a VA 10 8.b VA 10 8.c D&S 15 8.d VA 15 2.b MA 15 2.c LPP a MA 20 3.b RA 15 3.c CA a MA 15 4.b RA 15 4.c CA 20 Section B 5 5.a PDE 10 5.b M&FD 10 5.c M&FD 10 Paper-II Section A Q. No Sub Q. No Topic Marks 1 1.a MA 10 1.b RA 10 1.c RA 10 1.d CA 10 1.e LP d NA&CP 10 5.e PDE a PDE 15 6.b M&FD 15 6.c NA&CP a PDE 15 7.b M&FD 20 7.c NA&CP 15 8 Reputed Institute for IAS/IFoS Exams Page 11

12 8.a PDE b M&FD 15 8.c NA&CP 15 IAS-2017 Maths question 4.a AG 15 4.b LA 15 4.c CAL 10 4.d CAL 10 & Topic wise Analysis Paper-I Section A Q. No Sub Topic Marks 1 1.a LA 10 1.b LA 10 1.c CAL 10 1.d AG 10 1.e AG a CAL 15 2.b AG 15 2.c AG 10 2.d LA a LA 15 3.b LA 10 3.c CAL 15 3.d AG 10 Section B 5 5.a ODE 10 5.b D&S 10 5.c D&S 10 5.d VA 10 5.e VA a(i) ODE 8 6.a(ii) ODE 8 6.b (i) ODE 10 6.b (ii) ODE 7 6.c D&S a VA 16 7.b (i) ODE 9 7.b (ii) ODE 8 7.c D&S 17 8 Reputed Institute for IAS/IFoS Exams Page 12

13 8.a D&S b ODE 17 8.c (i) VA 9 8.c(ii) VA 8 4.a CA 15 4.b LP 15 4.c RA 20 IAS-2017 Maths question & Topic wise Analysis Section B Paper-II Section A Q. No Sub Q. No Topic Marks 1 1.a RA 10 1.b MA 10 1.c RA 10 1.d CA 10 1.e LP a RA 15 2.b CA 15 2.c MA a MA 15 3.b CA 15 3.c LP a PDE 10 5.b NA&CP 10 5.c NA&CP 10 5.d PDE 10 5.e M&FD 10 6.a PDE 15 6.b NA&CP 15 6.c M&FD 20 7.a PDE 15 7.b NA&CP 20 7.c M&FD 15 8.a PDE 20 8.b NA&CP 15 8.c M&FD 15 Reputed Institute for IAS/IFoS Exams Page 13

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15 IAS Mathematics Optional Books List PAPER I Books 1. Linear Algebra 1. Linear Algebra A.R. Vasistha (Krishna Series) 2. Matrices A. R. Vasistha (Krishna Series) 2. Calculus 1. Differential Calculus A.R. Vasistha, Dr. S.K Sharma (Krishna Series) 2. Advanced Integral Calculus Dr. D.C. Agarwal ( Krishna Series) 3. Analytic Geometry 1. 3D Geometry P.N. Chatterjee 2. Solid Geometry -- Shanti Narayan (S. Chand) 4. Ordinary Differential Equations Ordinary and Partial Differential Equations M.D. Raisinghania (S. Chand) 5. Dynamics & Statics Krishna Series 1. Statics Krishna Series 2. Dynamics Krishna Series 6. Vector Analysis 1. Vector Calculus A.R. Vasistha& J.N. Sharma 2. Vector Calculus Shanti Narayana 3. Curves in Spaces P.N. Chatterjee (Class Handout) Reputed Institute for IAS/IFoS Exams Page 15

16 PAPER II Books 1. Algebra 1. Modern Algebra Vasistha (Krishna Series) 2. A course in Abstract Algebra Khanna and Bhambri 3. Modern Algebra I. N. Herstein (John Wiley Publications) 4. Modern Algebra A Galliean 2. Real Analysis 1. Elements of Real Analysis - M.D. Raisinghania (S. Chand Series) 3. Complex Analysis 1. Functions of a Complex Variable J.N. Sharma (Krishna Series) 2. Complex Analysis Schaum's Series 4. Linear Programming 1. Operations Research KantiSwarup, P. K. Gupta, ManMohan (S. Chand) 2. Operations Research S.D.Sharma 5. Partial Differential Equations 1. M.D. Raisinghania ( Refer Paper I Same book) 6. Numerical Analysis & Computer Programming 1. A. R. Vasistha ( Krishna Series) 2. Introductory Methods of Numerical Analysis Sastry 3. Numerical Methods V. RajaRaman 4. Computer Programming Class Handout 7. Mechanics&Fluid Dynamics 1. Fluid Dynamics M.D. Raisinghania 2. Mechanics S. Chand Publications Reputed Institute for IAS/IFoS Exams Page 16

17 UNION PUBLIC SERVICE COMMISSION IAS-2018 & IFoS-2018 EXAMINATIONS INFORMATION S. No. Name of Examination Date of Notification Last Date for receipt of Applications Date of commencement of Exam Duration of Exam Civil Services (Preliminary) Examination, 2018 Indian Forest Service (Preliminary) Examination, 2018 through CS(P) Examination 2018 Civil Services (Main) Examination, 2018 Indian Forest Service (Main) Examination, (SUNDAY) 1 DAY (MONDAY) 5 DAYS (SUNDAY) 10 DAYS Regular Batches (Tuesday to Sunday) Batch No I II III IV Timings 8:00 AM to 10:30 AM 11:00 AM to 1:30 PM 2:30 PM to 5:00 PM 5:30 PM to 8:00 PM Note: Classes will be Tuesday to Sunday and Monday will be Chapter/unit wise Tests for whatever we have covered during the last 6 days (Tuesday to Sunday). Why because revision & presentation of answers is very important for what you have understood during the daily classes. Reputed Institute for IAS/IFoS Exams Page 17

18 Weekend Batches Saturday & Sunday only Batch No I II Timings 8:00 AM to 1:30 PM (Including 30min Break) 2:30 PM to 5:30 PM (Including 30min Break) Note: Classes will be only on Saturday & Sunday and Every 6 PM will be Chapter/unit wise Tests for whatever we have covered during the last 2 days (Saturday & Sunday). Why because revision & presentation of answers is very important for what you have understood during the weekend classes. The following Special and salient features makes us why we are different from the others in the market. Teaching based organization Permanent, full-time, highly qualified and dedicated faculty Cooperative, caring administrative staff Appreciable result ratio of successful student to enrolled students Scientifically designed, clear and precise study material Ample questions capturing all flavors and difficulty levels Formula booklet for quick revision Lots of home assignments for practice Complete academic year planning at start of session Regular Tests (weekly / chapter-wise / phase / complete length / E-Test series) Thorough discussion on each test in successive lecture Fixed timetable Individual doubt clearance sessions Comfortable speed of syllabus coverage with enough buffers Prime focus on concept building & Problem solving techniques Complete information on various competitive examinations Motivational counseling sessions Reasonable fees. Finishing the Syllabus in time 20 weeks Classes (5 months Classes) Small Batches i.e., Batch Size 35 Individual attention to each and every aspirant Reputed Institute for IAS/IFoS Exams Page 18

19 Limited seats Hurry up!!! Fee Structure details Batch Fees What you will get benefits from us REGULAR WEEKEND Rs.48,000 Rs.48,000 CSAT PAPER-II Rs. 12,000 Maths Optional Test Series Rs.13,500 CSAT PAPER-I Test Series Rs CSAT PAPER-II Test Series Rs a) 6 Month Classes b) Study Materials c) Test series d) Personal & Individual Guidance, Strategy e) Previous year Questions Solutions f) Guaranteed 300+ Marks in your Mains Maths Optional a) 6 Month Classes b) Study Materials c) Test series d) Personal & Individual Guidance, Strategy e) Previous year Questions Solution f) Guaranteed 300+ Marks in your Mains Maths Optional a) 2 Months Classes b) Study Materials c) Test series d) Personal & Individual Guidance, Strategy e) Previous year Questions Solutions f) Guaranteed 100+ Marks in your Prelims CSAT PAPER- II a) Test Series with Solutions b) Paper correction on in time c) Personal & Individual Guidance, Strategy d) Guaranteed 300+ Marks in your Mains Maths Optional a) Test Series Answers sheet & Explanations b) Paper correction on in time c) Personal & Individual Guidance, Strategy d) Guaranteed 120+ Marks in your Mains Maths Optional a) Test Series Solutions b) Paper correction on in time c) Personal & Individual Guidance, Strategy d) Guaranteed 66+ Marks in your Mains Maths Optional Reputed Institute for IAS/IFoS Exams Page 19

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RAJASTHAN PUBLIC SERVICE COMMISSION, AJMER

RAJASTHAN PUBLIC SERVICE COMMISSION, AJMER SYLLABUS FOR EXAMINATION FOR THE POST OF LECTURER - MATHEMATICS, (SCHOOL EDUCATION) Paper - II Part I (Senior Secondary Standard) 1 Sets, Relations and Functions