## UPSC MAINS MATHEMATICS

**1.Our Toppers**

**2.ELIGIBILITY CRITERIA FOR IAS**

**Educational Qualification**

**NOTE I :**Candidates who have appeared at an examination the passing of which would render them educationally qualified for the Commission’s examination but have not been informed of the results as also the candidates who intend to appear at such a qualifying examination will also be eligible for admission to the Preliminary Examination. All candidates who are declared qualified by the Commission for taking the Civil Services (Main) Examination will be required to produce proof of passing the requisite examination with their application for the Main Examination failing which such candidates will not be admitted to the Main Examination. The applications for the Main Examination will be called sometime in the month of August/September.

**NOTE II :**In exceptional cases the Union Public Service Commission may treat a candidate who has not any of the foregoing qualifications as a qualified candidate provided that he/she has passed examination conducted by the other Institutions, the standard of which in the opinion of the Commission justifies his/her admission to the examination.

**NOTE III :**Candidates possessing professional and technical qualifications which are recognised by Government as equivalent to professional and technical degree would also be eligible for admission to the examination.

**NOTE IV :**Candidates who have passed the final professional M.B.B.S. or any other Medical Examination but have not completed their internship by the time of submission of their applications for the Civil Services (Main) Examination, will be provisionally admitted to the Examination provided they submit along with their application a copy of certificate from the concerned authority of the University/ Institution that they had passed the requisite final professional medical examination. In such cases, the candidates will be required to produce at the time of their interview original Degree or a certificate from the concerned competent authority of the University/Institution that they had completed all requirements (including completion of internship) for the award of the Degree.

**NATIONALITY:**

**AGE LIMIT:**

**NOTE I :**Candidates belonging to the Scheduled Castes and the Scheduled Tribes and the Other Backward Classes who are also covered under any other clauses of para 3(ii)(b) above, viz. those coming under the category of Ex-servicemen, persons domiciled in the State of J & K, blind, deaf-mute and orthopaedically handicapped etc. will be eligible for grant of cumulative age-relaxation under both the categories.

**NOTE II :**The term ex-servicemen will apply to the persons who are defined as ex-servicemen in the Ex-servicemen (Reemployment in Civil Services and Posts) Rules, 1979, as amended from time to time.

**NOTE III :**The age concession under para 3(ii)(b)(v) and (vi) will not be admissible to Ex-Servicemen and Commissioned Officers including ECOs/SSCOs who are released on own request.

**NOTE IV :**Notwithstanding the provision of age-relaxation under para 3 (ii) (b) (vii) above, a physically disabled candidate will be considered to be eligible for appointment only if he/she (after such physical examination as the Government or appointing authority, as the case may be, may prescribe) is found to satisfy the requirements of physical and medical standards for the concerned Services/posts to be allocated to the physically disabled candidates by the Government.

**SAVE AS PROVIDED ABOVE THE AGE LIMITS PRESCRIBED CAN IN NO CASE BE RELAXED.**

**NOTE 1 :**Candidates should note that only the Date of Birth as recorded in the Matriculation/Secondary Examination Certificate or an equivalent certificate as on the date of submission of applications will be accepted by the Commission and no subsequent request for its change will be considered or granted.

**NOTE 2 :**Candidates should also note that once a Date of Birth has been claimed by them and entered in the records of the Commission for the purpose of admission to an examination, no change will be allowed subsequently (or at any other examination of the Commission) on any grounds whatsoever.

**NOTE 3 :**The candidate should exercise due care while entering their date of birth in column 3 of the Application Form for the Preliminary Examination. If on verification at any subsequent stage, any variation is found in their date of birth from the one entered in their matriculation or equivalent Examination certificate, disciplinary action will be taken against them by the Commission under the Rules.

**NUMBER OF ATTEMPTS :**

**NOTE:**

**(IV)RESTRICTIONS ON APPLYING FOR THE EXAMINATION :**

**(VI) PHYSICAL STANDARDS :**

## REGULAR CLASSROOM PROGRAMS

**REGULAR CLASSROOM PROGRAMS**

These are very comprehensive programmes which run over the span of 4-6 months depending on the course. Under these programmes the classes are conducted 4-6 hrs per day for 5 to 6 days in a week. The class schedules are designed in a manner that every student in the class gets equal opportunity to learn and apply.

As the understanding level of all the students in a class may not be uniform, we try to distinguish weaker so called average students in the class and work over them. For such students we have developed **Basic Building Measures** (BBM) which has two components

**1. BBM- Tests:** After 2-3 lectures on any topic the academy offers a test to all the students. This test (Called BBM Test) contains very basic and fundamental questions about that topic. The performances over this test are analyzed comprehensively and on the basis of their performance, those students are identified who could not cross minimum thresh hold and requires extra care.

**2. BBM Classes: **The students Identified by BBM tests are clubbed into various groups and dedicated faculty are assigned to each group. These groups are given extra classes (BBM Classes). In these classes, this faculty helps the students clear their doubts and concept so that they too can equally participate in the regular classes along with the so called average plus students.

The RCPs of Rising Star Academy are complete in its nature. In the span of almost half a year we try to bridge the gap between your degree and learning so that you can appear in any competitive exam of your eligibility and interest.

**IMPORTANT DATES**

Batches |
UPSC Mains |

Registration Open | 01 June 2017 |

Open Seminar/Scholarship Test | 23-July-2017 |

Batch Starts | 23-July-2017 |

**FEE STRUCTURE**

Course |
Fee |

UPSC |
40,000/- |

## IAS Mains Mathematics Syllabus

**PAPER-I**

**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.

**Calculus:**Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange's method of multipliers, Jacobian.

**Analytic Geometry:**Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

**Ordinary Differential Equations:**Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut's equation, singular solution. Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution.

**Dynamics & Statics:**Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; Work and energy, conservation of energy; Kepler's laws, orbits under central forces.

**Vector Analysis:**Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations. Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.

**PAPER-II**

**(1) Algebra:**Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem.

**Real Analysis:**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.

**Complex 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.

**Linear Programming:**Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality.

**Partial differential equations:**Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear 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.

**Numerical Analysis and Computer programming:**Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and 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.

**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.