Join  our Virtual Interactive Classroom NOW! Try out our Sample Test  Watch our Sample Video Attend our  Orientation Programme Call: +91 9000018804 Follow us on Face Book Connect with Linked-in Follow us on twitter
Login  
The Official Website Online IAS Academy - The Official Website
Home | | | | | | | | Contact Us
DISCUSSION FORUM
 
 
 

MATHEMATICS (IAS Main Optional) CIVIL SERVICES

Course Highlights


Duration:

60 hrs of Online Test Solution Classes

Faculty:
  • Mr. V.Venkanna and Mr Satyanarayana
  • Course Fee: Rs. 11,000 Rs
    Course Features:
  • 20 Tests Total
  • Test duration               : 3 hrs
  • Max Marks                   : 250 Marks
  • Multi Topic Tests          : 5 Tests
  • Paper-I Mock Tests       : 5 Tests
  • Paper-II Mock Tests      : 5 Tests
  • Grand Tests Covering Full Syllabus : 5 Tests
  • Join:
    Contact For any further queries regarding the course, contact
    Phone: +91 9000018804
    Email: info@indiancivils.com
       
     
    Course Details

     

     
     
    Faculty

    The Mathematics course is handled by Mr. V. Vemana.

    Mathematics Optional Syllabus


    The following is the syllabus for Mathematics - Main Examination - Paper I and Paper II.

    MATHEMATICS SYLLABUS for PAPER - 1

    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; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues.
    2. Calculus:
      • Real numbers, functions of a real variable, limits, continuity, differentiability, meanvalue 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.
      • Riemann's definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.
    3. 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.
    4. 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.
      • Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters.
      • Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.
    5. 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.
      • Equilibrium of a system of particles; Work and potential energy, friction; common catenary;
      • Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions.
    6. 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.

    MATHEMATICS SYLLABUS for PAPER 2

    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.
      • Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields.
    2. 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.
      • 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:
      • 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.
    5. 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.
    6. 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.
      • 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 inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.

    Online Classroom Sessions


    • All the Test solutions will be solved in an interactive online Video Classroom sessions every Sunday after the test from 7:00PM to 10:00PM. Total Tests for a duration of 60 hours.

    Mathematics Optional Test Series TimeTable


    SNO Test ID DATE Test Time Live Class Time Test Details Test Center
    Multi Topic Tests
    1 Test-1 28/08/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Linear Algebra,Algebra,Solid Geometry Delhi,Hyderabad,Jaipor,Kolkata and Online
    2 Test-2 04/09/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Calculus,ODE and Vector Analysis Delhi,Hyderabad,Jaipor,Kolkata and Online
    3 Test-3 11/09/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Dynamics and Statics,Real Analysis,Complex Analysis Delhi,Hyderabad,Jaipor,Kolkata and Online
    4 Test-4 18/09/2016 10:00AM to 1:00PM 7:00PM to 10:00PM Linear Programming,Numerical analysis,Programming Delhi,Hyderabad,Jaipor,Kolkata and Online
    5 Test-5 18/09/2016 2:00PM to 5:00PM 7:00PM to 10:00PM PDE, Fluid Dynics and Mechanics Delhi,Hyderabad,Jaipor,Kolkata and Online
    Paperwise Tests
    6 Test-6 25/09/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - I Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    7 Test-7 02/10/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - II Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    8 Test-8 09/10/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - I Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    9 Test-9 16/10/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - II Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    10 Test-10 23/10/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - I Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    11 Test-11 30/10/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - II Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    12 Test-12 30/10/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - I Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    13 Test-13 06/11/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - II Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    14 Test-14 06/11/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - I Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    15 Test-15 13/11/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Paper - II Syllabus Delhi,Hyderabad,Jaipor,Kolkata and Online
    Complete Syllabus Tests
    16 Test-11 13/11/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Syllabus of Paper - I && II Delhi,Hyderabad,Jaipor,Kolkata and Online
    17 Test-12 20/11/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Syllabus of Paper - I && II Delhi,Hyderabad,Jaipor,Kolkata and Online
    18 Test-13 20/11/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Syllabus of Paper - I && II Delhi,Hyderabad,Jaipor,Kolkata and Online
    19 Test-14 27/11/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Syllabus of Paper - I && II Delhi,Hyderabad,Jaipor,Kolkata and Online
    20 Test-15 27/11/2016 2:00PM to 5:00PM 7:00PM to 10:00PM Complete Syllabus of Paper - I && II Delhi,Hyderabad,Jaipor,Kolkata and Online

    Popularity of Mathematics as an optional subject


    The following are the suggested books / references that the students can consult while preparing for Mathematics - Main Examination - Paper I and Paper II.

    • Mathematics is best fit as an optional for students who are passionate about the subject.
    • Since this is logical subject, scoring is quite straightforward and rote-learning is not required.
    • Engineering Mathematics Students can score very well in this subject as only standard models of sums are asked in the question papers.

    Suggestions for Preparation of Mathematics Optional Subject


    The following are simple preparation tips to score well in the Mathematics - Main Examination - Paper I and Paper II.

    • Prepare selective topics and be thorough in these problems.
    • Linear Algebra, Linear Programming, Vector Calculus, Numerical Methods, Real and Complex Analysis, Ordinary Differential Equations and Partial Differential Equations are some examples of topics thay are relatively easy for most people.
    • Solve problems from previous years questions papers as the same models of the sums normally repeat every year.
    • Solve each problem highlighting each step while arriving at the solution. Do not skip any step thinking it is trivial.
    • Concentrated on the solved examples from B S Grewal Reference book suggested for the UPSC exam.
    • Monitor your speed during practice and try to improve it. Lack of time is the main challenge in this paper.

    Joining the course


    Regular Student

    • Students can register as a regular user for any of the courses offered by Indiancivils by making the full payment for the course online.
    • Registered students would receive intimation about the scheduled virtual classroom sessions on their registered mobile and email ids. Further, an automated reminder would be sent to the registered mobile number 10 minutes before the online session.

    Feedbacks


     

     
    Discussion Forum
       ©2012   |   Disclaimer             Home   |   Email   |   Sitemap   |   Contact Us