Mathematics K.Venkanna IAS and IFOS Notes IMS Delhi downloaded version

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This is booklet total 18 pdf , but pdf no. of 18 is buller and print is not proper.

 

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Mathematics K.Venkanna IAS and IFOS Notes IMS Delhi for IAS exam preparation clues are given below…

Linear Algebra:

  • Vector spaces over R and C,
  • linear dependence and independence,
  • congruence’s and similarity
  • Rank of a matrix;
  • Inverse of a matrix;
  • Solution of system of linear equations;

Calculus:

  • limits, continuity,
  • Curve tracing;
  • Functions of two or three variable
  • limits,
  • partial derivatives
  • Indefinite integrals;

Analytic Geometry:

  • Cartesian and polar coordinates in three dimensions,
  • Second-degree equations in three variables, reduction to canonical forms, straight lines,
  • reduction to canonical forms, straight lines,
  • straight lines,

Ordinary Differential Equations:

  • Formulation of differential equations;
  • Equations of first order and first degree,
  • integrating factor; Orthogonal trajectory;
  • Euler-Cauchy equation;

Dynamics & Statics:

  • Rectilinear motion,
  • simple harmonic motion,
  • friction; common catenary;
  • Principle of virtual work;
  • Stability of equilibrium,

Vector Analysis:

  • Scalar and vector fields,
  • Gradient, Curvature and torsion;
  • Serret-Frenet’s formulae.
  • Gauss and Stokes’ theorems,
  • Green’s identities.

Exam Paper-II

(1) Algebra:

  • Groups, subgroups,
  • cyclic groups,
  • a homomorphism of groups,
  • basic isomorphism theorems.

Real Analysis:

  • Sequences, limit of a sequence,
  • improper integrals;
  • Fundamental theorems of integral calculus.
  • Uniform convergence,

Complex Analysis:

  • Analytic functions,
  • Cauchy-Riemann equations,
  • Cauchy’s theorem, Cauchy’s integral formula,
  • Taylor’s series; Singularities;

Linear Programming:

  • Linear programming problems,
  • basic solution,
  • Duality.
  • Transportation and assignment problems.

Partial differential equations:

  • canonical form;
  • Equation of a vibrating string
  • heat equation

Numerical Analysis and Computer programming:

  • Regula-Falsi and Newton-Raphson methods;
  • signed integers and reals,
  • double precision reals and long integers.

Mechanics and Fluid Dynamics 

  • Generalised coordinates;
  • D’ Alembert’s principle and Lagrange’s equations;
  • Motion of rigid bodies in two dimension
  • The equation of continuity

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