UPSC IFOS Mathematics Paper I Syllabus

UPSC IFOS Mathematics Paper I: topic-wise syllabus

1. 1

   Linear Algebra

   Section A

   • Vector spaces, subspaces, bases and dimension
   • Linear dependence and independence
   • Matrices and Cayley-Hamilton theorem
   • Eigenvalues and eigenvectors
   • Matrix of a linear transformation
   • Rank, echelon form and canonical forms
   • Orthogonal, symmetric, unitary and hermitian matrices
   • Quadratic and hermitian forms
2. 2

   Calculus

   Section A

   • Limits, continuity and differentiability
   • Mean value theorems and Taylor's theorem
   • Indeterminate forms, maxima, minima and asymptotes
   • Functions of several variables and partial derivatives
   • Lagrange's multipliers and Jacobian
   • Definite, improper integrals, beta and gamma functions
   • Double and triple integrals
   • Areas, surfaces, volumes and centre of gravity
3. 3

   Analytic Geometry

   Section A

   • Cartesian and polar coordinates in two and three dimensions
   • Second degree equations and canonical forms
   • Straight lines and shortest distance between skew lines
   • Plane, sphere, cone and cylinder
   • Paraboloid, ellipsoid and hyperboloids
4. 4

   Ordinary Differential Equations

   Section B

   • Formation, order and degree
   • First order first degree equations and integrating factor
   • Equations not of first degree and Clairaut's equation
   • Singular solutions
   • Higher order linear equations with constant coefficients
   • Euler-Cauchy equation
   • Second order equations with variable coefficients
   • Variation of parameters
5. 5

   Dynamics, Statics and Hydrostatics

   Section B

   • Rectilinear and simple harmonic motion
   • Projectiles and constrained motion
   • Work, energy and impulsive forces
   • Kepler's laws and central orbits
   • Equilibrium, friction and common catenary
   • Virtual work and stability of equilibrium
   • Fluid pressure, centre of pressure and thrust
   • Floating bodies and metacentre
6. 6

   Vector Analysis

   Section B

   • Scalar and vector fields and triple products
   • Gradient, divergence and curl
   • Vector identities
   • Curves in space, curvature and torsion
   • Serret-Frenet formulae
   • Gauss and Stokes' theorems and Green's identities