CSS Applied Mathematics is one of the most important compulsory papers of this competitive exam, as it covers all the basic knowledge required for a bureaucrat about Pakistan. A lot of preparatory material is in the market, but updated, reliable, and comprehensive material is required to clear this paper in this competitive exam.
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| CSS PMS English Precis & Composition
Vector Calculus (10%)
- Vector algebra; scalar and vector products of vectors; gradient divergence and curl ofa vector; line, surface and volume integrals; Green’s, Stokes’ and Gauss theorems.
Statics (10%)
- Vector algebra; scalar and vector products of vectors; gradient divergence and curl ofa vector; line, surface and volume integrals; Green’s, Stokes’ and Gauss theorems.
Dynamics (10%)
- Motion in a straight line with constant and variable acceleration; simple harmonic motion; conservative forces and principles of energy.
- Tangential, normal, radial and transverse components of velocity and acceleration; motion under central forces; planetary orbits; Kepler laws;
Ordinary differential equations (20%)
- Equations of first order; separable equations, exact equations; first order linear equations; orthogonal trajectories; nonlinear equations reducible to linear equations, Bernoulli and Riccati equations.
- Equations with constant coefficients; homogeneous and inhomogeneous equations; Cauchy-Euler equations; variation of parameters.
- Ordinary and singular points of a differential equation; solution in series; Bessel and Legendre equations; properties of the Bessel functions and Legendre polynomials
Fourier series and partial differential equations (20%)
- Trigonometric Fourier series; sine and cosine series; Bessel inequality; summation of infinite series; convergence of the Fourier series.
- Partial differential equations of first order; classification of partial differential equations of second order; boundary value problems; solution by the method of separation of variables; problems associated with Laplace equation, wave equation and the heat equation in Cartesian coordinates.
Numerical Methods (30%)
- Solution of nonlinear equations by bisection, secant and Newton-Raphson methods; the fixed- point iterative method; order of convergence of a method.
- Solution of a system of linear equations; diagonally dominant systems; the Jacobi and Gauss-Seidel methods.
- Numerical differentiation and integration; trapezoidal rule, Simpson’s rules, Gaussian integration formulas.
- Numerical solution of an ordinary differential equation; Euler and modified Euler methods; Runge- Kutta methods.