CSS Applied Mathematics 2025 Group 2

CSS Applied Mathematics Syllabus 2025

This article covers the CSS Applied Mathematics complete Syllabus 2025.

The syllabus of CSS Applied Mathematics consists of 6 parts of a collective 100% marks i.e.200 marks. 

The examination for CSS Applied Mathematics is the Group 2 exam for CSS candidates.

CSS Applied Mathematics Syllabus 2024

Paper-I

(Marks-100)

Vector Calculus (10%)

• • Vector algebra; scalar and vector products of vectors; gradient divergence and curl of a vector; line, surface and volume integrals; Green’s, Stokes’ and Gauss theorems.

Statics (10%) 

• • Composition and resolution of forces; parallel forces and couples; equilibrium of a system of coplanar forces; centre of mass of a system of particles and rigid bodies; equilibrium of forces in three dimensions.

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.

This is the complete syllabus for preparation of CSS Applied Mathematics.

The Candidates should prepare thoroughly to succeed in the examination.

Therefore, here are a few suggested books you can buy for better learning about CSS Applied Mathematics from your favorite Multan Kitab Ghar online bookstore.

Suggested Reading Books for CSS Applied Mathematics 2025 Group 2

• An Introduction to Vector Analysis by Khalid Latif
• Introduction to Mechanics by Q.K. Ghori
• An Intermediate Course in Theoretical Mechanics by Khalid Latif
• Differential Equations with Boundary Value Problems by D. G. Zill and M. R. Cullen
• Elementary Differential Equations by E.D. Rainville, P.E. Bedient and R.E. Bedient
• Introduction to Ordinary Differential Equations by A.L.Rabenstein
• Advanced Engineering Mathematics by E. Kreyszig
• An Introduction to Numerical Analysis by Mohammad Iqbal
• Numerical Analysis by R.L Burden and J.D Faires
• Elements of Numerical Analysis by F. Ahmad and M.A Rana
• Mathematical Methods by S. M. Yousaf, Abdul Majeed and Muhammad Amin