Applied Mathematics CSS Syllabus (100 MARKS)
FPSC Applied Mathematics CSS Syllabus is comprehensive and a better optional subject for aspirants with a maths background. After reviewing the syllabus, go through the Applied Mathematics CSS Past Papers to see how FPSC has tested topics such as vector calculus, statics, dynamics, differential equations, Fourier series, and numerical methods in previous CSS exams.
I. Vector Calculus (10%)
- Vector algebra
- Scalar and vector products of vectors
- Gradient, divergence and curl of a vector
- Line integrals
- Surface integrals
- Volume integrals
- Green’s theorem
- Stokes’ theorem
- Gauss theorem
II. Statics (10%)
- Composition of forces
- Resolution of forces
- Parallel forces and couples
- Equilibrium of a system of coplanar forces
- Centre of mass of a system of particles
- Centre of mass of rigid bodies
- Equilibrium of forces in three dimensions
III. Dynamics (10%)
- Motion in a straight line with constant acceleration
- Motion in a straight line with variable acceleration
- Simple harmonic motion
- Conservative forces
- Principles of energy
- Tangential components of velocity and acceleration
- Normal components of velocity and acceleration
- Radial components of velocity and acceleration
- Transverse components of velocity and acceleration
- Motion under central forces
- Planetary orbits
- Kepler laws
IV. 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 equations
- Riccati equations
- Equations with constant coefficients
- Homogeneous equations
- Inhomogeneous equations
- Cauchy-Euler equations
- Variation of parameters
- Ordinary points and singular points of a differential equation
- Solution in series
- Bessel equations
- Legendre equations
- Properties of the Bessel functions
- Properties of the Legendre polynomials
V. Fourier Series and Partial Differential Equations (20%)
- Trigonometric Fourier series
- Sine series
- 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
- Heat equation
- Cartesian coordinates
VI. Numerical Methods (30%)
- Solution of nonlinear equations by:
- Bisection method
- Secant method
- Newton-Raphson method
- Fixed-point iterative method
- Order of convergence of a method
- Solution of a system of linear equations
- Diagonally dominant systems
- Jacobi method
- Gauss-Seidel method
- Numerical differentiation
- Numerical integration
- Trapezoidal rule
- Simpson’s rules
- Gaussian integration formulas
- Numerical solution of an ordinary differential equation
- Euler method
- Modified Euler method
- Runge-Kutta methods
FPSC RECOMMENDED BOOKS List for APPLIED MATHEMATICS CSS SYLLABUS
| S.No. | Title | Author |
|---|---|---|
| 1. | An Introduction to Vector Analysis | Khalid Latif |
| 2. | Introduction to Mechanics | Q.K. Ghori |
| 3. | An Intermediate Course in Theoretical Mechanics | Khalid Latif |
| 4. | Differential Equations with Boundary Value Problems | D. G. Zill and M. R. Cullen |
| 5. | Elementary Differential Equations | E.D. Rainville, P.E. Bedient and R.E. Bedient |
| 6. | Introduction to Ordinary Differential Equations | A.L. Rabenstein |
| 7. | Advanced Engineering Mathematics | E. Kreyszig |
| 8. | An Introduction to Numerical Analysis | Mohammad Iqbal |
| 9. | Numerical Analysis | R.L. Burden and J.D. Faires |
| 10. | Elements of Numerical Analysis | F. Ahmad and M.A. Rana |
| 11. | Mathematical Methods | S. M. Yousaf, Abdul Majeed and Muhammad Amin |
FPSC Official Applied Mathematics CSS Syllabus
Here is the link to the Applied Mathematics CSS Syllabus on the FPSC official website
