APPLIED MATHEMATICS CSS SYLLABUS (100 MARKS)
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
