Applied Mathematics CSS Syllabus | Dogar Brothers

Applied Mathematics CSS Syllabus

Applied Mathematics CSS Syllabus 2016 is available here. Just catch-up a Book of Dogar Brother’s to get selected through CSS exams. Keep connected with dogar.com.pkFacebookTwitterPinterest and Google Plus to get latest updates.

Applied Mathematics CSS Syllabus:

Applied Mathematics CS Syllabus 2016 is given below:

1. 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.

2. 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.

3. 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;

4. 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.

5. 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.

6. 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.

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