CSS Syllabus Applied Mathematics – 100 Marks
I. 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.
II. 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.
III. 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;
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 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.
V. 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.
VI. 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.
|1.||An Introduction to Vector Analysis||Khalid Latif,|
|2.||Introduction to Mechanics||Q.K. Ghori|
|3.||An Intermediate Course in Theoretical
|4.||Differential Equations with Boundary
|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
|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|