CSS Applied Mathematics Syllabus — FPSC PDF Download

Applied Mathematics pays the fast hand. It starves the slow reader. The CSS Applied Mathematics syllabus covers vectors, mechanics, and differential equations. It carries 100 marks, and technique decides the result. Our analysis covers papers from 2009 to 2023. Differential equations with constant coefficients come first. They drew 44 questions. First-order equations add 36 questions. Vector algebra adds 38 questions at 10.8% weight. Mechanics holds its ground too. Forces and equilibrium drew 36 questions, and motion drew 34. Speed beats storage here every single time. You win this paper in practice sets, not textbooks. Solve problems daily and time every set. Redo each failed question until the method turns automatic. Skip nothing in differential equations. The topic bank feeds this paper year after year. Take it when mathematics or engineering trained your hands. Theory collectors should walk away.

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, 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.

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APPLIED MATHEMATICS Frequency Analysis (2009–2023)

APPLIED MATHEMATICS Top 5 Most Repeated Topics (2009–2023)

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. (36 Questions)

Equations with constant coefficients; homogeneous and inhomogeneous equations; Cauchy-Euler equations; variation of parameters. (44 Questions)

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. (38 Questions)

Equations of first order; separable equations, exact equations; first order linear equations; orthogonal trajectories; nonlinear equations reducible to linear equations, Bernoulli and Riccati equations. (36 Questions)

Solution of nonlinear equations by bisection, secant and Newton-Raphson methods; the fixed- point iterative method; order of convergence of a method. (36 Questions)