ASSISTANT PROFESSOR (Mathematics)

Test: ASSISTANT PROFESSOR (Mathematics)

Authority: Federal Public Service Commission

Syllabus Content

Max Marks: 200 Qualifying Standard: 50%

(Note: Negative marking of 0.25/ wrong answer)

Part-I (For all Categories): 100 Marks (MCQ)

I. English (50 Marks)

 Comprehension

 Grammar Usage

 Vocabulary

 Sentence Structuring

 Sentence Correction

 Grouping of Words

 Pairs of Words

 Idiomatic Phrases

 Synonyms/ Antonyms

 Translation

II. Teaching Methodology (50 Marks)

 Teaching Methodology

 Elements of Curriculum.

 Curriculum Development Process:

 Classroom Communication

 Classroom Assessment and Evaluation

 Types of Test and characteristics of a Good Test

 Research Instruments

Part-II: 100 Marks (MCQ) (For Mathematics)

I. Vector Calculus

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

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

 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

 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

 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

 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 solution of an ordinary differential equation; Euler and modified Euler

methods; Runge- Kutta methods.