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BCSWritten
BCS written syllabus
General and technical cadres · 235 pages
Compulsory subjects and post-related subjects for professional and technical cadres. Confirm the applicable subject code in the recruitment notice.
Published by BPSC. Collected 2026-11-14. Confirm the edition and subject against your recruitment notice before studying.
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SYLLABUS FOR BCS (WRITTEN) EXAMINATION
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APPLIED MATHEMATICS
Part-II
Marks: 100
Group-A: Real Analysis
(a) Metric Spaces: Definition and examples. Open and closed sets, Compact sets, perfect set and cantor
set.
(b) Sequence: Convergent sequence, bounded‘ sequence, subsequence, Cauchy sequence, and
completeness of IR.
(c) Differentiation: Continuous function. Derivative of a function. Rolle‘s Theorem , Mean -value
theorem, Toylor‘s theorem.
(d) Functions of Several Variables: Limit and Continuity. Partial differentiation. Schwarz‘s theorem,
Young‘s theorem.
Group-B: Complex Analysis
(a) Complex Functions: Single and many valued functions. Limit, Continuity and differentiability of
complex function.
(b) Analytic Functions: Necessary and sufficient conditions. Harmonic functions. Mobius transformation
and power series.
(c) Complex Integration: Zeros of analytic functions, Cauchy‘s theorem, Morera‘s theorem, Cauchy‘s
integral formula, Singularities, Classification of singularities.
(d) Complex integration: The open mapping theorem, Taylor‘s and Laurent series. Fundamental theorem
of algebra, Rouches theorem, The residue theorem, Contour integration.
Group-C: Numerical Analysis
(a) Solution of algebraic and transcendental equation, Interpolation.
(b) Numerical solution of linear and non-linear system of equations.
(c) Numerical differentiation and integration.
(d) Numerical solutions of ordinary differential equation.
Group-D: Hydrodynamics
(a) Velocity and acceleration of fluid particles, Steady and unsteady flows, Unifor m and non -uniform
flows, Stream lines, path lines, vortex lines and velocity potential. Rotational and irrotational flows.
Equation of continuity.
(b) Euler‘s equation of motion, conservative field force. Lamb‘s equations of motion. Bernouli‘s
equation.
(c) Motion in two-dimensions, stream function and its physical meaning, velocity in polar coordinates,
relation between stream function and velocity.
(d) Sources, sinks and doublets. Complex potential and complex velocity, stagnation points, Complex
potential due to a s ource and a doublet. Circulation and vorticity, relation between circulation and
vorticity. Kelvin‘s Circulation theorem.