GBTU 2012Mathematics Syllabus
Paper - 2 Mathematics:
Algebra: Set relations & functions,
De-Morgan's Law, Mapping Inverse relations, Equivalence relations,
Peano's axioms, Definition of rationals and integers through
equivalence relation, Indices and surds, Solutions of simultaneous
and quadratic equations, A.P., G.P. and H.P., Special sums
i.e. ?n2 and ?n3 (n?N ), Partial fraction, Binomial theorem
for any index, exponential series, Logarithm and Logarithmic
series. Determinants and their use in solving simultaneous
linear equations, Matrices, Algebra of matrices, Inverse of
a matrix, Use of matrix for solving equations.
Probability: Definition, Dependent and independent
events, Numerical problem on addition and multiplication,
theorem of probability.
Trigonometry: Identities, Trigonometric
equations, properties of triangles, solution of triangles,
heights and distances, Inverse function, Complex numbers and
their properties, Cube roots of unity, De-Moivre's theorem.
Co-ordinate Geometry: Pair of straight lines,
Circles, General equation of second degree, parabola, ellipse
and hyperbola, tracing of conics.
Calculus: Limits & continuity of functions,
Differentiation of function of function, tangents & normal,
Simple examples of Maxima & Minima, Indeterminate forms,
Integration of function by parts, by substitution and by partial
fraction, definite integral, application to volumes and surfaces
of frustums of sphere, cone and cylinder. Differential equations
of first order and of first degree.
Vectors : Algebra of vectors, scalar and
vector products of two and three vectors and their applications.
Dynamics : Velocity, composition of velocity,
relative velocity, acceleration, composition of accelerations,
Motion under gravity, Projectiles, Laws of motion, Principles
of conservation of momentum and energy, direct impact of smooth
Statics: Composition of coplanar, concurrent
and parallel forces moments and couples resultant of set of
coplanar forces and condition of equilibrium, determination
of centroid in simple cases, Problems involving friction.