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Syllabus
CAL
Calculus (Syllabus)
CALCULUS
UNIT-I
Hyperbolic functions, higher order derivatives, Leibnitz rule and its applications to problems of the type e ax+b sinx ,e ax+b cosx ,(ax+b) n sinx ,(ax+b) n cosx, concavity and inflection points, asymptotes, curve tracing in Cartesian coordinates, tracing in polar coordinates of standard curves, L’ Hospitals rule, Application in business ,economics and life sciences.
UNIT-II
Riemann integration as a limit of sum, integration by parts, Reduction formulae, derivations and illustrations of reduction formulae of the type ∫sin n xdx ,∫cos n
xdx ,∫tann xdx ,∫sec n xdx ,∫(logx) n dx ,∫sinn x cos n xdx , definite integral, integration by substitution.
UNIT-III Volumes by slicing, disks and washers methods, volumes by cylindrical shells, parametric equations, parameterizing a curve, arc length, arc length of parametric curves, area of surface of revolution, techniques of sketching conics, reflection properties of conics, rotation of axes and second degree equations, classification into conics using the discriminant, polar equations of conics.
UNIT-IV
Triple product, introduction to vector functions, operations with vector-valued functions, limits and continuity of vector functions, differentiation and integration of vector functions, tangent and normal components of acceleration.
DM
Discrete Mathematics (Syllabus)
DISCRETE MATHEMATICS
UNIT-I
Sets, relations, Equivalence relations, partial ordering, well ordering, axiom of choice, Zorn’s lemma, Functions, cardinals and ordinals, countable and uncountable sets, statements, compound statements, proofs in Mathematics, Truth tables, Algebra of propositions, logical arguments, Well-ordering property of positive integers, Division algorithm, Divisibility and Euclidean algorithm, Congruence relation between integers, modular arithmetic, Chinese remainder theorem, Fermat’s little theorem.
UNIT-II
Principles of Mathematical Induction, pigeonhole principle, principle of inclusion and exclusion Fundamental Theorem of Arithmetic, permutation combination circular permutations binomial and multinomial theorem, Recurrence relations, generating functions, generating function from recurrence relations.
UNIT-III
Matrices, algebra of matrices, determinants, fundamental properties, minors and cofactors, product of determinant, adjoint and inverse of a matrix, Rank and nullity of a matrix, Systems of linear equations, row reduction and echelon forms, solution sets of linear systems, applications of linear systems, Eigen values, Eigen vectors of a matrix.
UNIT-IV
Graph terminology, types of graphs, sub-graphs, isomorphic graphs, Adjacency and incidence matrices, Paths, Cycles and connectivity, Eulerian and Hamiltonian paths, Planar graphs.