Krishna's BCA Mathematics -I

SYLLABUS- BCA MATHEMATICS-I,
Unit-I
Determinants:
Definition, Minors, Cofactors, Properties of Determinants MATRICES: Definition, Types
of Matrices, Addition, Subtraction, Scalar Multiplication and Multiplication of Matrices,
Adjoint, Inverse, Cramer's Rule, Rank of Matrix Dependence of Vectors, Eigen Vectors of a
Matrix, Caley-Hamilton Theorem (without proof).
Unit-II
Limits & Continuity:
Limit at a Point, Properties of Limit, Computation of Limits of Various Types of Functions,
Continuity at a Point, Continuity Over an Interval, Intermediate Value Theorem, Type of
Discontinuities.
Unit-III
Differentiation:
Derivative, Derivatives of Sum, Differences, Product & Quotients, Chain Rule,
Derivatives of Composite Functions, Logarithmic Differentiation, Rolle's Theorem, Mean
Value Theorem, Expansion of Functions (Maclaurin's & Taylor's), Indeterminant Forms,
L' Hospital's Rule, Maxima & Minima, Curve Tracing, Successive Differentiation &
Leibnitz Theorem.
Unit-IV
Integration:
Integral as Limit of Sum, Fundamental Theorem of Calculus (without proof.), Indefinite
Integrals, Methods of Integration Substitution, By parts, Partial Fractions, Reduction
Formulae for Trigonometric Functions, Gamma and Beta Functions (definition).
Unit-V
Vector Algebra:
Definition of a Vector in 2 and 3 Dimensions; Double and Triple Scalar and Vector Product
and physical interpretation of area and volume.