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Krishna's BCA Mathematics - Edition-13B
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.