BCA Mathematics - 1

Elementary logic, Real number system, Field and ordered axioms of real numbers, Intervals, rational and irrational numbers, Absolute value, and its properties, complex numbers and their properties, Ordered pairs, Cartesian product, relation, equivalence relation, inverse relation, Functions, composite functions, types of functions, Graphs of different types of functions.

Sequence and Series (Arithmetic, Geometric and Harmonic) and their properties, Means (AM, GM, and HM), and theorems to show the relation among them, nth term and sum of arithmetic series, & finite and infinite geometric series, Sum of first n-natural numbers, their squares and cubes, Arithmetico-geometric series.

Definitions and types of matrices, algebra of matrices, Determinants, transpose, minors, and cofactors of matrices, Properties of determinants (without proof), singular, non-singular, adjoint, and inverse of a matrix, Rank of a matrix, Linear and orthogonal transformation, composite transformation, and its applications to computer graphics, Characteristic equations, Eigenvalues and Eigenvectors.

Defining terms of conic sections, Standard equations of circle, parabola, ellipse, hyperbola and their graphs, Conic sections in terms of eccentricity, Polar equations of the circle, ellipse, parabola and hyperbola.

Definition of vector and scalar, magnitude and distance and unit vector, Operations on vectors (addition, subtraction, scalar multiplication), Scalar product and vector product of two and three vectors with their geometrical interpretations, Vector space, subspace, Linear combination, linear dependence and independence, Scalar product, norm and orthogonality.