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SEMESTER – 1
BCA -101 : MATHEMATICS – 1
Max. Marks : 50
Min. Marks : 17
OBJECTIVE : The objective of this course is to familiarize the students with
Calculus.
EXAMINATION
The internal examination will carry 20% marks i.e. 10 marks. The external
examination will be of 80% marks i.e. 40 marks. The question paper will contain
questions equally distributed in all units. The balance of the paper will be maintained
by including appropriate (numerical/objective/conceptual/analytical/theoretical)
combination of subsection in each question.
UNIT - I
Review of concepts of function of one variable: define a function. Types of function:
Limits: define working rule for finding out the limit, fundamental property of limit,
problems based on limits:
Continuity : define point of discontinuity, classification of discontinuity, problems
based on continuity & discontinuity
Differentiability : condition for derivability and problems.
UNIT - II
Successive differentiation, Rolles theorem, Mean value theorem, Taylor’s theorem,
Taylor’s & Maclaurin’s series, Intermediate forms.
UNIT - III
Tangents, Normals, Curvature, asymptotes, integration of hyperbolic function and
reduction formula
UNIT - IV
Differentiation of vector function, gradient, directional derivatives, divergence and
curl, vector function of several scalar variables and their partial derivative, level
surface gradient in Cartesian and polar coordinates, divergences of vector and curl of
a vector.
UNIT - V
Matrix – definition, types of matrix, special matrix elementary transformation of
matrix, inverse of matrix – adjoint methods and Gaussian elimination, normal from
of matrix, rank of matrix, nullity of matrix (their applications) consistency and
solution of linear simultaneous equations

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