Mathematics
[Syllabus for B.A./B.Sc]
[Under Choice Based Credit System]
Semester I (Syllabus)
Mat/ Sem I/ C 1 – Analytical Geometry 2D, Trigonometry
Instruction: -
Ten questions will be set. Candidates will be required to answer Seven Questions.
Question no. 1 will be Compulsory consisting of 10 short answer type
covering entire syllabus uniformly. Each question will be of 2 marks. Out of
remaining 9 questions candidates will be required to answer 6 questions selecting at
least one from each group. Each question will be of 10 marks.
GROUP - A
ANALYTICAL GEOMETRY OF TWO DIMENSIONS
Change of rectangular axes. Condition for the general equation of second degree to
represent parabola, ellipse, hyperbola and reduction into standard forms. Equations
of tangent and normal (Using Calculus). Chord of contact, Pole and Polar. Pair of
tangents in reference to general equation of conic. Axes, centre, director circle in
reference to general equation of conic. Polar equation of conic. 5 Questions
GROUP - B
HIGHER ALGEBRA & TRIGONOMETRY
Statement and proof of binomial theorem for any index, exponential and
logarithmic series. 1 Question
De Moivre’s theorem and its applications. Trigonometric and Exponential
functions of complex argument and hyperbolic functions.
Summation of Trigonometrical series.
Factorisation of sinθ , cosθ . 3 Questions
Books Recommended:
1. Analytical Geometry & Vector Analysis – B. K. Kar, Books & Allied Co., Kolkata
2. Analytical Geometry of two dimension – Askwith
3. Coordinate Geometry – S L Loney.
4. Trigonometry – Das and Mukherjee
5. Trigonometry - Dasgupta
SYLLABUS Semester I Mat/ Sem II/ C 2 –
Differential Calculus and Vector Calculus
Instruction: -
Ten questions will be set. Candidates will be required to answer Seven Questions.
Question no. 1 will be Compulsory consisting of 10 short answer type
covering entire syllabus uniformly. Each question will be of 2 marks. Out of
remaining 9 questions candidates will be required to answer 6 questions selecting at
least one from each group. Each question will be of 10 marks.
GROUP - A
DIFFERENTIAL CALCULUS
Successive differentiation, Leibnitz’s theorem. Maclaurin and Taylor series
expansion. 1 Question
Partial differentiation, Euler’s theorem for functions of two variables, Total differential,
Jacobian.
2 Questions
Tangent and normal, curvature. Asymptotes, Maxima and Minima of functions of two
variables, Lagrange’s multipliers. 2 Questions
GROUP - B
VECTOR CALCULUS
Product of three and four vectors, work done, moment of a vector about a point and
a line. Scalar and vector point functions, differentiation of a vector function of scalar
variables. Gradient, Divergence and Curl, second order operators in Cartesian
coordinate system. 4 Questions
Books Recommended:
1. Calculus – G B Thomas & R L Finney.
2. Differential Calculus – Das & Mukherjee.
3. Vector Calculus – Dasgupta.
4. Vector Calculus – Shanti Narayan
CBCS PATTERN SYLLABUS
Mat/ Sem1/ GE 1 – MATHEMATICS – I F.M: - 150
Instruction for Generic Elective: - 7x10
Eleven Questions will be set. Candidates will be required to answer Eight Questions.
Question no. 1 will be Compulsory consisting of 10 short answer type covering
entire syllabus uniformly. Each question will be of 3 marks. Out of remaining 10 questions
will be required to answer 7 questions selecting at least one from each group. Each question
will be of 10 marks.
GROUP - A
DIFFERENTIAL CALCULUS I
Successive differentiation, nth order derivative of some standard functions. Leibnitz’s
theorem. nth derivative of rational functions. Taylor’s and Maclaurin's series expansions of
functions. Applications of Taylor's and Maclaurin's series. Tangent and Normal, their
equations in the Cartesian form, parametric form, Tangents at the origin. Angle between two
curves. Length of tangent, normal, sub tangent, subnormal in Cartesian forms .2 Questions
INTEGRAL CALCULUS I
Integration of rational and irrational functions. Integration by partial fractions, Integration by
transformations, Integration by substitution, Integration by parts. 2 Questions
GROUP - B
VECTORS I
Scalar and Vector point functions, vector function of a scalar variables, Continuity of a vector
function. differentiation of a vector with respect to the scalar variable “t”. Differentiation of a
vector function. Derivatives of a sum of vectors, derivatives of a product of vectors ( both
scalar and vector products.)
2 Questions
COORDINATE GEOMETRY OF TWO DIMENSION I
Change of rectangular axes, Rotation and Shifting of origin. Transformation of the general
equation of the second degree. Conditions for the general equation of second degree to
represent a parabola, ellipse and hyperbola. Equations of the tangent and normal to a given
curve using calculus. 2 Questions
REAL ANALYSIS I
Sequence: Definition, Bounds, Limit of a sequence, Monotonic Sequences and their
Convergence, Algebraic operations and limits, Cauchy Sequence, General principle of
convergence of a sequence.
2 Questions
BOOKS RECOMMENDED
1. Differential Calculus : A Das Gupta & S B Prasad
2. Integral Calculus : A Das Gupta
3. Vector Analysis : Lalji Prasad/ A Das Gupta & S B Prasad
4. Coordinate Geometry : A Das Gupta
5. Real Analysis : Lalji Prasad
