Mathematics is an undergraduate degree in the domain of Mathematical studies. The course aims at providing knowledge about disciplines of Maths such as Calculus, Differentiation, Integration, Linear programming, etc.
It is a 4-year professional degree course pursued by aspirants willing to make a career in the Mathematical domain and related disciplines.
COURSE STRUCTURE OF MATHEMATICS
The subjects of Mathematics course are designed in such a way that they primarily focus on developing mathematical skills in algebra, calculus and data analysis. B.Sc. Mathematics
Undergraduate Course Structure
B.A/B.Sc Part – I
(Effective from Sessions 2009-10)
There shall
be three papers each consisting of 5 units. Each unit will have 14 lectures
schedule and hence 70 lectures per paper. Each paper will have 50 marks to its
credit. One question with an alternate will be asked from each Unit. Students
will have to attempt all questions.
PAPER I: GEOMETRY
Unit – 1
Polar
Coordinates:
Polar equation of a parabola,
ellipse and hyperbola when focus in taken as pole, Polar equations of the chord
joining two points, tangent, normal, polar (chord of contact), pair of
tangents, asymptotes, director circle and auxiliary circle of a conic.
Unit – 2
Straight
Lines & Planes (Using Vector technique)
Normal form of equation, intercept
form of equation and general equation of a plane, plane passing through three
points, angle between two planes, two sides of a plane, Length of perpendicular
from a point to a plane, Bisectors of angles between two planes, Planes passing
through the line of intersection of two Planes.
Symmetrical and non-symmetrical form
of equations of a line, transformation of non-symmetrical form to symmetrical
form, Planes passing through a line, coplanar lines, The shortest distance
between two lines, Length of perpendicular from a point to a line, Orthogonal
projection of point and a line on a plane, Lines intersecting two lines,
intersection of three planes, volume of a tetrahedron, pair of Planes.
Unit – 3
SPHERES
Equation of a sphere, Plane section
of a sphere and Itersection of two spheres , spheres passing through a circle,
tangent plane, plane of contact, pola lines, angle of intersection of two
spheres, power of a point, radical plane, line, centre of spheres, coaxial
system of spheres, rthogonal systems of spheres.
Unit – 4
(a) CONES
& CYLINDERS
Cones and cylinders with given base,
intersection of a one and a plane passing through the vertex of the cone,
tangent lines and planes reciprocal cones, normal plane passing through a
generator of the cone, right circular cones and cylinders.
(b)
GENERATING LINES
Ruled surfaces, generating lines of
a hyperboloid of one sheet and hyperbolic paraboloid and its properties,
generators through a point on the principal elliptic section of hyperboloid of
one sheet, (ΙΈ) point on hyperboloid of one, sheet and equations of generations
at() point.
Unit – 5
CENTRAL
CONICOIDS & PARABOLOIDS:
Standard equations of central
conicoids and paraboloids, tangent lines and planes, polar planes and polar
lines, enveloping cones and cylinders section with of intersection of three
mutually perpendicular tangent planes to central conicoids paraboloid, Cone
passing through the normal drawn from a point to central conicoid and
paraboloid, Conjugate diameters of an ellipsoid and its properties.
(Effective from Session 2009-2010)
PAPER-II: ELEMENTAY ANALYSIS
Unit – 1
Statements, Connectives
(Conjunction, Disjunction, Negation, Conditional and Bi-conditional Joins)
Statement formulas, Tautologies, Implication and equivalences, Statement
Functions, Quantifiers, Sets, Relations, Equivalence and Order relations,
Partitions, Functions, Direct and inverse images of subsets under maps.
Axiomatic introduction of IR as a
complete ordered Field, Existence of square roots of positive real numbers.
Unit – 2
Properties
of integers and Sequences
Natural numbers, First Principle of
induction, Well Ordering property of N, Second Principle of Induction, Integers
and rational numbers, Archimedean Property, Rational and Irrational Density Theorems,
Division and Euclidean Algorithm in Z, Primes, Fundamental Theorem of
Arithmetic, Irrationality of surds.
Intervals in IR, Real Sequences and
their algebra, Limit of a sequence, bounded, convergent, monotone and Cauchy
sequences, Cauchy’s general principle of convergence, Algebra of limits
(passage to limits under addition, multiplications, inversions and inequality),
Divergence of sequences.
Unit – 3
Limits and Continuity:
Real valued Functions of one variable, their graphs and algebra, Neighborhoods
of a point and limit points of subsets of IR, Limit of a function, Algebra of
limits, one sided limits, Limit of a function as x --> ±∞ infinite limits.
Continuity, Local boundedness and local
maintenances of sign, Boundedness and intermediate value properties of continuous
functions over closed intervals, Image of a closed interval under continuous maps.
Unit – 4
Differentiability
Differentiability of a function at a
point and its geometrical interpretation, algebra of differentiable functions,
Chain rule of differentiation, sign of derivatives and monotonicity of
functions, interior extremum Theorem. Rolle’s Theorem, Lagrange’s Mean value
Theorem, Cauchy’s Mean value Theorem.
Unit – 5
Applications
of Derivatives
Higher derivatives, Leibnitz Theorem, Taylor’s and McLaurin’s
Theorem with Lagrange’s and Cauchy’s forms of reminders, Maxima and minima,
Local extremum points (necessary and sufficient conditions), Indeterminate
Form, L’Hospital’s rule, Convexity and concavity, Points of inflexion,
curvature of curves in explicit form y=f(x), Darboux’S Theorem on intermediate
value property of derivatives.
B.A/B.Sc Part – I
(Effective from Sessions 2009-10)
PAPER III: DIFFERENTIAL EQUATIONS AND
VECTOR CALCULUS
Unit – 1
Origin, concept
and formation of an ordinary differential equation and its solution,
initial-value problems and statement of Existence and Uniqueness Theorems,
order and degree of differential equation, First order equations, separable
equations, equations reducible to separable form, exact equations.
Integrating factors, linear
equations, Geometrical meaning of a different equation and its solution,
isoclines and direction field.
Unit – 2
Picard’s
iteration method, Curves under given geometrical conditions, orthogonal
trajectories, mechanical applications (Newton’s law of cooling, growth and
decay problems, motion in a resisting medium, escape velocity), Equations
solvable for p,x or y, Clairaut’’s equations, singular solutions.
Unit – 3
Homogeneous
linear differential equations, linearly dependent and independent solutions,
fundamental system of solutions, equations with constant operators for
determining particular integrals, Euler-Cauchy equations.
Unit – 4
(a) Applications to
damped and forced oscillations, linear systems of differential equations with
constant coefficients.
(b) Derivatives of a
vector function of a single scalar variable, scalar and vector fields,
gradient, divergence and curl, vector identities.
Unit – 5
Orthogonal curvilinear coordinates,
spherical polar and cylindrical polar coordinates double integrals. Line,
surface and volume integrals, Green’s, stokes.
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