JM College, Bhurkunda All Questions

Syllabus Maths(Hons.)

Semester 1

Core course 1

ANALYTIC GEOMETRY 2D, HIGHER ALGEBRA & TRIGONOMETRY

Theory: 75 Lectures; Tutorial:15 Lectures

UNIT I - ANALYTICAL GEOMETRY OF 2D

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.

UNIT II - HIGHER ALGEBRA & TRIGONOMETRY

Statement and proof of binomial theorem for any index, exponential and logarithmic series.

De Moivre’s theorem and its applications.

Trigonometric and Exponential functions of complex argument and hyperbolic functions.

Summation of Trigonometrical series.

Factorisation of sin , cos .

Books Recommended:

Analytical Geometry & Vector Analysis – B. K. Kar, Books & Allied Co., Kolkata

Analytical Geometry of two dimension – Askwith

Coordinate Geometry – S L Loney.

Trigonometry – Das and Mukherjee

Trigonometry - Dasgupta

Core Course 2

DIFFERENTIAL CALCULUS & VECTOR CALCULUS

Theory: 75 Lectures; Tutorial:15 Lectures

UNIT I - DIFFERENTIAL CALCULUS

Successive differentiation, Leibnitz’s theorem. Maclaurin and Taylor series expansion.

Partial differentiation, Euler’s theorem for functions of two variables, Total differential, Jacobian.

Tangent and normal, curvature. Asymptotes. Maxima and Minima of functions of two variables,

Lagrange’s multipliers.

UNIT II - 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.

Suggested Readings

Calculus – G B Thomas & R L Finney.

Differential Calculus – Das & Mukherjee.

Vector Calculus – Dasgupta.

Vector Calculus – Shanti Narayan

Semester 2

Core Course 3

ANALYSIS - I Theory: 75 Lectures; Tutorial:15 Lectures

UNIT I – ANALYSIS - I

The axiom of least upper bound and greatest lower bound in R. The completeness property of R,

Archimedean property, density of rational and irrational numbers in R. Neighbourhoods and limit

point of a set, open and closed sets, isolated points, Bolzano – Weierstrass theorem for sets (Statement

only).

Sequences, bounded sequence, convergent sequence, monotonic sequence, subsequence, Cauchy

sequence and Cauchy’s general principle of convergence.

Infinite series, Convergence and divergence of infinite series of real numbers, Pringsheim’s theorem,

Comparison test, Cauchy’s root test, D’Alembert’s ratio test, Raabe’s test, De-Morgan’s and

Bertrand’s test, Gauss’s ratio test, Cauchy’s condensation test, Integral test, Alternating Series,

Leibnitz test, Absolute and conditional convergence.

Books Recommended:

Elements of Real Analysis – Shanti Narayan & M D Raisinghania.

Higher Algebra – S Bernard & J M Child

Core Course 4

LNTEGRAL CALCULUS & ANALYTIC GEOMETRY 3D

Theory: 75 Lectures; Tutorial:15 Lectures

UNIT I – INTEGRAL CALCULUS

Integration of rational and irrational functions.

Evaluation of definite integrals, Special integrals, differentiation and integration under the sign of

integration (Beta and Gamma functions are excluded), reduction formulae.

Point of inflexion, double point, curve tracing. Length of plane curve and area bounded by plane

curves. Volume and surface area of solid of revolution.

UNIT II – ANALYTICAL GEOMETRY 3D

Rectangular, spherical-polar and cylindrical co-ordinates, direction cosines.

Angle between straight lines, equation of planes and straight lines, shortest distance between the lines.

Sphere.

Suggested Readings

Calculus – G B Thomas & R L Finney.

Integral Calculus – Das & Mukherjee.

Integral Calculus – Lalji Prasad.

Coordinate Geometry of 3D – J T Bell

Analytical Geometry of 3D – Lalji Prasad.

Semester 3

Core Course 5

THEORY OF REAL FUNCTIONS Theory: 75 Lectures; Tutorial:15 Lectures

UNIT I

Limit of functions: Limit, algebra of limit of functions. Continuity and discontinuities, algebra of

continuous functions. Intermediate value theorem, location of roots theorem, preservation of intervals

theorem. Uniform continuity, functions of bounded variations

And more download the pdf syllabus from the Vinoba Bhave University Site or Ranchi University(same syllabus) site

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