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    JM College, Bhurkunda Highlights

    ParameterDescription
    Established1979
    Courses6 Degrees and 8 Courses
    AccreditationsNAAC
    Institute TypeAffiliated College
    GenderCo-ed
    Student Count2925
    Faculty Count41
    Campus Size5.00 acres

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    What is the latest syllabus of maths hons in Jm College bhurkunda

    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

    Best Regards


    JM College, Bhurkunda Contact Address

    Address:
    JM College, Bhurkunda, Patel Nagar, Near Bank More, Ramgarh, Pincode-829106, Jharkhand, India

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