GOVERNMENT ARTS COLLEGE (AUTONOMOUS), KARUR . Manickavasagam, Pillai Others, ... Text Books: 1. S.Narayanan, T.K. Manickavasagam Pillai, ... GOVERNMENT ARTS COLLEGE (AUTONOMOUS) KARUR

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  • 1

    GOVERNMENT ARTS COLLEGE (AUTONOMOUS), KARUR 639 005B.Sc. MATHEMATICS COURSE STRUCTURE UNDER CBCS SYSTEM

    (For the candidates admitted from the year 2011-2012 onwards)

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    Tamil - I Tamil I U11L1T1 6 3 3 25 75 100English - I English - I U11L1E1 6 3 3 25 75 100Core Course - I Differential Calculus and Trigonometry U11MM1C1 6 5 3 25 75 100Core Course - II Probability and Statistics - 3 - - - - -First Allied Course I Allied Physics - I U11PH1A1 5 3 3 25 75 100First Allied Course - II Allied Physics II (Practical) - 2 - - - - -Environmental Studies Environmental Studies UES1 2 2 3 25 75 100

    30 16 500

    II

    Tamil - II Tamil II U11L2T2 6 3 3 25 75 100English II English II U11L2E2 6 3 3 25 75 100Core Course II Probability and Statistics U11MM2C2 3 4 3 25 75 100

    Core Course III Analytical Geometry of 3D and IntegralCalculus

    U11MM2C3 6 5 3 25 75 100

    First Allied Course II Allied Physics II (practical) U11PH2A2P 2 4 3 25 75 100First Allied Course III Allied Physics III U11PH2A3 5 3 3 25 75 100Value Education Value Education UVE2 2 2 3 25 75 100

    30 24 700

    III

    Tamil III Tamil- III U11L3T3 6 3 3 25 75 100English III English - III U11L3E3 6 3 3 25 75 100Core Course IV Sequences and Series U11MM3C4 6 5 3 25 75 100Core Course V Classical Algebra - 3 - - - - -Second Allied Course I Allied Chemistry - I U11CH3A1 5 3 3 25 75 100Second Allied Course II Allied Chemistry II Practical - 2 - - - - -Non Core Elective I Fundamentals of Information Technology U11CS3N1 2 2 3 25 75 100

    30 16 500

    IV

    Tamil IV Tamil- IV U11L4T4 6 3 3 25 75 100English IV English -IV U11L4E4 6 3 3 25 75 100Core Course V Classical Algebra U11MM4C5 2 4 3 25 75 100Core Course VI Vector Calculus and Fourier Series U11MM4C6 5 5 3 25 75 100Second Allied Course II Allied Chemistry Practical U11CH4A2P 2 4 3 25 75 100Second Allied Course III Allied Chemistry III U11CH4A3 5 3 3 25 75 100Skill Based Elective I Introduction to C & C++ U11MM4S1 2 4 3 25 75 100Non Core Elective II Office Automation and HTML U11CS4N2 2 2 3 25 75 100

    30 28 800

    V

    Core Course VII Algebra U11MM5C7 5 5 3 25 75 100Core Course VIII Real Analysis U11MM5C8 5 4 3 25 75 100Core Course IX Differential Equation and Transforms U11MM5C9 5 4 3 25 75 100Core Course - X Statics U11MM5C10 6 4 3 25 75 100Core Elective I Operations Research U11MM5E1 5 5 3 25 75 100Skill Based Elective II Advanced level of C++ U11MM5S2 2 4 3 25 75 100Skill Based Elective III C++ Practical U11MM5S3P 2 4 3 25 75 100

    30 30 700

    VI

    Core Course XI Complex Analysis U11MM6C11 6 5 3 25 75 100Core Course XII Dynamics U11MM6C12 6 5 3 25 75 100Core Course XIII Methods in Numerical Analysis U11MM6C13 6 5 3 25 75 100Core Elective - II Graph Theory U11MM6E2 5 5 3 25 75 100Core Elective - III Discrete Mathematical Structure U11MM6E3 6 4 3 25 75 100

    Extension ActivitiesExtension Activities 1

    Gender Education 8UEA6 1 1 3 25 75 10030 26 600

    TOTAL 180 140 3800

    CHAIRMANBOARD OF STUDIES IN MATHEMATICS CONTROLLER OF EXAMINATIONS

  • 2

    Sl. No.: Subject Code:

    GOVERNMENT ARTS COLLEGE (AUTONOMOUS) KARUR-05

    B.Sc., MATHEMATICS - I SEMESTER CORE COURSE - I(For the candidates admitted from 2011 -12 onwards)

    DIFFERENTIAL CALCULUS AND TRIGONOMETRY

    UNIT I Methods of successive differentiation Leibnitzs Theorem and its application Increasing and Decreasing function Maximum and Minimum of functionof two variables. (Ch 3 & 1.1 2.2: Ch 4 & 2.1, 2.2 and Ch 8 & 4 and 4.1[1])

    UNIT- II Curvature Radius of Curvature in Cartesian and in Polar co ordinates Centre of curvature Evolutes and Involutes. (Ch 10 & 2.1 2.6[1])

    UNIT-III Expansion of sinnx, cosnx, tanx, - Expansion of sinx, cosx Expansions ofsinx, cosx, tanx in powers of x. ( Ch 1 & 1.1 1.4[2])

    UNIT-IV Hyperbolic functions relation between hyperbolic and circular functions Inverse hyperbolic functions. (Ch 2 & 2.1 2.2[2])

    UNIT-V Logarithm of a complex number summation of trigonometric series Difference method Angles in arithmetic progression method Gregorysseries. (Ch 3 and Ch 4, 4.1, 4.2 and 4.2[2])

    Text Books:

    1. T.K. Manichavasagam Pillai and others, Differential Calculus, S.V. Publications. Chennai

    1985. Revised Edition.

    2. S.Arumugam and others, Trigonometry, New Gamma Publications 1985 revised edition.

    CHAIRMAN BOS COE

    1125 U11MM1CI

  • 3

    Sl. No.: Subject Code:

    GOVERNMENT ARTS COLLEGE (AUTONOMOUS) KARUR-05

    B.Sc., COMPUTER SCIENCE - I SEMESTER FIRST ALLIED COURSE - I(For the candidates admitted from 2011 -12 onwards)

    ALGEBRA AND CALCULUS

    UNIT- I Theory of Equations: Relations between roots and co efficients Transformation of Equation Diminishing, Increasing & Multiplying the rootsby a constant Forming equations with the given roots Rolles theorem,Descartes rule of signs (statement only) Simple problems.

    UNIT- II Singular matrices Inverse of a non singular matrix using Adjoint method Rank of a matrix Consistency Characteristics equation Eigen values,Eigen Vectors Cayley Hamilton theorem (proof not needed) Simpleapplications only.

    UNIT-III Differentiation - Maxima & Minima Concavity Convexity Points ofinflexion Partial differentiation Eulers theorem Total Differentialcoefficient (proof not needed) Simple problems only.

    UNIT-IV Evaluation using integration by parts Properties of definite integrals Fourier series in the range (0, 2 ) odd & Even functions Fourier HalfRange sine and cosine series.

    UNIT-V Differential Equations: Variables Separable Linear Equations Second orderof types aD2 + bD + cy = F(x) where a, b, c are constants and F(x) is one of thefollowing types (i) ekx (ii) sin (kx) (or) cos(kx) (iii) xn, n being an integer (iv)ekxf(x)

    Text Book:

    1. T.K. Manickavasagam, Pillai & Others, Algebra Volume I, S.V.Publications, 1985 Revised

    Edition (Units I,II)

    2. S.Narayanan, T.K.Manickavasagam Pillai, Calculus, Volume II, S.V. Publications 2003 (Units

    III, IV, V).

    Reference:

    1. M.L. Khanna, Differential Calculus, Jaiprakashnath and Co. Meerut - 2004

    CHAIRMAN BOS COE

    1126 U11MM1A1

  • 4

    Sl. No.: Subject Code:

    GOVERNMENT ARTS COLLEGE (AUTONOMOUS) KARUR-05

    B.Sc., I - SEMESTER FIRST ALLIED COURSE I

    (FOR GEOGRAPHY MAJOR)

    (For the candidates admitted from 2011 - 12 onwards)

    STATISTICS - I

    UNIT- I Functions and Limitations of Statistics Uses of Statistics Collection of dataprimary and Secondary

    UNIT- II Classification Different types of classification Objectives Tabulation ofdata objectives Forming frequency distribution.

    UNIT-III Diagrammatic and Graphic representation Objectives and Difference Bardiagram Simple, Component, Compound, Histogram, Frequency Polygonand Curves, Pie- Chart and Ogives.

    UNIT-IV Measures of central tendency Properties Mean, Median, Mode, Harmonicmean, Quartiles, Deciles.

    UNIT-V Measures of Dispersion Range, Quartile, Deviation, Mean Deviation aboutthe mean, Standard Deviation and Co efficient of variation.

    Text Books:

    1. S.P.Gupta, Elementary Statistical methods. Sultan Chand and sons, New Delhi.

    CHAIRMAN BOS COE

    1127 U11GE1A1

  • 5

    Sl. No.: Subject Code:

    GOVERNMENT ARTS COLLEGE (AUTONOMOUS) KARUR-05

    B.Sc. I & III - SEMESTER FIRST / SECOND ALLIED COURSE I

    (FOR CHEMISTRY & PHYSICS MAJOR)

    (For the candidates admitted from 2011 -12 onwards)

    ALLIED MATHEMATICS I

    CALCULUS AND FOURIER SERIES

    UNIT- I Successive differentiation nth derivative of standard functions (Derivationnot needed) simple problems only Leibnitz Theorem (Proof not needed) andits applications. Curvature and radius of curvature in Cartesian only (proof notneeded) Jacobians of two & Three variables Simple Problem only.

    UNIT- II Evaluation of integrals of types

    1. xbadx

    cos2. xba

    dx

    sin3. dx

    rxqxp

    cxbxa

    )sincos(

    )sincos(

    UNIT-III General properties of Definite integrals Evaluation of definite integrals oftypes

    1. b

    a

    dxxbax ))(( 2. dxxbax

    b

    a ))(( 3. dxxb

    axb

    a

    )(

    )(

    Reduction formula when n is a positive integer for

    (1). b

    a

    nax ndxxe (2). xdxb

    a

    n sin (3). xdxb

    a

    n cos (4). x

    nax ndxxe0

    (5). xdxn2/

    0

    sin

    without proof (6) xdxx n

    a

    n cossin2

    and examples.

    UNIT-IV Evaluation of Double and Triple integrals in simple cases Changing the orderand evaluating of the double integration. (Cartesian only)

    UNIT-V Definition of Fourier Series Finding Fourier Co efficients for a givenperiodic function with period 2 - Use of Odd and Even functions inevaluation Fourier Co efficients Half range sine & Cosine series.

    Text Books:

    1. S.Narayanan, T.K. Manickavasagam Pillai, Calculus, Vol. I S.Viswanathan Pvt Limited,

    2003

    2. S.Arumugam, Issac and Somasundaram, Trigonometry & fourier Series, New Gamma

    Pub