Department of Computer Science and Engineering

B.Tech. II (CO) Semester - 4

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MH 210: ENGINEERING MATHEMATICS III (IS-III)

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COURSE OBJECTIVES
  • Introduce the Fourier series and its application.
  • Introduce concepts of Fourier transforms.
  • Introduce concepts of complex variables and Bilinear transformations.
  • Introduce the basic statistical data analysis.
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    COURSE OUTCOMES
    After successful completion of this course, student will be able to
    • Understand basic knowledge of widely used Fourier transform techniques and their applications.
    • Understand basic knowledge of Linear and Bilinear Transformation of complex domain.
    • Understand different probability distributions.
    COURSE CONTENT
    BASIC CONCEPTS OF INTEGRALS AND VECTOR CALCULUS

    (04 Hours)

    Reorientation of concepts of integrals, line integrals, scalar and vector point function, differential operator, gradient, directional derivative, physical meaning of gradient, divergence, curl and laplacian with their properties.
    FORIER SERIES

    (06 Hours)

    Periodic function, Trigonometric series, Fourier series for any function of period 2L. Fourier series and cosine series, Fourier half range series.
    FOURIER TRANSFORM AND FOURIER TRANSFORM OF AN INTEGRAL

    (06 Hours)

    Fourier Transform and its operational properties, Fourier Integral theorem, Fourier Cosine and solution, transforms of derivatives. Inversion formula for Fourier transforms.
    COMPLEX VARIABLES

    (06 Hours)

    Basic mathematical concept, Analytic function, Cauchy-Riemann equations, Harmonic functions, its applications, Linear transformation of complex domain, bilinear transformations, conformal mapping and its application, complex integration over closed contour.
    BASICS OF STATISTICS AND PROBABILITY DISTRIBUTION

    (06 Hours)

    Reorientation of random experiments, events, probability and its distributions of Binomial & Poisson's, their properties, normal distribution, jointly distributed random variables, expected values, function of random variable moments, moment generating functions.
    SAMPLING THEORY AND ESTIMATION

    (07 Hours)

    Some basics of sampling, statistical inference, Random samples, sampling distribution, sample mean, variance and other statistics, point estimate and interval estimate confidence of interval, maximum likehood estimate.

    TESTING OF HYPOTHESIS

    (07 Hours)

    Sampling and test of significance, statistical hypothesis and significance, Type I and Type II errors, Test of significance. Level of significance, single tail and two tails test hypothesis test. ??2test, t-test of significance of the mean of a random sample, t-test for difference of means of two small samples, Snedecor's variance ratio test or F-test and its application.

  • Tutorials will be based on the coverage of the above topics separately

    • (14 Hours)

    (Total Contact Time: 42 Hours + 14 Hours = 56 Hours)
    BOOKS RECOMMENDED

    1. Kreyszing E., "Advanced Engineering Mathematics", John Wiley, Int. Student Ed, 1995.
    2. Wiley C. R., "Advanced Engineering Mathematics", MGH Int. Student Ed, 1993.
    3. O'Neil Peter, "Advanced Egg. Mathematics", Thompson, Singapore, Ind. Ed, 2002.
    4. Jay L Devore, "Probability and statistics for Engineering and Sciences", 5/E, Thomson Asia, Singapore, 2002.
    5. Athanasios Papoulis "Probability, Random Variables, and Stochastic Processes", 4/E, McGraw-Hill, 2002.
    6. Sheldon Ross,"Probability models for computer science", 7/E, Prentice Hall, 2005.