UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN GEOPHYSICS
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester V - Paper VII - Geo - Statistics and Geo - Mathematics

Duration: 3 hrs
Maximum Marks: 100
Credits: 4

Unit I

Introduction - Various schemes of classifying and tabulating the data - Representation of data as diagrams and graphs, simple bar, sub divided bar, pie diagrams, graphs on natural and logarithmic scales, histogram, frequency polygon, Ogives - Measures of central tendency - arithmetic mean, median and mode for ungrouped, discrete and grouped data, measures of dispersion - range, mean deviation, standard deviation, and quartile deviation for ungrouped discrete and grouped data.

Unit II

Geological population - Numerical data in geology - Sampling techniques, sampling distribution, level of significance, degrees of freedom, sample test based on chi squared and F-distributions - Concept of probability - Theorems of addition and multiplication. - Binomial, Poisson's and normal distribution - Simple correlation, linear regression, rank correlation, regression equations and method of least squares.

Unit III

Integral calculus - double and triple integrals, change of order of integration, change of variable from cartesian to polar, Beta and Gamma functions - Vectors - Scalar and vector products, triple products, differentiation of a vector, directional derivative of a scalar function, scalar fields, gradient of scalar fields, vector fields and their divergence and curl line and surface integrals.

Unit IV

Transformation of coordinates, orthogonal curvilinear coordinates, Cartesian, cylindrical, spherical and bipolar coordinates, arc length and volume element, gradient, divergence, curl and Laplacian tenns of curvilinear coordinates, functions of a complex variable - Exponential, trigonometric hyperbolic and logarithmic functions, differentiation of analytical function.

Unit V

Integral transform - Laplace transform, elementary transform, general theorem, transform of derivatives, unit step, pulse, error and periodic function, inverse, transform, Fourier integral and Fourier transform and their properties, convolution theorem.

Books Recommended

Advanced Mathematics for Engineers by Prasad, C.

Mathematical methods for Physics and Engineering by Dettman, J.W.

Statistics and Data analysis by Davis, J.C. and Simpson R. J; John Wiley & Sons, New York, 1973.

Introduction of Statistics by Milton, J.S., McTeer, P.M. and Corbet, J.J., the McGraw Hill Company New York, 1999.

Elements of Practical Statistics by Kapur, S.K., Oxford IBH, New Delhi, 1989.