# GITAM University Maths II IV SEM Syllabus

B.Tech. (BT) IV Semester

ENGINEERING MATHEMATICS-II

Course Code : EURBT401 Category: MT

Credits: 3 Hours : 3 per week

UNIT-I

Partial Differentiation and its application:

Functions of two or more variables, partial derivatives, Homogeneous functions –

Euler’s theorem, total derivative, differentiation of implicit functions, Geometrical

interpretation, Tangent plane and normal to a surface, change of variables, Jacobians,

Taylor’s theorem for functions of two variables, Errors and approximations, total

differential Maxima and Minima of functions of two variables, Lagrange’s method of

undetermined multipliers.

UNIT-II

Multiple Integrals and their applications:

Double Integrals, Change of order of integration, Double integrals in polar

coordinates, Areas enclosed by plane curves, Triple integrals, volume of solids,

change of variables, Area of curved surface, calculation of mass, center of gravity,

center of pressure, moment of inertia, product of inertia, principle axes, Beta function,

Gamma function, relation between Beta and Gamma functions, Error function or

probability integral.

UNIT-III

Fourier Series:

Euler’s formulae. Conditions for a Fourier expansion, functions having points of

discontinuity, change of interval, odd or even functions – expansions of odd or even

periodic functions, Half range series. Parseval’s formulae. Practical Harmonic

analysis.

UNIT-IV

Introduction to statistics and probability, sampling and sampling methods,

presentation of data, curve fitting, linear regression. Measures of central tendency,

(mean/mode/median), measures of dispersion: range, mean deviation, standard

deviation, variance, standard error.

Test of significance. Testing of hypothesis, level of significance, confidence limits.

Review of binomial, poisson and normal distribution, student’s t-distribution,

f-distribution, Fisher’s Z-distribution and Chi-square distribution.

UNIT-V

Numerical Analysis: Solution of linear algebraic equations using Jacobi, Gauss-

Seidel iterative methods, eigen values, eigen vectors using power method.

Numerical Solutions of ODE’s and PDE’s: Numerical solutions of ODE’s by

Picard’s method, Euler’s method, Runge-Kutta method and numerical methods for

solution for PDE’s (1) Elliptic (Liebmann iteration process) (2) Parabolic (Schmidt

explicit formula) (3) Hyperbolic and (4) Poisson’s equations (Gauss-siedel method).

Text Books:

1. Higher Engineering Mathematics by Dr.B.S.Grewal. 35th ed. 2000. Khanna publishers.

2. Mathematics for Engineering by Chandrica Prasad.

Reference Books:

1. Higher Engineering Mathematics by Dr.M.K.Venkataraman. 1994. National publishing company.

2. Advance Engineering Mathematics by Erwin Kreyszig.8th ed. 2004. John wiley and sons.