**GITAM University Engineering Mathematics II Syllabus**

B.Tech. (CE)II SEMESTER

ENGINEERING MATHEMATICS – II

Code: EURMT202 Category: MT

Credits: 3 Hours: 3 per week

Department: BSH

The objective of the course is to impart knowledge in Basic concepts of Mathematics relevant to Engineering applications.

Unit – I (10 hours)

PARTIAL DIFFERENTIATION:

Introduction to Partial differentiation, 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.

Unit –II 08 hours)

APPLICATIONS OF PARTIAL DIFFERENTIATION :

Total differential, Maxima and Minima of functions of two variables, Lagrange’s method of undetermined multipliers, Differentiation

under the integral sign, Leibnitz’s Rule.

Unit-III (10 hours)

PARTIAL DIFFERENTIAL EQUATIONS :

Introduction, Formation of partial differential equations, Solutions of partial differential equations, Equations solvable by direct

integration, Linear equations of the first order, Non-linear equations of the first order, Homogeneous linear equations with constant

coefficients, Rules for finding the complementary function, Rules for finding the particular integral.

Unit-IV (08 hours)

LINEAR ALGEBRA-1:

Rank of Matrix, Elementary transformations, Elementary matrices, Inverse, Normal form, Consistency of linear system of equations,

Linear transformations.

Unit-V (10 hours)

LINEAR ALGEBRA – 2:

Eigen values and Eigen vectors of a matrix, Cayley-Hamilton theorem, Reduction to diagonal form, Quadratic forms and canonical

forms, Hermitian and Skew- Hermitian matrix, Unitary matrix.

Text Books Prescribed :

Higher Engineering Mathematics, Dr.B.S Grewal. Khanna Publishers.

References :

Advanced Engineering Mathematics, Erwin Kreyszig. Wiley Eastern Pvt. Ltd.

Textbook of Engineering Mathematics, N.P.Bali. Laxmi Publications (P) Ltd.

Higher Engineering Mathematics, Dr.M.K.Venkata Raman. National Pub. Co.

Note: The figures in parentheses indicate approximate number of expected hours of Instruction.