# NIT Raipur Syllabus 1st Year Basic Engineering Mathematics-2

# NIT-RAIPUR

## BASIC ENGG. MATHEMATICS – II

(Theory Periods – 40, Tutorial periods – 12)

Unit – I Group, Ring, Field and Vector Space :

Definition and examples of Group, Ring and Field, Vector

Space: General Properties of Vector spaces, Vector subspaces, Algebra of subspaces, Linear span, Linear

sum of two subspaces, Linear dependence and linear independence of vectors, Basis of a vector space,

Finite dimensional vector spaces, Dimension of a vector space, Dimension of a subspace.

Unit – II Differential Equations of higher order:

Linear differential equations of higher order with

constant coefficients, method of variation of parameters, Cauchy’s and Legendre’s linear equations,

simultaneous linear equations with constant coefficients.

Unit – III Multiple Integrals:

Double and triple integrals, change of order of integration, Beta and

Gamma functions, Application to area and volume, Centre of gravity.

Unit – IV Vector Calculus:

Vector operator ; directional derivative, gradient, divergence and curl;

line, surface & volume integrals, Green’s , Gauss’s & Stoke’s theorem (without proof) & applications.

Unit – V Matrices and Sequence of Real Numbers: Matrices:

Rank and inverse by elementary

transformation, system of linear equations, eigen values & eigen vectors, Caley-Hamilton theorem,

Reduction to diagonal form.

**Sequences: **Definition, Convergent sequences, Divergent sequences,

Bounded sequences, Monotone sequences, Cauchy’s theorem on limits, Cauchy’s sequences.

TEXT BOOKS:

1. Higher Engineering Mathematics by B.S.Grewal (38

th edition)- Khanna Publishers.

2. Advanced Engineering Mathematics by Erwin Kreyszig (8

th edition)- John Wiley & Sons.

3. Higher Algebra by H.S. Hall & S.R.Knight- A.I.T.B.S. Publishers.

REFERENCE BOOKS:

1. Integral Calculus by Gorakh Prasad- Pothishala Private Limited.

2. Advanced Engineering Mathematics by R.K.Jain & S.R.K. Iyengar- Narosa Publishing House.

3. Applied Mathematics for Engineers and Physicsts by Louis A. Pipes- Mc Graw Hill.

NIT Raipur Syllabus 1st Year Basic Engineering Mathematics-2