Page 9 - REC :: B.E. EEE Curriculum and Syllabus - R2019

3 Communication Skills, Pushplata, Sanjay Kumar, Oxford University Press
4 Practical English Usage. Michael Swan. OUP. 1995.
5 Remedial English Grammar. F.T. Wood. Macmillan.2007
6 On Writing Well. William Zinsser. Harper Resource Book. 2001
7 Study Writing. Liz Hamp-Lyons and Ben Heasly. Cambridge University Press. 2006.
8 Exercises in Spoken English. Parts. I-III. CIEFL, Hyderabad. Oxford University Press

Subject Code Subject Name Category L T P C
MA19152 LINEAR ALGEBRA AND APPLIED CALCULUS BS 3 1 0 4
Common to I sem. B.E.- Computer Science and Engineering
,Biomedical Engineering, Electronics and Communication
Engineering & Electrical and Electronics Engineering
and
B.Tech. – Information Technology

Objectives:
 To gain knowledge in using matrix algebra techniques and the concepts of basis and dimension in vector spaces.
 To understand the techniques of calculus which are applied in the Engineering problems.

UNIT-I MATRICES 12
Symmetric and skew – symmetric matrices , orthogonal matrices – Eigen values and Eigen vectors - Cayley –
Hamilton theorem (without proof) and applications - orthogonal transformation and quadratic forms to canonical
forms - Nature of quadratic forms.
UNIT-II VECTOR SPACES 12
Vector space – Linear dependence and independence of vectors, bases, dimensions - range and kernel of a linear map,
rank and nullity – matrix of Linear transformation - inverse of a linear transformation - rank nullity theorem –
composition of Linear maps – Matrix Associated with Linear Map - inner products and norms – Gram – Schmidt
orthogonalisation.
UNIT-III DIFFERENTIAL CALCULUS AND APPLICATIONS 12
Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of curvature – Evolutes and Envelopes -
Partial derivatives: Definitions and Simple problems - Jacobian and properties – Taylor’s series for functions of two
variables – Lagrange’s method of undetermined multipliers.
UNIT-IV APPLICATION OF INTEGRATION AND IMPROPER INTEGRALS 12
Evaluation of area, surface area and volume of revolution - Centre of Gravity – Moment of inertia – Improper
integrals: Beta and Gamma integrals and their properties .
UNIT-V MULTIPLE INTEGRAL 12
Double integrals – Change of order of integration – Double integrals in polar coordinates – Area enclosed by plane
curves – Triple integrals – Volume of solids – Change of variables in double and triple integrals.
Total Contact Hours : 60

Course Outcomes:
On completion of the course students will be able to
 Apply the concept of Eigenvalues and eigenvectors, diagonalization of a matrix for solving problems.
Use concepts of basis and dimension in vector spaces in solving problems and to construct orthonormal basis

using inner products.
Analyze, sketch and study the properties of different curves and to handle functions of several variables and

problems of maxima and minima.
 Apply the techniques of Integration in Engineering problems.
 Evaluate surface area and volume using multiple integrals.
Text Books: