MATHS II

MA 121                                                                         No. of hrs/week = 04

                                                                                                No. of credits  = 04

Functions with two and more variables, partial differentiation, chain rule, composite and implicit function differentiation, total differentials, error and approximation.  Maxima and minima for functions of two and more variables, Lagranges method of undetermined multipliers.

Multiple integrals - double and triple integrals, changing the order of integration, Jacobian of polar, cylindrical and spherical coordinate systems.  Application of multiple integrals to find area and volumes.

Linear algebra-n-dimensional vectors, vector spaces, linear combination, linear dependence, linear independence, spanning set, basis, orthogonal and orthonormal basis, Gram-Schmidt orthogonalisation process.

Linear system of equations - Gauss elimination process, consistency.

Vectors - Vector differentiation, Divergence, Gradient and Curl and their physical interpretation and simple applications. Vector integration, Greens theorem in a plane, Gauss Divergence theorem, Stoke’s theorem and simple applications

Curvilinear coordinates systems- Spherical and cylindrical coordinate systems.

REFERENCE:

Calculus   and   Analytical   Geometry  -  IV   Edn. -  George   B.Thomas, Jr.(1992) Addison Wesley Publications.

Calculus &  Analytical Geometry -  George  B.Thomas  Jr  &     Ross  L. Finney (1990), Addison Wesley Publications.

Linear Algebra G.H.Hardley - Narosa Publishing.

Vector  Analysis  - Murra  R. Speiegel, Edn. 1959,  Schaum Publishing company.

Higher Engineering Mathematics-Dr.B.S. Grewal, 36^th Edition, Khanna Publishers.