Syllabus For The Subject ANALYTICAL MECHANICS AND TENSER ANALYSIS

UNIT - 01

INTRODUCTION - TRANSFORMATION OF CO-ORDINATES - SUMMATION CONVERSION

KRONECKER DEITA.

UNIT - 02

CO-VARIANT - CONTRA VARIANT VECTORS - SECOND - HIGHER ORDERS TENSORS -

SYMMETRIC - SKEW SYMMETRIC TENSOR.

UNIT - 03

CONTRACTION - OUTER & INNER PRODUCT - QUOTIENT LAW - CONJUGATE - RELATIVE

TENSORS.

UNIT - 04

CONJUGATE TENSOR - ASSOCIATE TENSOR - MAGNITUDE PHYSICAL COMPONENTS.

UNIT - 05

GENERAL ORTHOGONAL CO-ORDINATES CYLINDRICAL COORDINATED - SPHERICAL COORDINATES

- SKEW - SYMMETRIC CO-VARIANT TENSOR.

UNIT - 06

CHAPTER - 06

CHRISTOFFEL SYMBOLS - TRANSFORMATION LAW OF CHRISTOFFEL SYMBOLS - COVARIANT

DIFFERENTIATION.

UNIT - 07

LAW OF CO-VARIANT DIFFERENTIATION - INTRISIC DIFFERENTIATION - GRADIENT

DIVERGENCE - LAPLACIAN AND CURL - PARALLELISM.

UNIT - 08

GEODESIC - EULER`S EQUATIONS - DIFFERENTIAL EQUATION FOR GEODESICS - COORDINATES.

UNIT - 09

RIEMANN - CHRISTOFFEL TENSOR - CURVATURE TENSOR.

UNIT - 10

RICCI TENSOR AND EINSTEIN TENSOR - RIEMANN CURVATURE - CONSTANT

CURVATURE.

UNIT - 11

CO-ORDINATE TRANSFORMATION - CARTESIAN TENSOR - PERMUTATION TENSOR -

TENSOR ALGEBRA

UNIT - 12

SCALAR & VECTOR PRODUCT OF TOW VECTORS - GRADIENT DIVERGENCE - CURL AND

LAPLACIAN - GAUSS & STOKES THEOREM - ISOTROPIC TENSOR.

Vinayaka Missions University,Directorate of Distance Education

Salem India

MASTER OF SCIENCE IN MATHEMATICS

1 Yr.

ANALYTICAL MECHANICS AND TENSER ANALYSIS(2030502)