Page 13 - Integrated M.Sc. Physics
P. 13

SASTRA Deemed to be University                                               M.Sc. in Physics (Integrated)

                                                                                     L   T   P  C
                    Course Code: MAT130                                              4   0   0   4
                    Semester: I
                                               ANCILLARY MATHEMATICS – I

                    Course Objectives:
                    This course aims to:
                         Enable  the  learner  to  understand  the  linear  system  of  equations,  reduction  to
                          diagonal form, quadratic form and to canonical form
                         Familiarize the learner with concepts of the co-ordinate systems, differentiation and
                          various methods of curve fitting.

                    Unit – I                                                           12 Periods
                    Matrices & Linear System of Equations
                    Introduction – Determinants, cofactor, Laplace’s expansion – Properties of determinants –
                    matrices,  special  matrices  –  Matrix  operations  –  related  matrices  –  rank  of  a  matrix  –
                    solution of linear system of equations consistency of linear system of equations – linear and
                    orthogonal transformations.

                    Unit – II                                                          12 Periods
                    Eigen Vectors & Quadratic Forms
                    Linear dependence – Eigen values and eigen vectors – properties of eigen values – Cayley-
                    Hamilton theorem – Reduction to diagonal form – reduction of quadratic form to canonical
                    form – nature of quadratic form – complex matrices.

                    Unit – III                                                         12 Periods
                    Analytical Geometry
                    Vectors – space coordinates, direction cosines – section formulae – products of two vectors
                    – physical applications – products of three or more vectors – equation of a plane – equations
                    of a straight line – condition for a line to lie in a plane – coplanar lines – S.D. between two
                    lines – intersection of three planes – equation of a sphere – tangent plane to a sphere.

                    Unit – IV                                                          12 Periods
                    Differential Calculus & Its Applications
                    Successive  differentiation:  standard  results  –  Leibnitz’s  theorem–  derivative  of  arc  –
                    curvature – radius of curvature – centre of curvature, evolute, chord of curvature – envelope
                    –  increasing  &  decreasing  function:  concavity,  convexity  &  point  of  inflexion  –  maxima  &
                    minima, practical problems.

                    Unit – V                                                           12 Periods
                    Curve Fittings
                    Introduction – graphical method – laws reducible to the linear law – principle of least squares
                    – method of least squares – fitting of other curves – method of group averages – fitting a
                    parabola.

                    TEXTBOOKS
                       1.  B. S. Grewal, Higher Engineering Mathematics. Khanna Publishers, 2011.
                       2.  P. K. Mittal, S. Narayan, A Text Book of Matrices. S.Chand Publications, 2010.

                                                                                                      13
   8   9   10   11   12   13   14   15   16   17   18