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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.
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