# NIT Trichy 1st year Syllabus Mathematics I

MATHEMATICS-I

Characteristic equation of a matrix –Eigen values and Eigen vectors – Properties of Eigen

values – Diagonalization of matrix – Cayley-Hamilton Theorem (without proof) verification
– Finding Inverse and Power of a matrix using it – Quadratic form – Definite and indefinite
forms – Orthogonal reduction of quadratic form to canonical form.
Sequences of real numbers – Limit of a sequence – Convergent and divergent sequences–
sub sequence- Cauchy’s sequence – monotone convergence theorem (without proof)-
Sequence with recurrence relations
Infinite series-Convergence Tests for positive term series – Comparison, Root, Ratio and
Raabe’s tests – Alternating series – Leibnitz’s rule – Absolute and Conditional Convergence.
Riemann rearrangement theorem (with out proof)-
Curvature – Radius, Centre and Circle of Curvature in Cartesian form –Evolute – Envelope
of family of curves with one and two parameters – Functions of several variables – Partial
B.Tech. Syllabus (2009-‘10)
National Institute of Technology: Tiruchirappalli – 620 015. 3
derivatives and Transformation of variables – Jacobian and its Properties- Maxima and
Minima of function of two variables.
Double integral – Changing the order of Integration – Change of variables from Cartesian to
Polar Coordinates – Area using double integral in Cartesian and Polar Coordinates – Triple
integral – Change of Variables from Cartesian to Spherical and Cylindrical Coordinates –
Volume using double and triple integrals.

Text Books

1. Kreyszig, E., Advanced Engineering Mathematics, 8th edition, John Wiley Sons, 2001.
2. Grewal, B.S., Higher Engineering Mathematics, 40th edition, Khanna Publications, Delhi,
2007.

Reference Books

1. Apostol, T.M. Calculus Volume I & II Second Edition, John Wiley & Sons (Asia)
2005.
2. Greenberg, M.D. Advanced Engineering Mathematics, Second Edition, Pearson
Education Inc. (First Indian reprint), 2002
3. Strauss. M.J, Bradley, G.L. and Smith, K.J. Calculus, 3rd Edition, Prentice Hall, 2002.