Dr. G. P. Singh >>MATHEMATICS-I

MAL101                        MATHEMATICS-I                                       L3 – T1 – P0 -C8

 

Differential Calculus:  Functions of single variable:  Limit, continuity and differentiability.  Mean value theorems:   Rolle’s theorem, Lagrange’s theorem, Cauchy’s theorem, Taylor’s theorem with remainders, indeterminate forms,curvature, curve tracing.

Integral Calculus: Fundamental theorem of Integral calculus, mean value theorems, evaluation of definite integrals, Applications in Area, length, volumes and surface of solids of revolutions, Improper integrals: Beta and Gamma functions, differentiation under integral sign.

Infinite series: Sequences, Infinite series of real and complex numbers, Cauchy criterion, tests of convergence, absolute and conditional convergence, improper integrals, improper integrals depending on a parameter, uniform convergence, power series, radius of convergence.

Matrices:  Rank of matrix, consistency of a system of equations, linear dependence  and independence, linear and orthogonal transformations, Eigen values and eigen vectors, Cayley – Hamilton theorem, reduction to diagonal form, Hermitian and skew Hermitian matrices, Quadratic forms.

 

Text Books

  1. Kreyszig, E. ;  Advanced Engineering Mathematics (Eighth Edition); John Wiley & Sons,  1999.
  2. Piskunov, N. : Differential and Integral calculus, Vol. 1, Vol. 2,  MIR Publishers, Moscow – CBS Publishers and Distributors (India),1996.

 

Reference Books:

  1. Thomas, G.B. and Finney, R.L.; Calculus and Analytic Geometry (Ninth Edition); Addison  Wesley Longman, Inc ; 1998.
  2. Michael D. Greenberg: Advanced Engineering Mathematics, Pearson Education Pvt. Ltd 2009 .
  3. Jain, R.K. and Iyengar, S.R.K.; Advanced Engineering Mathematics; Narosa Publishers 2005.