PART – A

Unit-I

Differential Calculus:

Radius of curvature – Cartesian, parametric, polar and pedal forms. Rolle’s theorem (without proof). Lagrange’s and Cauchy’s mean value theorems. Taylor’s Theorem for a function of a single variable and Maclaurin’s  series expansions (without proof).                                                                         6 Hours

Unit-II

Indeterminate forms –  L’Hospital’s rule (without proof) Taylor’s theorem for a function of two variables (without proof)–Maxima and Minima for function of two variables. Lagrange’s method of undetermined multipliers for extreme values  (with one subsidiary condition).                                                                                       

                                                                                                              6 Hours

Unit-III

Integral Calculus:

Multiple Integrals - Evaluation by change of order of integration –change of variables   and applications to area and volume. Beta and gamma functions.                                                                                                                        

                                                                                                          8 Hours

Unit-IV

Vector   Integration:

Line integrals, Surface integrals and volume integrals. Green’s,  Stoke’s, Gauss’s theorems (without proof) and problems.  Orthogonal curvilinear coordinates.                                                                                               

8 Hours

PART – B

Unit-V

Differential Equations:

Linear differential equations of second and higher order with constant coefficients.  Method of undetermined coefficients.                          6 Hours

Unit-VI

Method of variation of parameters. Solutions of Cauchy’s homogeneous linear equation and and Legender’s linear differential equations - solutions of initial and boundary value problems.                                                  6Hours

Unit-VII

Laplace Transforms:

Definition - Transforms of elementary functions. Derivatives and integrals of transforms – Problems.  Periodic function. Unit step function and unit impulse function.

                                                                                                               6 Hours

Unit-VIII

Inverse transforms – Properties.  Convolution Theorem. Solutions of linear differential equations and simultaneous differential equations.  Applications to Engineering problems.                                                                      6 Hours

Text Books:

1. B. S. Grewal, “Higher Engg. Mathematics”, 36th Edn, July 2001.

              Chapter – 4:             4.4 to 4.8 & 4.13, 4.14

              Chapter – 5:             5.9, 5.12, 5.13

              Chapter – 7:             7.1 to 7.5. 7.6(2), 7.7, 7.14 to 7.16

              Chapter – 8:             8.11 to 8.21

              Chapter – 13:           13.1 to 13.9, 13.11

              Chapter – 14:           14.1, 14.2

              Chapter – 21:           21.2 to 21.19

Reference Book:

1.       Advanced Engineering Mathematics by – E Kreyszing

     - John Wiley & Sons, 6^th Edn.

2.    A Short Course in Differential Equations – Raincille E.D.,                                                                                    -  4^th Edition  1969

Note: 1) One Question is to be set from each Unit

          2) Students have to answer five questions, choosing at least two    questions from  each Part. 

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