PART – A

Unit-I

Differential Calculus:

Determination of nth derivative of standard functions. Leibnitz’s theorem (without proof) and Problems. Polar curves and angle between Polar curves. Pedal equations of polar curves.                                                           

7 Hours

Unit-II

Partial differentiation:

Partial Derivatives, Euler’s Theorem. Total differentiation. Differentiation of Composite and implicit functions. Jacobians and their properties.  Errors and approximations.                                                                                               

6 Hours

 Unit-III

Integral Calculus:

Reduction formulae for the integration of sinⁿx, cosⁿx, tanⁿx, cotⁿx, secⁿx, cosecⁿx, and sin^mxcosⁿx and evaluation of these integrals with standard limits – Problems. Tracing of standard curves in Cartesian form, Parametric form and Polar form.                                                                                    

6 Hours

Unit-IV

Applications of Integral Calculus:

Derivative of arc length. Applications to find area and length of given curves. Volumes and surface areas of solids of revolution. Differentiation under integral sign (Integrals with constant limits)                                       

6 Hours

PART – B

Unit-V

Differential Equations:

Solution of  first order and first degree differential equations: variables separable, homogeneous, exact, linear and equations reducible to above types. Illustrative examples from Engineering Field. Orthogonal trajectories of Cartesian and polar curves.                                                               

8 Hours 

Unit-VI

Infinite Series:

Convergence, divergence and oscillation of an infinite series, comparison test, p-series, D’Alembert’s ratio test, Raabe’s test, Cauchy’s root test, Cauchy’s integral test (all tests without proof) for series of positive terms. Alternating series, Absolute and Conditional convergence. Leibnitz’s test (without proof) and Problems.                                                              

6 Hours

Unit-VII

Analytical Geometry in three dimensions:

Direction cosines and direction ratios. Planes, Straight lines, Angle between planes / straight lines, Coplanar lines. Shortest distance between two skew lines.   

                                                                                                         7 Hours

Unit-VIII

Vector Calculus:

Vector differentiation. Velocity, Acceleration of a particle moving on a space curve. Vector point function. Gradient, Divergence, Curl, Laplacian.  Solenoidal and Irrotational vectors - Problems.

                                                                                                              6 Hours

Text Book:                                    

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

               Chapter – 3:               3.13 to 3.17 and 3.21, 3.22

               Chapter – 4:               4.1 to 4.3, 4.10, 4.11

               Chapter – 5:               5.1, 5.2, 5.4, 5.5, 5.7, 5.8, 5.10, 5.11

               Chapter – 6:               6.2 to 6.4 , 6.9 to 6.13 & 8.1 to 8.10

               Chapter – 9:               9.3 to 9.7, 9.9, 9.10(1), 9.11 to 9.13

               Chapter – 11:             11.6 to 11.11

               Chapter – 12:             12.3, 12.4 (example 12.8), 12.5 (4)

Reference Books:

1.       Advanced Engineering Mathematics by – E Kreyszing  - John Wiley & Sons, 8^th Edn.

2.    A Short Course in Differential Equations – Rainville E.D., 4^th Ed.  1969.

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

          2) To Answer Five questions choosing at least TWO questions from  each Part.      

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