FIRST SEMESTER BE SYLLABUS

Engineering Mathematics – I

Subject Code:                                                                                                                                                                                                                   IA Marks: 25

Hours/Week: 4                                                                                                                                                                                                                 Exam Hours: 3

Total Hours: 52                                                                                                                                                                                                                Exam Marks: 100

SECTION A

Unit I

Differential Calculus:

Determination of nth derivative of standard functions, Leibnitz’s theorem (without proof) and Problems, Polar curves and angle between the 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 sinmxcosnx 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, length, volume and surface area of given curves. Differentiation under integral sign (Integrals of constant limits)                                                                                                    6 Hours

 

SECTION B

Unit V

Differential Equations:

Solution of 1st order and 1st degree differential equations, variable separable, Homogeneous, Exact, Linear and reducible to above types. Illustrative examples from Engg. 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’Almbert’s ration 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).                                                    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 vector point function-Gradient, Divergence, Curl, Laplacian Solenoid, Irrotational vectors and their properties.                                                                                                6 Hours

 

Text Books:                      

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)

2. Rainville E. D., “A short course in differential equations” – 4th Edn, 1969.

Reference Book:

 1. “Advanced Engg. Mathematics”, by E. Kreyszing, John Wiley & Sons, 6th Edn..

 

Note: Answer any FIVE questions choosing at least TWO questions from each section.