**FIRST SEMESTER BE
SYLLABUS**

**Engineering
Mathematics – I**

Subject Code:
IA Marks: 25

Hours/Week: 4 Exam
Hours: 3

Total Hours: 52
Exam Marks: 100

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

**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 sin^{n}x,
cos^{n}x, tan^{n}x, cot^{n}x, sec^{n}x, cosec^{n}x,
and sin^{m}xcos^{n}x and Evaluation of these integrals with
standard limits – Problems, Tracing of standard curves in Cartesian form,
Parametric form and Polar form.
6
Hours

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

**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

**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

**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

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