Syllabus BASIC ELECTRICAL ENGINEERING EE 401  for Tribhuvan University Institute of Engineering All BE first year first part
ENGINEERING
MATHEMATICS II
SH 451
Lecture:
3 Year:
1
Tutorial:
2 Part:
II
Practical
Course Objectives: i) To develop the skill of solving
differential equations and to provide knowledge of vector algebra and calculus
ii) To make students familiar with calculus
of several variables
and infinite series
and infinite series
1.
Calculus of two or more variables (6
hours)
1.1.
Introduction:
limit and continuity
1.2.
Partial
derivatives
1.2.1.
Homogeneous
function, Euler’s theorem for the function of
two and three variables
two and three variables
1.2.2.
Total
derivatives
1.3.
Extrema
of functions of two and three variables; Lagrange’s Multiplier
2.
Multiple Integrals (6
hours)
2.1.
Introduction
2.2.
Double
integrals in Cartesian and polar form; change of order of integration
2.3.
Triple
integrals in Cartesian, cylindrical and spherical coordinates;
2.4.
Area
and volume by double and triple integrals
3.
Three Dimensional Solid Geometry (11
hours)
3.1.
The
straight line; Symmetric and general form
3.2.
Coplanar
lines
3.3.
Shortest
distance
3.4.
Sphere
3.5.
Plane
Section of a sphere by planes
3.6.
Tangent
Planes and lines to the spheres
3.7.
Right
circular cone
3.8.
Right
circular cylinder
4.
Solution of
Differential Equations in Series and Special Functions (9 hours)
4.1.
Solution
of differential equation by power series method
4.2.
Legendre’s
equation
4.3.
Legendre
polynomial function; Properties and applications.
4.4.
Bessel’s
equation
4.5.
Bessel’s
function of first and second kind. Properties and applications
5.
Vector Algebra and Calculus (8
hours)
5.1.
Introduction
5.2.
Two
and three dimensional vectors
5.3.
Scalar
products and vector products
5.4.
Reciprocal
System of vectors
5.5.
Application
of vectors: Lines and planes
5.6.
Scalar
and vector fields
5.7.
Derivatives
– Velocity and acceleration
5.8.
Directional
derivatives
6.
Infinite Series (5
hours)
6.1.
Introduction
6.2.
Series
with positives terms
6.3.
convergence
and divergence
6.4.
Alternating
series. Absolute convergence
6.5.
Radius
and interval of convergence
Reference books:
1.
Erwin Kreyszig, Advanced
Engineering Mathematics , John Wiley and Sons Inc
2.
Thomas, Finney, Calculus and
Analytical geometry Addison Wesley
3.
M. B. Singh, B. C.
Bajrachrya, Differential calculus,
Sukunda Pustak Bhandar,Nepal
4.
M. B. Singh, B. C.
Bajrachrya, A text book of Vectors,
Sukunda Pustak Bhandar,Nepal
5.
M. B. Singh, S. P. Shrestha, Applied Mathematics,
6.
G.D. Pant, G. S. Shrestha,
Integral Calculus and Differential Equations, Sunila Prakashan,Nepal
7.
Y. R. Sthapit, B. C.
Bajrachrya, A text book of Three
Dimensional Geometry, Sukunda Pustak
Bhandar,Nepal
8.
Santosh Man Maskey, Calculus,
Ratna Pustak Bhandar, Nepal
Evaluation
Scheme:
The questions will cover all the chapters
in the syllabus. The evaluation scheme will be as indicated in the table below:
Chapter

Hours

Mark
distribution *

1.

06

10

2.

06

10

3.

11

20

4.

09

15

5.

08

15

6.

05

10

Total

45

80

* There
may be minor deviation in marks distribution.
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