Syllabus  Engineering Mathematics I  for Tribhuvan University, Institute of Engineering first year first semester of all faculties
ENGINEERING MATHEMATICS I
SH 401
Lecture: 3 Year:
I
Tutorial:
2 Part:
I
Practical
:
Course Objectives: To provide students a sound
knowledge of calculus and
analytic geometry to apply them in their relevant fields.
analytic geometry to apply them in their relevant fields.
1.
Derivatives and their Applications (14
hours)
1.1. Introduction
1.2. Higher order derivatives
1.3. Mean value theorem
1.3.1. Rolle’s Theorem
1.3.2. Lagrange’s mean value theorem
1.3.3. Cauchy’s mean value theorem
1.4. Power series of single valued function
1.4.1. Taylor’s series
1.4.2. Maclaurin’s series
1.5. Indeterminate forms; L’Hospital rule
1.6. Asymptotes to Cartesian and polar curves
1.7. Pedal equations to Cartesian and polar
curves; curvature and radius of curvature
2.
Integration and its Applications (11
hours)
2.1. Introduction
2.2. Definite integrals and their properties
2.3. Improper integrals
2.4. Differentiation under integral sign
2.5. Reduction formula; Beta Gama functions
2.6. Application of integrals for finding
areas, arc length, surface and
solid of revolution in the plane for Cartesian and polar curves
solid of revolution in the plane for Cartesian and polar curves
3.
Plane Analytic Geometry (8
hours)
3.1. Transformation of coordinates: Translation
and rotation
3.2. Ellipse and hyperbola; Standard forms,
tangent, and normal
3.3. General equation of conics in Cartesian
and polar forms
4.
Ordinary Differential Equations and their
Applications (12
hours)
4.1. First order and first degree differential
equations
4.2. Homogenous differential equations
4.3. Linear differential equations
4.4. Equations reducible to linear differential
equations; Bernoulli’s equation
4.5. First order and higher degree differential
equation; Clairaut’s equation
4.6. Second order and first degree linear
differential equations with constant
coefficients.
4.7. Second order and first degree linear
differential equations with variable coefficients; Cauchy’s equations
4.8. Applications in engineering field
Reference books:
1.
Erwin Kreyszig, Advance
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, S. P. Shrestha, Applied Mathematics,
5.
G.D. Pant, G. S. Shrestha,
Integral Calculus and Differential Equations, Sunila Prakashan,Nepal
6.
M. R. Joshi, Analytical
Geometry, SukundaPustak Bhandar,Nepal
7.
S. P. Shrestha, H. D.
Chaudhary, P. R. Pokharel,
A Textbook of Engineering Mathematics  Vol I
A Textbook of Engineering Mathematics  Vol I
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:
Chapters

Hours

Mark
distribution*

1.

14

25

2.

11

20

3.

08

15

4.

12

20

Total

45

80

* There may be minor
deviation in marks distribution.
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