SH401

 

Subject: Engineering Mathematics

Studybook // Notes

Studybook - Solution set // Practice book

Old Question Set

Course objectives:

The main objective of the IOE TU Engineering Mathematics course is to provide students with a strong foundation in mathematical concepts and techniques that are essential for solving engineering problems. This course aims to develop the mathematical skills of students and equip them with the ability to apply mathematical techniques in real-world engineering applications. The course covers topics such as calculus, linear algebra, differential equations, complex variables, and Fourier series, among others. By the end of the course, students are expected to have a solid understanding of these mathematical concepts and be able to apply them to analyze and solve engineering problems.

Derivatives and their Applications

• Introduction
• Higher order derivatives
• Mean value theorem.
• Rolle’s theorem
• Lagrange’s mean value theorem
• Cauchy’s mean value theorem
• Power series of single valued functionTaylor’s series
• Maclaurin’s series
• Indeterminate forms: L Hospital rule
• Asymptotes to Cartesian and polar curves
• Pedal equations to Cartesian and polar curves; curvature and radius of curvature

Integration and its application

• Introduction
• Definite integrals and their properties
• Improper integrals
• Differentiation under integral signs
• Reduction formula: Beta Gama functions
• Application of integrals for finding areas arc length, surface and solid of revolution in the plane for Cartesian and polar curves

Plane Analytic Geometry

• Transformation of coordinates: Translation and rotation
• Ellipse and hyperbola: Standard forms, tangent and normal
•   General equation of conics in Cartesian and polar forms

Ordinary Differential equations and their applications

• First order and first degree differential equations
• Homogenous differential equations
• Linear differential equations
• Equation reducible to linear differential equations: Bernoulli’s equation
• First order and higher degree differential equation: Clairaut’s equation
• Second order and first degree linear differential equations with constant coefficients
• Second order and first degree linear differential equations with variable coefficients: Cauchy’s equation
• Applications in Engineering field

References:

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
8. Santosh Man Maskey, Calculus, Ratna Pustak Bhandar, Nepal
9. IOE Notes

Evaluation Scheme:

Chapters	Hours	Mark distribution
Derivatives and their Application	14	25
Integration and their Application	11	20
Plane analytical Geometry	8	15
Ordinary differential eqn. and their application	12	20
Total	45	80

* There may be a minor deviation in mark distribution.