Engineering Mathematics I
Course Objectives: To provide students a sound knowledge of calculus and analytic geometry to apply them in their relevant fields.
 Derivatives and their Applications(14 hours)
 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 Function
 Taylor’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 Applications(11 hours)
 Introduction
 Definite Integrals and their properties
 Improper Integrals
 Differentiation under Integral Sign
 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(8 hours)
 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 (12 hours)
 First order and first degree Differential equations
 Homogenous Differential equations
 Linear differential equations
 Equations 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 equations
 Applications in Engineering field
Reference books:
 Erwin Kreyszig," Advance Engineering Mathematics" , John Wiley and Sons Inc
 Thomas,Finney",Calculus and Analytical geometry" Addison Wesley
 M. B. Singh, B. C. Bajrachrya," Differential Calculus", Sukunda Pustak Bhandar,Nepal
 M. B. Singh, S. P. Shrestha, "Applied Mathematics"
 G.D. Pant, G. S. Shrestha, "Integral Calculus and Differential Equations", Sunila Prakashan,Nepal
 M. R. Joshi, "Analytical Geometry", SukundaPustak Bhandar,Nepal
 S. P. Shrestha, H. D. Chaudhary, P. R. Pokharel,
"A Textbook of Engineering Mathematics  Vol I"
 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 
Marks Distribution* 
1 
14 
25 
2 
11 
20 
3 
08 
15 
4 
12 
20 
Total 
45 
80 
*Note: There may be minor deviation in marks distribution.
