Engineering Mathematics II
Course Objectives:
 To develop the skill of solving differential equations and to provide knowledge of vector algebra and calculus
 To make students familiar with calculus of several variables and infinite series
 Calculus of Two or more variables(6 hours)
 Introduction: Limit and Continuity
 Partial Derivatives
 Homogeneous function, Euler’s theorem for the function of two and three variables
 Total Derivatives
 Extrema of functions of two and three variables: Lagrange’s Multiplier
 Multiple Integrals(6 hours)
 Introduction
 Double Integrals in Cartesian and Polar form: Change of order of integration
 Triple Integrals in Cartesian, Cylindrical and Spherical coordinates
 Area and Volume by Double and Triple Integrals
 Three Dimensional Solid Geometry(11 hours)
 The Straight Line; Symmetric and General form
 Coplanar Lines
 Shortest Distance
 Sphere
 Plane Section of a Sphere by Planes
 Tangent Planes and Lines to the Spheres
 Right Circular Cone
 Right Circular Cylinder
 Solution of Differential Equations in Series and Special Functions(9 hours)
 Solution of Differential Equation by Power Series Method
 Legendre’s Equation
 Legendre's Polynomial function: Properties and Applications.
 Bessel’s Equation
 Bessel’s Function of First and Second kind: Properties and Applications
 Vector Algebra and Calculus(8 hours)
 Introduction
 Two and Three dimensional vectors
 Scalar Products and Vector Products
 Reciprocal System of Vectors
 Application of Vectors: Lines and Planes
 Scalar and Vector fields
 Derivatives– Velocity and Acceleration
 Directional Derivatives
 Infinite Series(5 hours)
 Introduction
 Series with Positives terms
 Convergence and Divergence
 Alternating series: Absolute convergence
 Radius and Interval of Convergence
References:
 Erwin Kreyszig, "Advanced 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, B. C. Bajrachrya, "A text book of Vectors", 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
 Y. R. Sthapit, B. C. Bajrachrya, "A text book of Three Dimensional Geometry", Sukunda Pustak Bhandar,Nepal
 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 
*Note: There may be minor deviation in marks distribution.
