# Engineering Math-I

### SH 401

Lecture:3 Year: I

Tutorial: 2 Part: I

Practical: 0

#### Course Objectives:

To provide students a sound knowledge of calculus and analytic geometry to apply them in relevant fields

- 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 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 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

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