# Engineering Mathematics - I

# 1. Derivatives and their Applications

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 application

2.1 Introduction

2.2 Definite integrals and their properties

2.3 Improper integrals

2.4 Differentiation under integral signs

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

3. Plane Analytic Geometry

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

4.1 First order and first-degree differential equations

4.2 Homogenous differential equations

4.3 Linear differential equations

4.4 Equation 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 equation

4.8 Applications in Engineering field

Evaluation / Marking Scheme:

Chapters | Hours | Mark distribution |

1. | 14 | 25 |

2. | 11 | 20 |

3. | 8 | 15 |

4. | 12 | 20 |

Total | 45 | 80 |

There may be a minor deviation in marks distribution.

Reference books:

1. Erwin Kreyszig, Advanced 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

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