# Engineering Mathematics Syllabus details and with their marks distribution

## Course Objectives:

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

From Chapter 1 - 25 marks
From Chapter 2 - 20 marks
From Chapter 3 - 15 marks
From Chapter 4 - 20 marks

Note:- These marks may be changed.

1) Derivatives and their Applications ( 14 h | 25 Marks )
1. Introduction
2. Higher-order derivatives
3. Mean value theorem
4. Power series of single-valued functions
5. Indeterminate forms: L-Hospital Rule
6. Asymptotes to cartesian and polar curves
7. Pedal equation to cartesian and polar curves: Curvature and radius of curvature
2) Integration and its applications ( 11 h | 20 Marks )
1. Introduction
2. Definite integrals and their properties
3. Improper integrals
4. Differentiation under the integral sign
5. Reduction formula: Beta Gama functions
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 ( 8 h | 15 Marks)
1. Transformation of coordinates: Translation and rotation
2. Ellipse and Hyperbola: Standard forms, Tangent and Normal
3. General equation of conics in cartesian and polar forms
4) Ordinary Differential Equations and their Applications ( 12 h | 20 Marks )
1. First-order and first-degree differential equations
2. Homogenous differential equations
3. Linear differential equations
4. Equations reducible to linear differential equations: Bernoulli's equations
5. First-order and Higher degree differential equation: Clairaut's equations
6. Second-order and First-degree linear differential equations with constant coefficients
7. Second-order and First-degree linear differential equations with variable coefficients: Cauchy's equations
8. Application in Engineering Field