**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 )

- Introduction
- Higher-order derivatives
- Mean value theorem
- Power series of single-valued functions
- Indeterminate forms: L-Hospital Rule
- Asymptotes to cartesian and polar curves
- Pedal equation to cartesian and polar curves: Curvature and radius of curvature

2) Integration and its applications ( 11 h | 20 Marks )

- Introduction
- Definite integrals and their properties
- Improper integrals
- Differentiation under the 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

3) Plane Analytic Geometry ( 8 h | 15 Marks)

- Transformation of coordinates: Translation and rotation
- Ellipse and Hyperbola: Standard forms, Tangent and Normal
- General equation of conics in cartesian and polar forms

4) Ordinary Differential Equations and their Applications ( 12 h | 20 Marks )

- First-order and first-degree differential equations
- Homogenous differential equations
- Linear differential equations
- Equations reducible to linear differential equations: Bernoulli's equations
- First-order and Higher degree differential equation: Clairaut's equations
- 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
- Application in Engineering Field

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