Salient features of this module are:

- Pre-requisites to polar curves
- Graphical visualization
- Concept testing
- Unravelling examiners mind
- Memory structure (for derivations)
- Model question paper

**Course Contents:Â **

**Pre-requisites to Elements of Differential Calculus**

**Sign of Trigonometric Identities**- Sign of Trigonometric Identities – Introduction
- Sign of Trigonometric Identities – Quad I
- Sign of Trigonometric Identities – Quad II
- Sign of Trigonometric Identities – Quad III
- Sign of Trigonometric Identities – Quad IV
- Sign of Trigonometric Identities – Summary
- Sign of Trigonometric Identities – 1
- Sign of Trigonometric Identities – 2

**General solution for TrigonometricÂ ratios**- General solution for Trigonometric ratios (Example 1)
- General solution for Trigonometric ratios (Example 2)
- General solution for Trigonometric ratios (Example 3)
- General solution for Trigonometric ratios (Example 4)

**Concept of derivate – Slope**- Concept of Derivative – Slope – Straight line
- Concept of Derivative – Slope – Curve

**Differentiation of Basic functions**- Introduction – Chain and Quotient Rules
- Derivative of tan x
- Derivative of sec x
- Derivative of cosec x
- Derivative of cot x
- Derivative of [y = e^x * x^n]
- Derivative of [y = tan^(-1) x
- Derivative of [y = x/(ax+b)] – Quotient rule
- Derivative of [y = x/(ax+b)] – Chain rule
- Derivative of [x^2 + y^2 = k]
- Derivative of [y = 1/sqrt(ax^2 +b)]
- Derivative of [y = a^x (log (1+x^2))]
- Derivative of [y = a^sinx (1+sin^2 (x)) sec x]
- Graphical understanding of trigonometric derivatives

**Application of Derivative**- Finding nature of the curve
- Interpreting curvature of a curve
- Linearization of a curve
- L-Hospital Rule
- Use of second derivative (curvature)
- Maxima & Minima – 1
- Maxima & Minima – 2

**Angle between Curves & Radius of curvature**- Essential trigonometric identities 1
- Essential trigonometric identities 2
- Essential trigonometric identities 3
- Essential trigonometric identities 4
- Essential trigonometric identities 5

**Angle between polar curves**

**Introduction to Polar curves**- Introduction

**Polar and Cartesian EquivalenceÂ**- Polar and Cartesian Equivalence

**Converting Cartesian and Polar curves**- Parabola â€“ Cartesian to Polar
- Circle – Polar to Cartesian
- Offset Circle – Cartesian to Polar
- Cardioid – Polar and Cartesian Equivalence
- Rose Curve – Polar and Cartesian Equivalence

**Parametric Equation for Cycloid**- Visualizing the Cycloid formation

**Parametric Equation for Ellipse**- Parametric Equation for Ellipse

**Polar Curves**- Introduction to angle between curves
- Evolution of angle between geometric entities
- Angle between radius and tangent vector – Purpose Definition
- Angle between radius and tangent vector – Understanding the Figure
- Angle between radius and tangent vector – Strategy
- Angle between radius and tangent vector – Derivation
- Angle between radius and tangent vector – Derivation 1 and Common Mistakes
- Angle between radius and tangent vector – Incidental Facts
- Angle between radius and tangent vector – Memory Structure
- Procedure for angle between two curves

**Solving angle between curvesÂ**- Problem 1 (circle)
- Problem 1 – Method 2 (circle)
- Problem 2 (cardioid)
- Problem 2 – Critical observations
- Problem 3
- Problem 4
- Problem 4 (Method 2)
- Problem 5 (Parabola)
- Problem 6 (Cardioid Slope)
- Problem 7
- Problem 8
- Unravelling the Examiners Mind

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