Salient features of this module are:

- Pre-requisites to Elements of Differential Calculus
- Graphical visualization
- Concept testing
- Unravelling examiners mind
- Memory structure (for derivations)
- Model question paper

**Course Contents: **

**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 Trigonometric 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

**JACOBIAN: **

**Jacobian – Understanding the Concept**- Purpose Definition
- Figure Discription
- Strategy
- Deriving the Jacobian

**Jacobian – (Formulating the Jacobian Matrix for Transformation)**- Formulating the Jacobian Matrix for Transformation

**Jacobian – Problems**- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Unravelling the Examiner’s Mind

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