Salient features of this module are:

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

**Course Contents: **

**Pre-requisites to Maxima & Minima**

**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

**PRE-REQUISITES – ELEMENTS OF INTEGRAL CALCULUS**

**Pre-requisites – Elements of Integral Calculus**- Understanding Integration
- Concept of Integration – Elementary Example
- Introducing the Learning matrix
- Why is Integration an anti-differentiation process?
- Useful Rules and Symbolisms of Integration – (Rule 1)
- Useful Rules and Symbolisms of Integration – (Rule 2)
- Introducing Standard Integrals
- Deriving Integrals of Basic function
- Deriving Specific Integrals – 1
- Deriving Specific Integrals – 2
- Deriving Specific Integrals – 3
- Deriving Specific Integrals – 4
- Deriving Specific Integrals – 5
- Useful Rules of Definite Integrals – (Rule 1)
- Useful Rules of Definite Integrals – (Rule 2)
- Useful Rules of Definite Integrals – (Rule 3)
- Useful Rules of Definite Integrals – (Rule 4)

**1ST ORDER DIFFERENTIAL EQUATION**

**Engineering Relevance**- Understanding Formation of DE’s
- Predicting the System Behavior
- Testing System Behavior
- Complexities in Solving DE’s
- Need for PDE’s for Solving DE’s
- Understanding Non-linearity in DE’s
- A Brief Histor of DE’s

**Differential Equation(1st order)**- Understanding the Representations of DE’s
- Mathematical Observation of DE’s
- Deriving the Integrating Factor (IF)

**Linear and Bernoulli’s DE’s – Problem**- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Unravelling the Examiner’s Mind

**Non – Linear Differential Equation**- Engineering Relevance
- Introduction

**Non – Linear Differential Equation – Problems**- Problem 1 – ‘p’ type
- Problem 2 – ‘p’ type
- Problem 3 – ‘Clairaut’ type
- Problem 4 – ‘Clairaut’ type
- Problem 5 – ‘Reducible Clairaut’ type
- Problem 6 – ‘Reducible Clairaut’ type
- Unravelling Examiner’s Mind

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