Salient features of this module are:

- Pre-requisites to Elements of Differential & Integral Calculus
- Graphical visualization
- Concept testing
- Unravelling examiners mind
- 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)

**2nd ORDER DIFFERENTIAL EQUATION **

**Higher Order Differential Equation (Practical Understanding of Complementary and Particular Solution)**- Higher Order Differential Equation (Practial Understanding of Complementary and Particular Solution)

**Higher Order Differential Equation – (Understanding General solution for Complementary Function(CF))**- Higher Order Differential Equation – (Understanding General solution for Complementary Function(CF))

**Higher Order Homogenous DE’s – Problems**- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Unravelling Examiner’s Mind

**Higher Order Differential Equations – (Understanding General solution for Particular Integral (PI)**- Higher Order Differential Equations – (Understanding General solution for Particular Integral (PI)

**Higher order Non-homogenous DE’s – Problems**- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Unravelling Examiner’s Mind

**Variation of Parameters: (Introduction to Variation of Parameters)**- Variation of Parameters: (Introduction to Variation of Parameters)

**Higher Order DE’s – Variation of Parameters – Problems**- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Unravelling Examiner’s Mind

**Cauchy and Legendre homogenous equations**- Introduction

**Cauchy and Legendre homogenous equations – Problems**- Problem 1 (Cauchy DE)
- Problem 2 (Cauchy DE)
- Problem 3 (Cauchy DE)
- Problem 4 (Cauchy DE)
- Problem 5 (Legendre DE)
- Problem 6 (Legendre DE)
- Problem 7 (Legendre DE)
- Unravelling Examiner’s Mind

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