Contents:

1. Integration

1.1 Introduction

Definition of Integration

Indefinite Integration or General Integral

Standard Formulae

1.2 Rules of Integration

Modification of Formulae for Linear Expression (nx + d)

Integration of Simple Rational Function

Integration by Trigonometric Transformation

1.3 Methods of Integration

Integration by Substitution

Important Deductions

Some Standard Substitutions

Integration by Parts and Partial Fraction

2. Definite Integration

2.1 Introduction

2.2 Definition

Rules of Definite Integrals

2.3 Properties of Definite Integrals

3. Application of Definite Integrals

3.1 INTRODUCTION

Tracing of Curves

Area between Two Curves

Volume of Revolution

Centre of Gravity 25

Centroid of Plane Lamina

Mean Value OR Average Value

Root Mean Square Value (RMS value)

4. Differential Equation

4.1 INTRODUCTION

Definition

Formation of Differential Equation

4.2 Solution of first order first degree differential Equation

Variable Separable

Equation Reducible to Method of Variables Separable form by suitable substitutions

Homogeneous Differential Equations

Equations Reducible to Homogeneous Form

Linear Differential Equations

Exact differential Equation

4.3 BERNOULLI’S Equations

(Non-linear differential equation)

5. Application of Differential Equation

5.1 Application of Differential equations

Introduction

Applications of Differential Equations

Kirchhoff’s Laws

Application to LRC Circuits

6. Interpolation

6.1 Introduction

Lagrange’s Interpolation Formula

6.2 Forward and Backward Differences

Forward Differences

Backward Differences

6.3 Newton’s Forward Difference Interpolation Formula

6.4 Newton’s Backward Difference Interpolation Formula

6.5 Concept of Extrapolation

7. Numerical differentiation and integration

7.1 Newton’s Forward and Backward Difference Formula for Differentiation

Newton’s Forward Difference Formula for Differentiation

Newton’s Backward Difference Formula for Differentiation

7.2 Numerical Integration

Trapezoidal Rule

Simpson’s One-third Rule

8. Numerical Solution of Ordinary Differential Equation

8.1 Introduction

8.2 Runge-Kutta Method of Second Order

8.3 Runge-Kutta Method for Fourth Order

9. Discrete Mathematics

9.1 Relational Algebra

9.2 Definition of a set

Methods for Describing Sets

9.3 Types of Sets

Operations on Set

Counting Principle

Principle of Inclusion – Exclusion

Cartesian Product

Relation

Function