Contents:

1. Integration

1.1 Introduction

1.2 Rules of Integration

1.3 Methods of Integration

2. Definite Integration

2.1 Introduction

2.2 Definition

2.3 Properties of Definite Integrals

3. Application of Definite Integrals

3.1 INTRODUCTION

Tracing of Curves

Area between Two Curves

Volume of Revolution

Answers for Exercise-III

Centre of Gravity

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. Laplace Transform

6.1 Introduction

6.2 Definition of Laplace Transform

6.3 Laplace Transform of Elementary Functions

Properties of Laplace Transform

First Shifting Property

Second Shifting Property

Multiplication by tn

Division by t Property

Use of Laplace transform in evaluation of certain integrals

6.4 Inverse Laplace Transform

Definition of Inverse Laplace transform

Inverse Laplace Transform of Standard Function

Properties of Inverse Laplace Transform

Inverse Laplace Transform by Method of Partial Fraction

6.5 Convolution Theorem

6.6 Laplace transform of Derivatives

6.7 Solution of Differential Equation using Laplace Transform (upto Second Order Equation)

7. Fourier Series

7.1 Introduction

7.2 Definition of Fourier Series (Euler’s Formula)

7.3 Series Expansion of continuous functions

Series Expansion of continuous Functions in (0, 2p)

Series expansion of continuous functions in (–p,p)

Series expansion of continuous functions in the interval (c, c + 2l)

Fourier Series expansion in (0, 2l)

Fourier Series Expansion in (–l, l)

7.4 Series Expansion of even and odd functions

Fourier Series Expansion of even and odd functions in (–p,p)

Fourier Series Expansion of Even and Odd Functions in (–l, l)

7.5 Half range Expansion

Half range cosine series

Half Range Sine Series

8. Numerical Solution of algebraic equation

8.1 Introduction

8.2 Bisection method

8.3 Regula Falsi method

8.4 Newton-Rapson method

9. Numerical solution of simultaneous equation

9.1 Introduction

9.2 Elimination method – Gauss elimination method

9.3 Gauss-Seidal method (Iterative Method)

9.4 Jacobi’s method