1. Relations and Functions

1.1 Introduction

1.2 Types of Relations

1.3 Types of Functions

1.4 Composition of Functions and Invertible Function

1.5 Binary Operations

2. Inverse Trigonometric Functions

2.1 Introduction

2.2 Basic Concepts

2.3 Properties of Inverse Trigonometric Functions

3. Matrices

3.1 Introduction

3.2 Matrix

3.3 Types of Matrices

3.4 Operations on Matrices

3.5 Transpose of a Matrix

3.6 Symmetric and Skew Symmetric Matrices

3.7 Elementary Operation (Transformation) of a Matrix

3.8 Invertible Matrices

4. Determinants

4.1 Introduction

4.2 Determinant

4.3 Properties of Determinants

4.4 Area of a Triangle

4.5 Minors and Cofactors

4.6 Adjoint and Inverse of a Matrix

4.7 Applications of Determinants and Matrices

5. Continuity and Differentiability

5.1 Introduction

5.2 Continuity

5.3 Differentiability

5.4 Exponential and Logarithmic Functions

5.5 Logarithmic Differentiation

5.6 Derivatives of Functions in Parametric Forms

5.7 Second Order Derivative

5.8 Mean Value Theorem

6. Application of Derivatives

6.1 Introduction

6.2 Rate of Change of Quantities

6.3 Increasing and Decreasing Functions

6.4 Tangents and Normals

6.5 Approximations

6.6 Maxima and Minima

Appendix 1: Proofs in Mathematics

A.1.1 Introduction

A.1.2 What is a Proof?

Appendix 2: Mathematical Modelling

A.2.1 Introduction

A.2.2 Why Mathematical Modelling?

A.2.3 Principles of Mathematical Modelling