1. Relations and Functions

1. Introduction
2. Types of Relations
3. Types of Functions
4. Composition of Functions and Invertible Function
5. Binary Operations

2. Inverse Trigonometric Functions

1. Introduction
2. Basic Concepts
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

7. Integrals

7.1 Introduction

7.2 Integration as an Inverse Process of Differentiation

7.3 Methods of Integration

7.4 Integrals of some Particular Functions

7.5 Integration by Partial Fractions

7.6 Integration by Parts

7.7 Definite Integral

7.8 Fundamental Theorem of Calculus

7.9 Evaluation of Definite Integrals by Substitution

7.10 Some Properties of Definite Integrals

8. Application of Integrals

8.1 Introduction

8.2 Area under Simple Curves

8.3 Area between Two Curves

9. Differential Equations

9.1 Introduction

9.2 Basic Concepts

9.3 General and Particular Solutions of a Differential Equation

9.4 Formation of a Differential Equation whose General Solution is given

9.5 Methods of Solving First order, First Degree Differential Equations

10. Vector Algebra

10.1 Introduction

10.2 Some Basic Concepts

10.3 Types of Vectors

10.4 Addition of Vectors

10.5 Multiplication of a Vector by a Scalar

10.6 Product of Two Vectors

11. Three Dimensional Geometry

11.1 Introduction

11.2 Direction Cosines and Direction Ratios of a Line

11.3 Equation of a Line in Space

11.4 Angle between Two Lines

11.5 Shortest Distance between Two Lines

11.6 Plane

11.7 Coplanarity of Two Lines

11.8 Angle between Two Planes

11.9 Distance of a Point from a Plane

11.10 Angle between a Line and a Plane

12. Linear Programming

12.1 Introduction

12.2 Linear Programming Problem and its Mathematical Formulation

12.3 Different Types of Linear Programming Problems

13. Probability

13.1 Introduction

13.2 Conditional Probability

13.3 Multiplication Theorem on Probability

13.4 Independent Events

13.5 Bayes’ Theorem

13.6 Random Variables and its Probability Distributions

13.7 Bernoulli Trials and Binomial Distribution

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