## Description

This textbook is meant for students of first course on Algebra and Trigonometry. The book provides balanced coverage of both theory and practice of concepts. A wide variety of problems and lucid language will help students understand and apply the concepts easily. The step-by-step solutions to solved problems enables clear understanding. A variety of solved and unsolved problems have been incorporated to help students ace university and competitive examinations.

## Table of Content

**Chapter 1 Infinite Series **

1.1 Introduction

1.2 Definitions

1.3 General Properties of Series

1.3.1 Comparison Test (Form I)

1.3.2 Convergence of the Series ∑_(n=1)^∞▒1/n!

1.3.3 Convergence of the p− series ∑_(n=1)^∞▒1/np

1.3.4 Cauchy’s Root Test

1.4 D’ Alambert’s Ratio Test

1.5 Alternating Series

1.5.1 Leibnitz Test for Convergence of an Alternating Series

1.5.2 Absolute and Conditional Convergence

**Chapter 2 Binomial, Exponential and Logarithmic Series**

2.1 Binomial Series

2.2 Some Standard Binomial Expansions

2.3 Expansions and Approximations

2.4 Summation of Series

2.5 Exponential Series

2.5.1 Exponential Theorem

2.6 Standard Exponential Expansions

2.7 Expansions and Approximations

2.8 Summation of Series

2.9 Logarithmic Series

2.9.1 Logarithmic Theorem

2.9.2 Some Standard Expansions

2.9.3 Expansion, Approximation and Summation

**Chapter 3 Matrices**

3.1 Introduction

3.2 Rank of a Matrix

3.3 Vectors

3.3.1 Addition of Vectors

3.3.2 Scalar Multiplication of a Vector

3.3.3 Linear Combination of Vectors

3.3.4 Linear Dependence and Linear Independence of Vectors

3.3.5 Methods of Testing Linear Dependence or

Independence of a Set of Vectors

3.4 Consistency of a System of Linear Algebraic Equations

3.4.1 Rouche’s Theorem

3.4.2 System of Homogeneous Linear

3.5 Eigenvalues and Eigenvectors

3.5.1 Properties of Eigenvalues

3.6 Cayley − Hamilton Theorem

3.7 Similar Matrices

3.8 Diagonalisation of a Matrix

3.8.1 Calculation of Power of a Matrix A

3.8.2 Diagonalisation by Orthogonal Transformation or

Orthogonal Reduction

**Chapter 4 Theory of Equations**

4.1 Introduction

4.2 Relations between the Roots and the Coefficients of an

Algebraic Equation

4.3 Transformation of Equations

4.4 Reciprocal Equations

4.5 Numerical Methods for Approximate Roots

4.5.1 Horner’s Method

4.5.2 Newton’s Method

**Chapter 5 Expansions of Trigonometric Functions**

5.1 Expansions of cos nθ and sin nθ

5.2 Expansion of tan nθ in Powers of tan θ

5.3 Expansions of cos θ and sin θ in Ascending Powers of θ

5.4 Expansion of tan θ in Powers of θ

5.5 Expansions of cosn θ and sinn θ

**Chapter 6 Hyperbolic Functions and Logarithms of**

Complex Numbers

6.1 Exponential Forms of Circular Functions

6.2 Euler’s Formula

6.3 Hyperbolic Functions

6.4 Relations between Circular Functions and Hyperbolic Functions

6.5 Formulas Involving Hyperbolic Functions

6.6 Inverse Hyperbolic Functions

6.7 Logarithms of Complex Numbers

## About The Author

**T. Veerarajan** is Dean (Retd.), Department of Mathematics, Velammal College of Engineering and Technology, Madurai, Tamil Nadu. A Gold Medalist from Madras University, he has had a brilliant academic career all through. He has 50 years of teaching experience at undergraduate and postgraduate levels in various established engineering colleges in Tamil Nadu including Anna University, Chennai.

## New Product Tab

Here's your new product tab.

## Reviews

There are no reviews yet.