## Description

This book is written for the undergraduate students of all Engineering disciplines. It offers comprehensive coverage of all topics with step by step problem solving procedures. This book gives the instructors maximum flexibility in selecting the material and tailoring it to their needs. The modern approach in this book will prepare the students for the future tasks. The material lays a good foundation of Engineering Mathematics that will help the students in their careers and in further studies.

• Pedagogy includes solved examples and exercise problems.

• Numerous specific examples clarifying the essence of the topics and methods for solving problems and equations along with real time applications.

• Concise and coherent survey of the most important definitions, formulae, equations, methods and theorems.

## Table of Content

**Chapter 1 Differential Calculus**

1.1 Representation of Functions

1.1.1 Representing a Function Numerically

1.1.2 Representing a Function Graphically

1.1.3 Piece wise Functions

Solved Problems (Problem 1.1 to 1.11)

1.1.4 Types of Function

Exercise 1.1

1.2 Limit of a Function

Solved Problems (Problem 1.12 to 1.50)

1.3 Continuity of a Function

Solved Problems (Problem 1.51 to 1.55)

Exercise 1.2

1.4 Derivatives

Solved Problems (Problem 1.56 to 1.69)

Exercise 1.3

Solved Problems (Problem 1.70 to 1.126)

Exercise 1.4

1.5 Test for Derivatives

Solved Problems (Problem 1.127 to 1.181)

Miscellaneous Problems

Exercise 1.5

**Chapter 2 Functions of Several Variables**

2.1 Partial Differentiation

Solved Problems (Problem 2.1 to 2.8)

2.2 Euler’s Theorem for Homogeneous Functions

Solved Problems (Problem 2.9 to 2.13)

Exercise 2.1

2.3 Partial Differentiation of Implicit Functions

Solved Problems (Problem 2.14 to 2.32)

Exercise 2.2

Solved Problems (Problem 2.33 to 2.47)

Exercise 2.3

Solved Problems (Problem 2.48 to 2.59)

Exercise 2.4

Solved Problems (Problem 2.60 to 2.71)

Exercise 2.5

Solved Problems (Problem 2.72 to 2.83)

Exercise 2.6

**Chapter 3 Integral Calculus**

3.1 Indefinite Integral and Definite Integral

3.1.1 Fundamental Theorem of Calculus

3.1.2 Riemann Sum

Solved Problems (Problem 3.1 to 3.6)

Exercise 3.1

3.2 Method of Substitution (Change of the Independent Variables)

Solved Problems (Problem 3.7 to 3.13)

3.3 Integration of Rational Function using Partial Fraction

3.3.1 Proper and Improper Functions

Solved Problems (Problem 3.14 to 3.20)

Exercise 3.2

Solved Problems (Problem 3.21)

3.4 Integration by Parts

Solved Problems (Problem 3.22 to 3.26)

Exercise 3.3

3.5 Trigonometric Integrals

Solved Problems (Problem 3.27 to 3.30)

Exercise 3.4

3.5.1 Trigonometric Substitutions

Solved Problems (Problem 3.31 and 3.32)

3.5.2 Integration of Special Functions

Solved Problems (Problem 3.33 to 3.38)

Exercise 3.5

3.6 Rational Function

Solved Problems (Problem 3.39 to 3.44)

3.7 Integration of Irrational Function

Solved Problems (Problem 3.45 to 3.48)

Exercise 3.6

3.8 Improper Integrals

Solved Problems (Problem 3.49 to 3.62)

Exercise 3.7

**Chapter 4 Multiple Integrals**

4.1 Double Integration in Cartesian Coordinates

Solved Problems (Problem 4.1 to 4.18)

Exercise 4.1

4.2 Double Integration in Polar Coordinates

Solved Problems (Problem 4.19 to 4.25)

Exercise 4.2

4.3 Change of Order of Integration

Solved Problems (Problem 4.26 to 4.35)

4.4 Change of Variables

Solved Problems (Problem 4.36 to 4.41)

Exercise 4.3

4.5 Area Enclosed by Plane Curves =

Solved Problems (Problem 4.42 to 4.49)

4.5.1 Polar Coordinates

Solved Problems (Problem 4.50 to 4.58)

Exercise 4.4

4.6 Triple Integration in Cartesian Coordinates

Solved Problems (Problem 4.59 to 4.76)

Exercise 4.5

**Chapter 5 Ordinary Differential Equation**

5.1 Differential Equation

5.1.1 Linear Differential Equations with Constant Coefficients

Solved Problems (Problem 5.1 to 5.49)

Exercise 5.1

Solved Problems (Problem 5.50 to 5.62)

5.1.2 Legendre’s Linear Equation

Solved Problems (Problem 5.63 to 5.68)

Exercise 5.2

5.1.3 Simultaneous First Order Linear Equation with Constant Coefficients

Solved Problems (Problem 5.69 to 5.78)

Exercise 5.3

5.2 Method of Variation of Parameters

Solved Problems (Problem 5.79 to 5.91)

Exercise 5.4

5.3 Method of Undetermined Coefficients

Solved Problems (Problem 5.92 to 5.100)

• Appendix A Solved Question Papers

• Appendix B Formulas and Theorems for Reference

• Appendix C Formulas (to differential equations)

## About The Authors

**Dr. C. Vijayalakshmi** is Associate Professor, Mathematics Division, School of Advanced Sciences, Vellore Institute of Technology, Chennai. She has 23 years of experience teaching both undergraduates and postgraduates.

** ****Dr. K. SIVASELVAN** is Associate Professor, Jeppiaar Engineering college, Chennai. He has 16 years of experience teaching both undergraduates and postgraduates.

**Dr. R. SUBRAMANI** is Assistant Professor, Kristu Jayanti Collge, Bengaluru. His area of specilisation includes Advanced Optimization Techniques and Stochastic Processes.

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