Engineering Mathematics Volume II

995

Author: Dr C Vijayalakshmi

ISBN Print Book: 9788195268719

Copy Right Year: 2023

Pages: 884

Binding: Soft Cover

Publisher:  Yes Dee Publishing

Out of stock

SKU: 9788195268719 Category:

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.

Additional information

Weight .45 kg
Dimensions 22 × 16 × 2 cm

Table of Contents

Chapter 1 Matrices

1.1 Introduction

1.2 Matrix – Definition

1.2.1 Order of a Matrix

1.2.2 General form of a Matrix

1.3 Types of Matrices

1.4 Characteristic Equation

Examples 1.1 to 1.2

1.5 Eigen values and Eigenvectors

1.5.1 Working Rule for Finding Eigenvalues and Eigenvectors

1.5.2 Problems in Non-symmetric Matrix with Non-repeated Eigenvalues

Examples 1.3 to 1.7

1.5.3 Problems in Non-symmetric Matrix with Repeated Eigenvalues

Examples 1.8 to 1.10

1.5.4 Problems based on Symmetric Matrices with Non-repeated Eigenvalues

Examples 1.11 to 1.13

1.5.5 Problems based on Symmetric Matrix with Repeated Eigenvalues

Examples 1.14 to 1.15

Exercise 1.1

1.6 Properties of Eigenvalues and Eigenvectors

Examples 1.16 to 1.22

Exercise 1.2

Examples 1.23 to 1.30

Exercise 1.3

Examples 1.31 to 1.36

Exercise 1.4

Examples 1.37 to 1.50

Exercise 1.5

 

Chapter 2 Vector Calculus

2.1 Gradient

Examples 2.1 to 2.10

2.1.1 Directional Derivatives (DD)

2.1.2 Normal Derivative

Examples 2.11 to 2.17

Exercise 2.1

Examples 2.18 to 2.23

Exercise 2.2

2.2 Divergence and Curl

2.2.1 Vector Identities

Examples 2.24 to 2.41

Exercise 2.3

2.3 Line Integrals

2.3.1 Line Integral Over a Plane Curve

Examples 2.42 to 2.46

2.3.2 Surface Integral –Area of a Curved Surface

2.4 Green’s Theorem (for Plane)

Examples 2.47 to 2.58

Exercise 2.4

Examples 2.59 to 2.67

Exercise 2.5

Examples 2.68 to 2.74

Exercise

 

Chapter 3 Analytic Function

3.1 Complex Numbers

3.2 Necessary Condition for f(z) to be Analytic [Cauchy – Riemann Equations]

Examples 3.1 to 3.17

3.3 Harmonic Functions

Examples 3.18 to 3.22

3.4 Properties of Analytic Functions

Examples 3.23 to 3.27

3.5 Construction of Analytic Function

Examples 3.28 to 3.47

3.6 Some Standard Transformations

3.6.1 Translation

Examples 3.48 to 3.52

3.6.2 Magnification and Rotation

Examples 3.53 to 3.56

3.6.3 Transformation w =1/z

Examples 3.57 to 3.65

3.6.4 Transformation w = z2

Examples 3.66 to 3.68

3.7 Bilinear Transformation

Examples 3.69 to 3.82

 

Chapter 4 Complex Integration

4.1 Fundamentals of Complex Integrals

4.2 Cauchy’s Integral Theorem or Cauchy’s Fundamental Theorem

Examples 4.1 to 4.5

4.3 Cauchy’s Integral Formula for Derivatives

Examples 4.6 to 4.21

Exercise 4.1

Examples 4.22 to 4.30

Exercise 4.2

Examples 4.31 to 4.49

Exercise 4.3

Examples 4.50 to 4.55

Exercise 4.4

Examples 4.56 to 4.67

Exercise 4.5

Examples 4.68 to 4.75

Exercise 4.6

Examples 4.76 to 4.92

 

Chapter 5 Laplace Transform

5.1 Laplace Transform – Sufficient Condition for Existence

5.2 Laplace Transform of Elementary Functions

Examples 5.1 to 5.5

Exercise 5.1

5.3 Properties of Laplace Transforms

Examples 5.6 to 5.9

Exercise 5.2

5.4 Derivatives of Laplace Transform [Multiplication by t]

Examples 5.10 to 5.11

Exercise 5.3

5.5 Integration of Laplace Transform [Division by t]

Examples 5.12 to 5.16

Exercise 5.4

5.6 Transforms of Derivatives and Integrals

5.7 Laplace Transforms of Integrals

Examples 5.17 to 5.20

Exercise 5.5

Examples 5.21 to 5.22

Exercise 5.6

5.8 Evaluation of Integrals Using Laplace Transform

Examples 5.23 to 5.24

Exercise 5.7

5.9 Initial and Final Value Theorems

Examples 5.25 to 5.32

Exercise 5.6

5.10 Unit Step Function or Heaviside’s Unit Step Function

Examples 5.33 to 5.34

5.11 Unit Impulse Function [Dirac Delta]

Examples 5.35 to 5.36

5.12 Laplace Transform of Periodic Functions

Examples 5.37 to 5.45

Exercise 5.9

5.13 Inverse Laplace Transform

Examples 5.46 to 5.48

Exercise 5.10

Examples 5.49 to 5.56

Exercise 5.11

5.14 Multiplication by s

Examples 5.57

5.15 Division by s

Examples 5.58

Exercise 5.12

5.16 Inverse Laplace Transform of Derivatives

Examples 5.59 to 5.61

Exercise 5.13

5.17 Inverse Laplace Transform by Method of Partial Fraction

Examples 5.62 to 5.70

5.18 Method of Convolution

Examples 5.71 to 5.80

Exercise 5.14

5.19 Application of Laplace Transform to the Solution of Linear Second Order

Ordinary Differential Equations with Constant Coefficients

Examples 5.81 to 5.102

Exercise 5.15

5.20 Solving Integral Equations

Examples 5.103 to 5.105

About the Author

Dr C Vijayalakshmi is Associate Professor, Department of Statistics and Applied Mathematics, Central University of Tamil Nadu, Thiruvarur, Tamil Nadu, India. She has 23 years of experience teaching both undergraduates and postgraduates.

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