ABSTRACT
This project work is on Elementary Study on Tensor Algebra focuses on how to tackle physical quantities that are more complicated in nature which cannot be described by scalars and vectors. This work lets us understand how to solve problem with more than three components which scalars and vector cannot tackle. Some key concepts of tensors like Rank and order of tensor, spaces in N-Dimension, coordinate transformation, zeroth-order tensors up to second-order tensors were taken into consideration. With solved problems, stress tensor have been explicitly considered as a backup in understanding this work.Â
TABLE OF CONTENTS
TITLE PAGE i
CERTIFICATION ii
DECLARATION iii
ACKNOWLEDGEMENTS v
ABSTRACT vi
TABLE OF CONTENTS vi
CHAPTER ONE: GENERAL INTRODUCTION
1.1 Introduction 1
1.2 Aim and Objectives of the Study 4
1.3 Scope of the Study 5
CHAPTER TWO: REVIEW OF BASIC CONCEPT IN VECTOR ANALYSIS
2.1 Representing Vector Quantities 9
2.2 Position Vectors                                                               10
2.3 Some Notation in Vectors 14
2.4 Addition of Vectors 15
2.5 Subtraction of Vectors 16
2.6 Gradient of a Scalar Function 17
2.7 The Divergence of a Vector Field 18
2.8 Curl of a Vector Field 19
CHAPTER THREE: METHODOLOGY
3.1 Properties of Tensors 25
3.2 Algebra of Tensor 26
3.3 Spaces of N Dimension 29
3.4 Coordinate Transformation 29
3.5 Rank and Order of Tensor 31
3.6 Tensor Field                                                                     32
3.7 Zeroth-Order Tensors 34
3.8 First-Order Tensor 35
3.9 Second-Order Tensors 37
3.10 Stress as a Second-Order Tensor 38
CHAPTER FOUR: ANALYSIS/RESULT
4.1 The Historical Example (Problem) 40
4.2 Problems and Solutions                                                  40
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION 47
REFERENCES 50
