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Transformations - Mathematics - Applications

Tensor Analysis for Engineers

Frontmatter

CONTENTS

Preface

About the Author

Chapter 1: Introduction

Chapter 2: Coordinate Systems Definition

Chapter 3: Basis Vectors and Scale Factors

Chapter 4: Contravariant Components and Transformations

Chapter 5: Covariant Components and Transformations

Chapter 6: Physical Components and Transformations

Chapter 7: Tensors—Mixed and Metric

Chapter 8: Metric Tensor Operation on Tensor Indices

Chapter 9: Dot and Cross Products of Tensors

Chapter 10: Gradient Vector Operator—Christoffel Symbols

Chapter 11: Derivative Forms—Curl, Divergence, Laplacian

Chapter 12: Cartesian Tensor Transformation—Rotations

Chapter 13: Coordinate Independent Governing Equations

Chapter 14: Collection of Relations for Selected Coordinate Systems

Chapter 15: Rigid Body Rotation: Euler Angles, Quaternions, and Rotation Matrix

Chapter 16: Worked-out Examples

Chapter 17: Exercise Problems

References

Index

Tensor analysis is used in engineering and science fields. This new edition provides engineers and applied scientists the tools and techniques of tensor analysis for applications in practical problem solving and analysis activities. The geometry is limited to the Euclidean space/geometry, where the Pythagorean Theorem applies, with well-defined Cartesian coordinate systems as the reference. Quantities defined in curvilinear coordinate systems, like cylindrical, spherical, parabolic, etc. are discussed and several examples and coordinates sketches with related calculations are presented.

Tensor analysis is used in engineering and science fields. This new edition provides engineers and applied scientists the tools and techniques of tensor...

Format

Tensor Analysis for Engineers

Transformations - Mathematics - Applications

Mehrzad Tabatabaian

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