Tensor Analysis for Engineers : : Transformations - Mathematics - Applications / / Mehrzad Tabatabaian.

• VerfasserIn: Tabatabaian, Mehrzad,
• Place / Publishing House: Dulles, VA : : Mercury Learning and Information, , [2023]; ©2023
• Year of Publication: 2023
• Language: English
• Physical Description: 1 online resource (234 p.)

Tensor analysis is used in engineering and science fields. This new edition provides engineers and applied scientists with the tools and techniques of tensor analysis for applications in practical problem solving and analysis activities. It includes expanded content on the application of mechanical stress transformation. 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. In addition, the book has several worked-out examples for helping the readers with mastering the topics provided in the prior sections.

Table of Contents

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: Mechanical Stress Transformation: Analytical and Mohr’s Circle Methods -- Chapter 17: The Worked Examples -- Chapter 18: Exercises -- References -- Index