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Tensor Analysis for Engineers
Tensor Analysis for Engineers

Tensor Analysis for Engineers: Mastering Coordinate Systems, Transformations and Applications using Mathematics

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Profile Icon Mercury Learning and Information Profile Icon Mehrzad Tabatabaian
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€59.99
eBook Aug 2024 196 pages 1st Edition
eBook
€59.99
Arrow left icon
Profile Icon Mercury Learning and Information Profile Icon Mehrzad Tabatabaian
Arrow right icon
€59.99
eBook Aug 2024 196 pages 1st Edition
eBook
€59.99
eBook
€59.99

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Key benefits

  • Covers foundational and advanced concepts in tensor analysis
  • Focuses on practical engineering applications and problem-solving
  • Includes numerous examples and exercises to reinforce learning

Description

This book is a comprehensive guide to tensor analysis for engineers and applied scientists, focusing on practical problem-solving in Euclidean space. It covers Cartesian coordinate systems and curvilinear coordinates like cylindrical and spherical, with examples and calculations. Expanded content includes rigid body rotation, Cartesian tensors, Euler angles, and quaternion methods. The course begins with coordinate systems, moving through curvilinear systems, basis vectors, and scale factors. It covers contravariant and physical components, tensor transformations, and mixed and metric tensors. Advanced topics include gradient operators, derivative forms, Cartesian tensor transformations, and coordinate-independent equations. The book features relations for selected coordinate systems, rigid body rotation methods, and numerous worked-out examples and exercises. Mastering tensor analysis is crucial for complex engineering and science problems. This book transitions from basic concepts to advanced applications, blending theory with practical examples. Clear explanations, figures, and exercises enhance learning, making this an essential resource for tensor analysis in Euclidean space.

Who is this book for?

Ideal for engineering students, professionals, and researchers who want to understand and apply tensor analysis in their work. Readers should have a basic understanding of linear algebra and calculus. No prior knowledge of tensor analysis is required.

What you will learn

  • Understand index notation and the Einstein summation convention
  • Learn to define and transform coordinate systems
  • Calculate dot and cross products of tensors
  • Apply metric tensor operations
  • Compute covariant and contravariant derivatives
  • Solve practical engineering problems using tensor analysis

Product Details

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Publication date, Length, Edition, Language, ISBN-13
Publication date : Aug 13, 2024
Length: 196 pages
Edition : 1st
Language : English
ISBN-13 : 9781836648246
Category :

What do you get with eBook?

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Product feature icon Download this book in EPUB and PDF formats
Product feature icon DRM FREE - Read whenever, wherever and however you want
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OR
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Product Details

Publication date : Aug 13, 2024
Length: 196 pages
Edition : 1st
Language : English
ISBN-13 : 9781836648246
Category :

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Table of Contents

20 Chapters
About the Author Chevron down icon Chevron up icon
Chapter 1: Introduction Chevron down icon Chevron up icon
Chapter 2: Coordinate Systems Definition Chevron down icon Chevron up icon
Chapter 3: Basis Vectors and Scale Factors Chevron down icon Chevron up icon
Chapter 4: Contravariant Components and Transformations Chevron down icon Chevron up icon
Chapter 5: Covariant Components and Transformations Chevron down icon Chevron up icon
Chapter 6: Physical Components and Transformations Chevron down icon Chevron up icon
Chapter 7: Tensors—Mixed and Metric Chevron down icon Chevron up icon
Chapter 8: Metric Tensor Operation on Tensor Indices Chevron down icon Chevron up icon
Chapter 9: Dot and Cross Products of Tensors Chevron down icon Chevron up icon
Chapter 10: Gradient Vector Operator—Christoffel Symbols Chevron down icon Chevron up icon
Chapter 11: Derivative Forms—Curl, Divergence, Laplacian Chevron down icon Chevron up icon
Chapter 12: Cartesian Tensor Transformation—Rotations Chevron down icon Chevron up icon
Chapter 13: Coordinate Independent Governing Equations Chevron down icon Chevron up icon
Chapter 14: Collection of Relations for Selected Coordinate Systems Chevron down icon Chevron up icon
Chapter 15: Rigid Body Rotation: Euler Angles, Quaternions, and Rotation Matrix Chevron down icon Chevron up icon
Chapter 16: Worked-out Examples Chevron down icon Chevron up icon
Chapter 17: Exercise Problems Chevron down icon Chevron up icon
References Chevron down icon Chevron up icon
Index Chevron down icon Chevron up icon
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