Modern Tensor Calculus/Continuum Mech Textbook

In summary, the person is looking for a textbook on tensor calculus/continuum mechanics with a modern, colourful, and illustrative approach, with lots of physical examples, exercises, and summaries. They prefer an emphasis on engineering and mention two books they like in this style. Their focus is on fluid mechanics and they mention two recommended textbooks: Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Grinfield and Principles of Continuum Mechanics by Narasimhan. They also mention that the Grinfield text is supported with YouTube lectures by the author.
  • #1
humphreybogart
22
1
Hi,

I'm looking for a modern, colourful, illustrative introductory textbook to work through on tensor calculus/continuum mechanics. I'd like one with lots of physical examples, exercises, summaries, etc. I'd like an emphasis on engineering.

Something in the mould of Frank White's Fluid Mechanics or Çengel & Boles Thermodynamics: An Engineering Approach. I really love these textbooks and seem to learn much more efficiently from textbooks of this style.

My focus is on fluid mechanics, so there are certain areas of continuum mechanics that are more important than others (I suppose continuum kinematics is more relevant than elasticity?).

Thanks :)
 
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  • #2
Both of the following books are very readable...

Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Grinfield
Principles of Continuum Mechanics by Narasimhan
 
  • #3
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What is tensor calculus?

Tensor calculus is a branch of mathematics that deals with the concept of tensors, which are mathematical objects that describe the relationships between different quantities in a multidimensional space. It is used in various fields such as physics, engineering, and computer science to analyze and model complex systems.

How is tensor calculus used in modern science?

Tensor calculus is used in a wide range of applications, including continuum mechanics, relativity, electromagnetism, and fluid dynamics. It allows scientists to describe and analyze complex physical systems and make predictions about their behavior.

What is the difference between tensor calculus and vector calculus?

While vector calculus deals with vectors, which have both magnitude and direction, tensor calculus deals with tensors, which can have multiple components in different directions. Tensor calculus is a more general and powerful tool that encompasses vector calculus.

What is continuum mechanics?

Continuum mechanics is a branch of mechanics that studies the behavior of materials and fluids as continuous, rather than discrete, entities. It uses concepts from tensor calculus to describe and analyze the deformation and motion of materials under different forces and conditions.

How can I learn tensor calculus and continuum mechanics?

There are many textbooks available on modern tensor calculus and continuum mechanics that provide a comprehensive introduction to the subject. It is also recommended to have a solid foundation in calculus, linear algebra, and differential equations before diving into these advanced topics.

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