A Geometrical Introduction to Tensor Calculus

Tensor calculus has a huge series of applications across the physical sciences. From machine learning to fundamental physics, a solid foundation in tensor calculus and differential geometry is becoming more essential. 

Despite these skills being in such high regard, the texts that currently exist to support the learning and reinforcement of tensor calculus are, for the most part, too terse and technical in nature. For students who are not inherently pure mathematicians (as is mostly the case), these texts are too proof-based, overtly technical and most egregiously do not show students how to apply these concepts to actual problems. For those of us with a physics background, such texts often present an insurmountable challenge to our education, and are often a deterrent for further study. 

A Geometrical Introduction to Tensor Calculus is a refreshing exploration of both the theory and (drawing on the author's research expertise) application of tensor calculus. 

As a trained physicist, the most exciting feature of this text is the use of component notation when talking about advanced topics such as differential forms. Never have I seen a textbook on the subject that has so painstakingly described the relationship between the language used by physicists to the more formal and precise notation used by professional differential geometers. 

An impressive feature of this text is how it explores applications beyond traditional fundamental physics. Drawing from the author's expertise, the text explores the use of tensor calculus in fields such as fluid mechanics, thermodynamics and seismology. This breath further aids in the accessibility of this text, in addition to the many excellent figures throughout.  

Another excellent feature of this text are actual worked examples of the methods being discussed through out. These examples (of which there are numerous) help give context to the student's previous studies as well as providing instruction in how to apply these techniques. 

From a personal level, I wished that I had a book like this when I was an undergraduate. 


A Geometrical Introduction to Tensor Calculus
by Jeroen Tromp
ISBN:9780691267982

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