Vector, Matrix and Tensor Algebras

time and location with D. 'Tony' Sun (dsun2019@hotmail.com)
semester if any  |  [Syllabus.PDF]  |  ------
Bibliography
Bertschinger, E. (Spring 1999). Introduction to Tensor Calculus for General Relativity. Physics 8.962 (MIT Physics).
Chapman, C. J. (2000). High Speed Flow. Cambridge University Press.
Dullemond, K. & Peeters, K. (2010). Introduction to Tensor Calculus.  Available at the author's website https://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf
Grow, D. E. (Spring 2015). Mathematics 5222 (Syllabus).
Levi-Civita, T. (1923). The Absolute Differential Calculus (Calculus of Tensors) [.pdf  commentary]. Blackie & Son Limited (London and Glasgow).
Learned-Miller, E. (n.d.). Vector, Matrix, and Tensor Derivatives. Retrieved from part of CS231n: Deep Learning for Computer Vision course materials (Stanford University).
Manias, E. (n.d.). Scalars, Vectors and Tensors. Notes of MatSE447 Rheology & Polymer Processing (Penn State).
Ricci, M. M. G., & Levi-Civita, T. (1900). Methods of the Absolute Differential Calculus and Their Applications. Mathematische Annalen, 54, 125-201.
Spain, B. (1960). Tensor Calculus: A Concise Course. Dover Publications, Inc.
Willmore, T. J. (1959). An Introduction to Differential Geometry. Oxford at the Clarendon Press.
Bauer & Curran. (November 4, 2022). Matrix Algebra Review: Video & Handouts on CenterStat.
Bray, R. (1967). "Vectors: A Study of Vector Analysis by H. B. Phillips." Honors Theses. 506. https://scholarlycommons.obu.edu/honors_theses/506
McGahagan, H. (Fall 2007). "Tensor Algebra I" from Math 190: Continuum Mechanics. Cal Santa Barbara.
Phillips, H. B. (1933). Vector Analysis. John Wiley & Sons, Incorporated; Later Printing edition. [Short Notices]
"Vector and Tensor Algebra (including Column and Matrix Notation)" of Materials Science and Engineering, Carnegie Mellon University.
The Math Sorcerer. (Jun 7, 2023). Tensor Analysis on Manifolds [YouTube video].


Scalars [.pdf]
Reading:  StackExchange post "What are elements of a field called"
Serge Lang's identification of scalars in Linear Algebra (1987) [excerpt]
Section 16.1 : Vector Fields from Paul's Online Notes
- [.pdf]
..physical quantities as "carriers" to each vector or tensor when it is instantiated with a particular applied context, such that every row/column and entry has a meaning..
- [.pdf]


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