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Stack :: Vector Algebra, Summation Convention
Usage Context
This package of lessons is useful for a first course on Selected Topics in Newtonian Mechanics.
It will be useful if the students had an exposure of vector algebra but have never use summation convention, Kronecker delta symbol and Levi-Civita symbol.
For instance this stack of lessons was delivered as part of Classical Mechanics course given at Chennai Mathematical Institute (2019).
Syllabus
Vector algebra Preliminaries: Kronecker delta and Levi-Civita symbol; Einstein summation convention. 123 notation for vector components. Dot and cross products of two vectors and vector identities.
Prerequisites
Vector algebra; dot and cross products; Triple product; Geometrical representation; Components of a vector in a system of coordinate axes; Vector algebra identities; Direction cosines; Matrix algebra; Determinants and their properties.
Lesson 1. A Quick Review of Vector Algebra
Lesson Overview
Vectors as Geometrical Objects
An Example
- Vector Algebra Identities
- Change of coordinate axes
- EndNotes
Lesson 2. Summation Convention, $\epsilon,\delta$ symbols and All That
- Learning Goals
- Einstein Summation Convention
- Kronecker Delta and Levi-Civita Symbols
- Examples
- Use of $\epsilon , \delta $ symbols in vector algebra
- EndNotes
References
Following is an incomplete list of reference for reading on introductory and
specialized range of topics in matrices and vector analysis.
- Shanti Narayan, {\it A Text Book of Matrices}, Revised by P. K. Mittal, S. Chand and Co, Delhi (2010)
- Andrilli S. and Hecker D., {\it Elementary Linear Algebra}, Academic Press, California USA Fourth edition (2010)
- Bellman R.,{\it Introduction to Matrix Analysis}, Textbook Publishers (2003)
- Khan Academy :: \href{https://www.khanacademy.org/math/algebra-home/alg-matrices} {\HighLight[MyLightYellow]{Introduction to matrices}}\\ \url{https://www.khanacademy.org/math/algebra-home/alg-matrices}
- Emma Thomas, \href{http://www.maths.surrey.ac.uk/explore/emmaspages/option1.html} {\HighLight[MyLightYellow]{Matrices and Determinants}}\\ \url{http://www.maths.surrey.ac.uk/explore/emmaspages/option1.html}\\ A page developed for The University of Surrey, England.
- Murphy G. M. and Margenau H. {\it The Mathematics of Physics and Chemistry},\\ Van Nostrand (1967).
- Spain B., {\it Vector Analysis}, Van Nostrand Reinhold (1967).
Download: STC-MM-17001-PRN.pdf (148.12 KB) Download: STC-MM-17001-MON.pdf (42.35 KB)
