Index notation - video overview

These short lectures on index notation (the basis of the theory of tensors) are intended for use by anyone who would benefit from improving their understanding of this useful mathematical technique. Index notation is an alternative to the usual vector and matrix notation that you're used to: it is more easily generalisable, and makes certain types of calculation much easier to carry out.

Index notation would be useful for students studying Electromagnetism in Junior Honours; it is essential for those studying Relativity and Fields or General Relativity. These latter two courses therefore contain a short introduction to the technique, but we felt it would be helpful to make a slightly more tutorial set of lectures available for those who need them.

Index notation problem sheet

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Part 1.1: Introduction to index notation

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Part 1.2: The scalar product of two vectors

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Part 1.3: Multiplying two matrices

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Part 1.4: Worked example: Scalar product of two vectors

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Part 1.5: Worked example: Matrix multiplication

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Part 1.6: Worked example: Multiplying several matrices

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Part 1.7: Worked example: Multiplying several matrices explicitly

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Part 1.8: The cross product

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Part 1.9: The Levi-Civita symbol

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Part 1.10: Worked example: The cross-product using the Levi-Civita symbol

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Part 1.11: The Levi-Civita identity

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Part 1.12: The Levi-Civita identity (continued)

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Part 1.13: Worked example: The vector triple product using the Levi-Civita identity (continued)

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Part 2.1: Review of key points so far

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Part 2.2: Vector calculus using index notation

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Part 2.3: Vector calculus using index notation (continued)

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Part 2.4: Worked example: Gradient

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Part 2.5: Worked example: The curl of the curl of a vector

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Part 2.6: Concluding remarks