Before Chapter 2, write down the index rules: dummy indices (summation), free indices (consistency), and when to place indices upstairs (contravariant) vs. downstairs (covariant). Chaki’s exercises on the quotient law are excellent tests.
Many universities in India (such as University of Delhi, BHU, and Calcutta University) explicitly list Chaki’s book as a reference for courses like Differential Geometry and Tensor Analysis.
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| Book Title | Author(s) | Free/Legal Source | |------------|-----------|-------------------| | A First Course in Tensor Calculus | Louis Brand (1967) | Archive.org (public domain in some countries) | | Tensor Calculus | J.L. Synge & A. Schild | Dover (inexpensive) | | Introduction to Vectors & Tensors | Ray Bowen & C.C. Wang | Available free online (Texas A&M repository) | | Lectures on Tensor Calculus | David J. Griffiths | Not free but chapter samples online |
For Indian students, the “Tensor Analysis” by S. C. Malik & Savita Arora follows a very similar syllabus and is often in print. Before Chapter 2, write down the index rules:
If you cannot afford the book, check your college library or ask a senior student for a borrowed scan. However, if you can purchase a legal PDF for the price of a coffee, do so—it supports the publication of future mathematical texts.
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Although the paperback is reasonably priced in India (often ₹200–₹400), access to foreign currency or localized pricing can be a barrier for students in developing nations.