Which Chapters In Mathematical Methods For Physicists Cover Tensors?

Okay, fast, practical take: when I want to learn tensors from 'Mathematical Methods for Physicists', I hunt down the chapter that carries the label 'tensor' or anything about 'tensor calculus' and then check nearby chapters on curvilinear coordinates and vector calculus. Different editions scatter the material differently, but the core chunks are usually together.

I like to break the reading into two passes. First pass—algebra and transformation rules: index notation, how components change under coordinate transforms, metric and delta symbols. Second pass—calculus and geometry: Christoffel symbols, covariant derivative, divergence/gradient in curved coordinates, and curvature tensors if present. Work the book’s worked examples and exercises: applying tensors to elasticity, electromagnetism in media, or coordinate transforms in PDEs makes the abstract rules stick. If you want a quick cross-check, grep the PDF for 'tensor' or 'Christoffel' — that always points me to the right chapters across different editions.

Short checklist I toss into my study notes: find chapters or sections titled 'Tensors', 'Tensor Analysis', 'Tensor Calculus', or look under 'Curvilinear Coordinates' and 'Differential Geometry' in 'Mathematical Methods for Physicists'. Key topics to cover in order are tensor algebra and index notation, metric tensor and raising/lowering, transformation laws, Christoffel symbols and covariant derivative, and finally curvature (Riemann/Ricci) if the book includes it. If the edition doesn’t have a standalone tensor chapter, those topics are usually folded into vector analysis or coordinate chapters—so scan the table of contents and the index for words like 'tensor', 'metric', 'covariant', and 'Christoffel'. From there I pick a few physics examples—electromagnetism in curved coordinates or a tiny GR calculation—to cement the concepts.

If you're flipping through 'Mathematical Methods for Physicists' hunting for tensors, my first tip is: look for chapter or section headings that explicitly say 'tensors', 'tensor analysis', or anything with 'curvilinear coordinates' and 'differential geometry'. In most editions the authors treat tensors as a self-contained topic but also sprinkle tensor techniques through chapters on coordinate systems, vector analysis, and differential operators.

Practically speaking, I study tensors in roughly this order when using that book: tensor algebra (index notation, symmetric/antisymmetric parts, Kronecker Delta, Levi-Civita symbol), the metric tensor and raising/lowering indices, coordinate transformations and tensor transformation laws, Christoffel symbols and covariant derivatives, and finally curvature (Riemann tensor, Ricci tensor) if the edition goes that far. Those ideas might be split across two or three chapters — one focusing on algebra and transformation laws, another on calculus in curved coordinates, and sometimes a later chapter that touches on curvature and applications to physics.

If the edition you have doesn’t make the structure obvious, use the index for 'tensor', 'metric', 'Christoffel', or 'covariant'. For extra clarity I cross-reference with a compact book like 'Mathematical Methods for Physicists' (the same title but different editions) and a geometry-oriented text such as 'Geometry, Topology and Physics' or 'Nakahara' for a deeper geometric viewpoint — they helped me connect the formal manipulations with physical intuition.