Most students breeze through Chapters 1-3 (Vectors, Gradient, Divergence, Curl). Chapter 4-5 (Covariant and Contravariant Tensors) introduces the first red alerts. But by Chapter 7, the mathematics becomes abstract.
In Nawazish Ali’s specific edition, Chapter 7 typically covers:
Without a clean "repack" of this chapter, students often encounter missing index notation, garbled Greek symbols, or completely missing pages. Hence, the demand for a corrected, repackaged PDF version. Without a clean "repack" of this chapter, students
In orthogonal coordinates $(u^1, u^2, u^3)$ with scale factors $(h_1, h_2, h_3)$: $$\nabla \phi = \frac1h_1 \frac\partial \phi\partial u^1 \hate_1 + \frac1h_2 \frac\partial \phi\partial u^2 \hate_2 + \frac1h_3 \frac\partial \phi\partial u^3 \hate_3$$
Note: In some advanced curriculums, Chapter 7 might cover Curvilinear Coordinates or introductory Tensor Analysis, depending on how the previous chapters on gradient, divergence, and curl were structured. Surface Integrals:
The term "repack" in the context of academic PDFs usually implies one of the following:
Benefits of the Repack Format:
❌ Typos in indices – Especially in repacked PDFs: upper/lower indices get swapped.
❌ Missing steps – Some covariant derivative expansions jump too fast.
❌ Outdated layout – Tensors are introduced late; vectors covered first, which can confuse if you need quick reference.
❌ No modern applications – Lacks tensor calculus for relativity or continuum mechanics (just basics).