5. Bonus: Let S be a regular surface, let w E X(S) be a vector field on S, and let f : S → R be a smooth function. The "product" of f with w is again a smooth vector field, it is denoted by fw E X(S), and given by the formula (fw)(p) = f(p)w(p) p€ S. State and prove the "product rule" for the covariant derivative, i.e., calculate D.(fw)(p).

5. Bonus: Let S be a regular surface, let w E X(S) be a vector field on S, and let f : S → R be a smooth function. The "product" of f with w is again a smooth vector field, it is denoted by fw E X(S), and given by the formula (fw)(p) = f(p)w(p) p€ S. State and prove the "product rule" for the covariant derivative, i.e., calculate D.(fw)(p).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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