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(a) V (fh)= fVh+2Vf.Vh+hV²f,where f and h are scaler fields.

(a) V (fh)= fVh+2Vf.Vh+hV²f,where f and h are scaler fields.

Advanced Engineering Mathematics
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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Problem 1: Prove the following identities: (a) V (fh) = fV°h+2Vf•Vh+hV²f , where f and h are scaler fields. (b) V (A•B) = A•V°B-B-V'A+2V•((B•V)A +B^(V^A)) (c) V (V^A)=V^(v²A) (d) V^(V^A)=V(V•A)-VA (e) V^(Vf)=0
Transcribed Image Text:Problem 1: Prove the following identities: (a) V (fh) = fV°h+2Vf•Vh+hV²f , where f and h are scaler fields. (b) V (A•B) = A•V°B-B-V'A+2V•((B•V)A +B^(V^A)) (c) V (V^A)=V^(v²A) (d) V^(V^A)=V(V•A)-VA (e) V^(Vf)=0
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