- Let A X R R And F Yr R Be Differentiable Scalar And Vector Fields Respectively Express Each Of The Following I The 1 (28.19 KiB) Viewed 59 times
Let A:X R³ → R and F:YR³ R³ be differentiable scalar and vector fields respectively. Express each of the following i.The unite vectors e. ii. Check the orthonormal of e. iii. grad A. iv. Div F then simplify. v. Curl F then simplify. vi. V² A then simplify. For the two coordinates systems - 1- Prolate Spheroidal Coordinates (u, p.0) r(u ,¢.0) = (a sinh u sin d cos 0, a sinh u sin ¢ sin 0, a cosh u cos) Where u 20,0 ≤O≤n, 0≤0 ≤ 2n 2- Oblate Spheroidal Coordinates (v.4.0) x = a cosh v cos cos 0, y = a cosh v cos sin 0, z = a sinh v sin Where v≥0,-≤ 0102 Then use MATHEMATICA or MATLAP to graph the families of surfaces in these systems.