Name: Instructor: Engr. Michael M. SalvahanCrs./Yr./Sec.: BS ECE / EE Date: October 24, 2015Assignment No. 1 Title: Vector Differentiation and Operator Del

1. If A=(2 x¿¿2 y−x4)i+(exy− ysinx ) j+(x2cosy )k ,¿ find:

∂ A∂x ,

∂ A∂ y , ∂

2 A∂x2

, ∂2 A∂ y2

, ∂2 A

∂ x∂ y , ∂2 A∂ y∂ x

2. If Φ ( x , y , z )=x y2 z and A=xz i−x y2 j+ y z2 k, find ∂3

∂ x2∂ z(ΦA ) at the point (2, -1, 1).

3. If A=t2 i−t j+ (2t+1 ) k and B=(2 t−3 ) i+ j−t k , find:

a.ddt

(A•B)

b.ddt

(A x B)

c.ddt

|A+B|

d.ddt

(A x d Bdt

) at t = 1.

4. If A=2 yzi−x2 yj+x z2k , B=x2i+ yzj−xyk and Φ=2 x2 y z3, find:

a. (A•∇)Φb. A•∇Φc. (B•∇) Ad. (A x∇)Φe. A x∇Φ

5. If ∇Φ=2 xy z3i+x2 z3 j+3x2 y z2 k , find Φ ( x , y , z ) if Φ (1 ,−2,2 )=4.