If the partial derivatives of A, B. U, and V are assumed to exist, then 1. V(U + V) = VU +V or grad (U+ V)3 grad u+ grad V 2. V (A+B)= V-A+V B or div (A + B) + div A + div B 3. Vx (A + B) = VxA+VxB or curl (A + B) = curlA+ curl B 4. V.(UA) = (VU) - A+ U(V A) Vx (UA) = (VU) x A +U(V x A) V (A x B) = B (Vx A)-A (Vx B) 5. 6. 7. Vx (A x B) = (B V)A- B(V A)-(A V)B+ A(V B) 8. V(A B) = (B V)A + (A V)B +B x (Vx A) + Ax (Vx B) 9. V.(VU)= VU = is called the Laplacian of U. ar dyz and V2 ar ay dz -is called the Lapacian operator. 0. Vx (VU)=0. The curl of the gradient of U is zero. 1. V.(Vx A) = 0. The divergence of the curl of A is zero. 2 Vx (Vx A) = V(V.A)-V A
If the partial derivatives of A, B. U, and V are assumed to exist, then 1. V(U + V) = VU +V or grad (U+ V)3 grad u+ grad V 2. V (A+B)= V-A+V B or div (A + B) + div A + div B 3. Vx (A + B) = VxA+VxB or curl (A + B) = curlA+ curl B 4. V.(UA) = (VU) - A+ U(V A) Vx (UA) = (VU) x A +U(V x A) V (A x B) = B (Vx A)-A (Vx B) 5. 6. 7. Vx (A x B) = (B V)A- B(V A)-(A V)B+ A(V B) 8. V(A B) = (B V)A + (A V)B +B x (Vx A) + Ax (Vx B) 9. V.(VU)= VU = is called the Laplacian of U. ar dyz and V2 ar ay dz -is called the Lapacian operator. 0. Vx (VU)=0. The curl of the gradient of U is zero. 1. V.(Vx A) = 0. The divergence of the curl of A is zero. 2 Vx (Vx A) = V(V.A)-V A
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)
Problem 29E
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