KCL Calculus 2 class test 3 formula 0.0 / 5 ? MathematicsCalculus 2 CT3UniversityOther Created by: johnpithersCreated on: 25-03-18 13:35 Integral of scalar function over curve ∫f(r(t))|r’(t)|dt 1 of 27 Arc length ∫|r’(t)|dt 2 of 27 Line integral (vector fields) ∮v.dr=∫v(r(t)).r’(t) dt 3 of 27 Integral of ∇f ∫∇f=f(q)-f(p) where C∈⟦p,q⟧ 4 of 27 what does v=∇f mean? ∮v.dr=0 (closed arc) 5 of 27 Area of U? ∫∫1.dx.dy 6 of 27 Integral when changing variables? ∫∫ ||J||du.dv 7 of 27 Polar co-ordinates change of variables? ∫∫f(rcosθ,rsinθ)r.dr.dθ 8 of 27 What is Green's theorem? ∮v.dr=∫∫((dQ/dx)-(dP/dy))dxdy 9 of 27 What are P and Q in Green's theorem? V(x,y)=P(x,y)i+Q(x,y)j 10 of 27 What is the test for a gradient field? ∮v.dr=0 11 of 27 What is the alternative formula for area (x,y)? 1/2∮(-y.dx+x.dy) 12 of 27 What is the parameterisation of a graph surface (x,y)? xi+yj+f(x,y)k 13 of 27 What is the formula for the fundamental vector product (u,v)? N(u,v)=dr/du x dr/dv (cross product) 14 of 27 Fundamental vector product (x,y)? -df/dx(i)-df/dy(j)+k for r=(x,y,f(x,y)) 15 of 27 What is the significance of N(u,v)? Perpendicular to surface at r(u,v) 16 of 27 What's the formula for a surface integral (u,v)? ∫∫g(r(u,v))||N(u,v)||dudv 17 of 27 What's the formula for a surface integral (x,y)? ∫∫f(x,y)√(1+(df/dx)^2+(df/dy)^2)dxdy for z=f(x,y) 18 of 27 Area of surface (u,v)? S=∫∫|N(u,v)| 19 of 27 Area of surface (x,y)? ∫∫√((df/dx)^2+(df/dy)^2+1)dxdy 20 of 27 Formula for flux? ∫∫v.ndσ=∫∫v.N(u,v) where v=vector field 21 of 27 Formula for flux (z=f(x,y))? ∫∫(-v1(df/dx)-v2(df/dy)+v3)dxdy 22 of 27 What is v in the flux formula? v=v1i+v2j+v3k across S in direction of upwards normal 23 of 27 What is Stoke's theorem? ∫∫(∇xv).ndσ=∮v.dr 24 of 27 What does it mean when surface is closed (Stoke's theorem)? ∫∫(∇xv).ndσ=0 25 of 27 What does cos^2(t) equal? 1/2(1+cos2t) 26 of 27 what does sin^2 equal? 1/2(1-cos2t) 27 of 27

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