1 Preparation For Calculus 2 Limits And Their Properties 3 Differentiation 4 Applications Of Differentiation 5 Integration 6 Differential Equations 7 Applications Of Integration 8 Integration Techniques, L’ho?pital’s Rule, And Improper Integrals 9 Infinite Series 10 Conics, Parametric Equations, And Polar Coordinates 11 Vectors And The Geometry Of Space 12 Vector-Valued Functions 13 Functions Of Several Variables 14 Multiple Integration 15 Vector Analysis expand_more
15.1 Vector Fields 15.2 Line Integrals 15.3 Conservative Vector Fields And Independence Of Path 15.4 Green's Theorem 15.5 Parametric Surfaces 15.6 Surface Integrals 15.7 Divergence Theorem 15.8 Stokes's Theorem Chapter Questions expand_more
Problem 65E: Vector Field Define a vector field in the plane and in space. Give some physical examples of vector... Problem 66E Problem 1E Problem 2E: In Exercise 5-8, match the vector field with its graph. [The graphs are labeled (a), (b), (c), and... Problem 3E: In Exercise 5-8, match the vector field with its graph. [The graphs are labeled (a), (b), (c), and... Problem 4E: In Exercise 5-8, match the vector field with its graph. [The graphs are labeled (a), (b), (c), and... Problem 5E Problem 6E Problem 7E Problem 8E Problem 9E: Sketching a Vector Field In Exercises 9-14, find F and sketch several representative vectors in the... Problem 10E Problem 11E Problem 12E Problem 13E Problem 14E Problem 15E: Finding a Conservative Vector Field In Exercises 19-28, find the conservative vector field for the... Problem 16E Problem 17E Problem 18E Problem 19E: In Exercises 19-28, find the conservative vector field for the potential function by finding its... Problem 20E Problem 21E Problem 22E: In Exercises 19-28, find the conservative vector field for the potential function by finding its... Problem 23E: In Exercises 19-28, find the conservative vector field for the potential function by finding its... Problem 24E Problem 25E Problem 26E Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E Problem 42E Problem 43E: Find curl F for the vector field at the given point F(x,y)=(xyz)i+(xyz)j+(xyz)k;(2, 1, 3). Problem 44E: Find Curl F for the vector field at the point F(x,y)=(x2z)i(2xz)j+(yz)k;(2,-1,3). Problem 45E: Find Curl of the vector field F at the given point F(x,y)=(exsiny)i(excosy)j; (0, 0, 1). Problem 46E: Find Curl of the vector field F at the given point F(x,y)=exyz(i+j+k);(3, 2, 0). Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 53E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 54E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 55E Problem 56E: Determine whether the vector field F is conservative. If it is, find a potential function for the... Problem 57E Problem 58E Problem 59E Problem 60E Problem 61E: Finding the Divergence of a Vector Field In Exercises 6164, find the divergence of the vector field... Problem 62E: Find the divergence of the vector field at the given point. F(x,y,z)=(x2z)i(2xz)j+(yz)k; (2,-1,3). Problem 63E Problem 64E Problem 78E Problem 67E Problem 68E Problem 69E Problem 70E: In Exercise 69 and 70, find curl (FxG)=x(FxG) F(x,y,z)=xizk G(x,y,z)=x2i+yj+z2k Problem 71E Problem 72E: In Exercises 71 and 72, curl (curlF)=x(xF) F(x,y,z)=x2zi2xzj+yzk Problem 73E Problem 74E: Divergence of a Cross Product In Exercises 73 and 74, find div(FG)=(FG).... Problem 75E Problem 76E Problem 77E: In parts (a) - (h), prove the property for vector fields F and G and scalar function f. (Assume that... Problem 83E Problem 79E Problem 80E Problem 81E Problem 82E format_list_bulleted