1 Limits And Continuity 2 The Derivative 3 Topics In Differentiation 4 The Derivative In Graphing And Applications 5 Integration 6 Applications Of The Definite Integral In Geometry, Science, And Engineering 7 Principles Of Integral Evaluation 8 Mathematical Modeling With Differential Equations 9 Infinite Series 10 Parametric And Polar Curves; Conic Sections 11 Three-dimensional Space; Vectors 12 Vector-valued Functions 13 Partial Derivatives 14 Multiple Integrals 15 Topics In Vector Calculus expand_more
15.1 Vector Fields 15.2 Line Integrals 15.3 Independence Of Path; Conservative Vector Fields 15.4 Green’s Theorem 15.5 Surface Integrals 15.6 Applications Of Surface Integrals; Flux 15.7 The Divergence Theorem 15.8 Stokes’ Theorem Chapter Questions expand_more
Problem 1QCE: If C is a piecewise smooth curve from 1,2,3to4,5,6, then Cdx+2dy+3dz= Problem 2QCE Problem 3QCE: A potential function for the vector field Fx,y,z=yzi+xz+zj+xy+y+1k is x,y,z=. Problem 4QCE: If a, b. and c are nonzero real numbers such that the vector filed x5yai+xbycj is a conservative... Problem 1ES: Determine whether F is a conservative vector field. If so, find a potential function for it.... Problem 2ES Problem 3ES: Determine whether F is a conservative vector field. If so, find a potential function for it.... Problem 4ES: Determine whether F is a conservative vector field. If so, find a potential function for it.... Problem 5ES Problem 6ES Problem 7ES: In each part, evaluate C2xy3dx+1+3x2y2dy over the curve C, and compare your answer with the result... Problem 8ES Problem 9ES: Show that the integral is independent of the path, and use Theorem 15.3.1 to find its value.... Problem 10ES Problem 11ES: Show that the integral is independent of the path, and use Theorem 15.3.1 to find its value.... Problem 12ES Problem 13ES: Show that the integral is independent of the path, and use Theorem 15.3.1 to find its value.... Problem 14ES Problem 15ES: Confirm that the force field F is conservative in some open connected region containing the points P... Problem 16ES: Confirm that the force field F is conservative in some open connected region containing the points P... Problem 17ES: Confirm that the force field F is conservative in some open connected region containing the points P... Problem 18ES: Confirm that the force field F is conservative in some open connected region containing the points P... Problem 19ES: Determine whether the statement is true or false. Explain your answer. If F is a vector field and... Problem 20ES: Determine whether the statement is true or false. Explain your answer. If Fx,y=ayi+bxj is a... Problem 21ES: Determine whether the statement is true or false. Explain your answer. If x,y is a potential... Problem 22ES Problem 23ES: Find the exact value of CFdr using any method. Fx,y=ey+yexi+xey+exjC:rt=sint/2i+lntj1t2 Problem 24ES Problem 25ES: Use the numerical integration capability of a CAS or other calculating utility to approximate the... Problem 26ES Problem 27ES: Is the vector field conservative? Explain. Problem 28ES: Is the vector field conservative? Explain. Problem 29ES Problem 30ES Problem 31ES: Prove: If Fx,y,z=fx,y,zi+gx,y,zj+hx,y,zk is a conservative field and f, g, and h are continuous and... Problem 32ES Problem 33ES: Find a nonzero function h for which fx,y=hxxsiny+ycosyi+hxxcosyysinyj is conservative. Problem 34ES: (a) In Example 3 of Section 15.1 we showed that x,y=cx2+y21/2 is a potential function for the... Problem 35ES: Use the result in Exercise 34(b). In each part, find the work done by the three-dimensional... Problem 36ES: Use the result in Exercise 34(b). Let Fx,y=yx2+y2ixx2+y2j. (a) Show that C1FdrC2Fdr if C1andC2 are... Problem 37ES: Prove Theorem 15.3.1 if C is a piecewise smooth curve composed of smooth curves C1,C2,...,Cn. Problem 38ES: Prove that (b) implies (c) in Theorem 15.3.2. Problem 39ES: Complete the proof of Theorem 15.3.2 by showing that /y=gx,y, where x,y is the function in (7). Problem 40ES Problem 41ES format_list_bulleted