1 Functions 2 Limits And Continuity 3 Derivatives 4 Application Of Derivatives 5 Integrals 6 Applications Of Definite Integrals 7 Trascendental Functions 8 Techniques Of Integration 9 First-order Differential Equations 10 Infinite Sequences And Series 11 Parametric Equations And Polar Coordinates 12 Vectors And The Geometry Of Space 13 Vector-valued Functions And Motion In Space 14 Partial Derivatives 15 Multiple Integrals 16 Integrals And Vector Fields 17 Second-order Differential Equations A.1 Real Numbers And The Real Line A.2 Mathematical Induction A.3 Lines, Circles, And Parabolas A.4 Proofs Of Limit Theorems A.5 Commonly Occurring Limits A.6 Theory Of The Real Numbers A.7 Complex Numbers A.8 The Distributive Law For Vector Cross Products A.9 The Mixed Derivative Theorem And The Increment Theorem expand_more
16.1 Line Integrals Of Scalar Functions 16.2 Vector Fields And Line Integrals: Work, Circulation, And Flux 16.3 Path Independence, Conservative Fields, And Potential Functions 16.4 Green's Theorem In The Plane 16.5 Surfaces And Area 16.6 Surface Integrals 16.7 Stokes' Theorem 16.8 The Divergence Theorem And A Unified Theory Chapter Questions expand_more
Problem 1GYR Problem 2GYR: How can you use line integrals to find the centers of mass of springs or wires? Explain.
Problem 3GYR Problem 4GYR Problem 5GYR Problem 6GYR Problem 7GYR Problem 8GYR Problem 9GYR Problem 10GYR Problem 11GYR: How do you calculate the area of a parametrized surface in space? Of an implicitly defined surface... Problem 12GYR Problem 13GYR: What is an oriented surface? What is the surface integral of a vector field in three-dimensional... Problem 14GYR Problem 15GYR Problem 16GYR Problem 17GYR Problem 18GYR Problem 1PE: The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,... Problem 2PE: The accompanying figure shows three polygonal paths joining the origin to the point (1, 1, 1).... Problem 3PE: Integrate over the circle r(t) = (a cos t)j + (a sin t)k, 0 ≤ t ≤ 2π.
Problem 4PE Problem 5PE: Evaluate the integrals in Exercises 5 and 6.
5.
Problem 6PE Problem 7PE Problem 8PE: Integrate F = 3x2yi + (x3 + l)j + 9z2k around the circle cut from the sphere x2 + y2 + z2 = 9 by the... Problem 9PE Problem 10PE: Evaluate the integrals in Exercises 9 and 10.
10.
C is the circle x2 + y2 = 4.
Problem 11PE Problem 12PE Problem 13PE Problem 14PE: Hemisphere cut by cylinder Find the area of the surface cut from the hemisphere x2 + y2 + z2 = 4, z ... Problem 15PE Problem 16PE Problem 17PE: Circular cylinder cut by planes Integrate g(x, y, z) = x4y(y2 + z2) over the portion of the cylinder... Problem 18PE Problem 19PE Problem 20PE Problem 21PE Problem 22PE Problem 23PE Problem 24PE Problem 25PE Problem 26PE Problem 27PE Problem 28PE Problem 29PE: Which of the fields in Exercises 29–32 are conservative, and which are not?
29. F = xi + yj + zk
Problem 30PE Problem 31PE: Which of the fields in Exercises 29–32 are conservative, and which are not?
31. F = xeyi + yezj +... Problem 32PE Problem 33PE Problem 34PE Problem 35PE: In Exercises 35 and 36, find the work done by each field along the paths from (0, 0, 0) to (1, 1, 1)... Problem 36PE: In Exercises 35 and 36, find the work done by each field along the paths from (0, 0, 0) to (1, 1, 1)... Problem 37PE: Finding work in two ways Find the work done by
over the plane curve r(t) = (et cos t)i + (et sin... Problem 38PE: Flow along different paths Find the flow of the field F = ∇(x2zey)
once around the ellipse C in... Problem 39PE Problem 40PE Problem 41PE Problem 42PE Problem 43PE Problem 44PE Problem 45PE Problem 46PE Problem 47PE Problem 48PE: Moment of inertia of a cube Find the moment of inertia about the z-axis of the surface of the cube... Problem 49PE: Use Green’s Theorem to find the counterclockwise circulation and outward flux for the fields and... Problem 50PE Problem 51PE Problem 52PE Problem 53PE: In Exercises 53–56, find the outward flux of F across the boundary of D.
53. Cube F = 2xyi + 2yzj +... Problem 54PE: In Exercises 53–56, find the outward flux of F across the boundary of D.
53. Spherical cap F= xzi +... Problem 55PE Problem 56PE Problem 57PE Problem 58PE Problem 59PE Problem 60PE Problem 1AAE Problem 2AAE: Use the Green’s Theorem area formula in Exercises 16.4 to find the areas of the regions enclosed by... Problem 3AAE Problem 4AAE: Use the Green's Theorem area formula in Exercises 16.4 to find the areas of the regions enclosed by... Problem 5AAE Problem 6AAE Problem 7AAE Problem 8AAE Problem 9AAE Problem 10AAE Problem 11AAE Problem 12AAE Problem 13AAE: Archimedes’ principle If an object such as a ball is placed in a liquid, it will either sink to the... Problem 14AAE Problem 15AAE: Faraday’s law If E(t, x, y, z) and B(t, x, y, z) represent the electric and magnetic fields at point... Problem 16AAE Problem 17AAE Problem 18AAE Problem 19AAE Problem 20AAE Problem 21AAE format_list_bulleted