MTH 234 Review for Exam 4
Sections 16.1-16.8.
50 minutes.
5 to 10 problems, similar to homework problems.
No calculators, no notes, no books, no phones.
No green book needed.
Review for Exam 4
(16.1) Line integrals.
(16.2) Vector elds, work, circulation,
Review for Exam 3
Tuesday Recitations: 14.7, 15.1-15.5, half 15.7.
Thursday Recitations: 15.1-15.5, 15.7.
50 minutes.
From ve 10-minute problems to ten 5-minutes problems.
Problems similar to homework problems.
No calculators, no notes, no books, no phone
Integrals of vector elds. (Sect. 16.2)
Vector elds on a plane and in space.
The gradient eld of a scalar-valued function.
The line integral of a vector eld along a curve.
Work done by a force on a particle.
The ow of a uid along a curve.
The ux across a p
Greens Theorem on a plane. (Sect. 16.4)
Review of Greens Theorem on a plane.
Sketch of the proof of Greens Theorem.
Divergence and curl of a function on a plane.
Area computed with a line integral.
Review: Greens Theorem on a plane
Theorem
Given a eld F =
Integrals along a curve in space. (Sect. 16.1)
Line integrals in space.
The addition of line integrals.
Mass and center of mass of wires.
Line integrals in space
Denition
The line integral of a function f : D R3 R along a curve
associated with the functio
Conservative elds and potential functions. (Sect. 16.3)
Review: Line integral of a vector eld.
Gradient elds.
Conservative elds.
Equivalence of Gradient and Conservative elds.
The line integral conservative elds.
Finding the potential of a gradient eld.
C
Greens Theorem on a plane. (Sect. 16.4)
Review: Line integrals and ux integrals.
Greens Theorem on a plane.
Circulation-tangential form.
Flux-normal form.
Tangential and normal forms equivalence.
Review: The line integral of a vector eld along a curve
Den
Integrals in cylindrical, spherical coordinates (Sect. 15.7)
Integration in spherical coordinates.
Review: Cylindrical coordinates.
Spherical coordinates in space.
Triple integral in spherical coordinates.
Cylindrical coordinates in space.
z
Denition
P
Th
Review for Exam 4
Sections 16.1-16.6.
50 minutes.
5 to 10 problems, similar to homework problems.
No calculators, no notes, no books, no phones.
No green book needed.
Review for Exam 4
(16.6) Surface integrals.
(16.5) Surface area.
(16.4) The Green Theore
The Divergence Theorem. (Sect. 16.8)
The divergence of a vector eld in space.
The Divergence Theorem in space.
The meaning of Curls and Divergences.
Applications in electromagnetism:
Gauss law. (Divergence Theorem.)
Faradays law. (Stokes Theorem.)
The div
The Stokes Theorem. (Sect. 16.7)
The curl of a vector eld in space.
The curl of conservative elds.
Stokes Theorem in space.
Idea of the proof of Stokes Theorem.
The curl of a vector eld in space
Denition
The curl of a vector eld F = F1 , F2 , F3 in R3 is
Surface area and surface integrals. (Sect. 16.5)
Review: Arc length and line integrals.
Review: Double integral of a scalar function.
Explicit, implicit, parametric equations of surfaces.
The area of a surface in space.
The surface is given in parametric
Surface area and surface integrals. (Sect. 16.6)
Review: The area of a surface in space.
Surface integrals of a scalar eld.
The ux of a vector eld on a surface.
Mass and center of mass thin shells.
Review: The area of a surface in space
Theorem
Given a sm