MATH 251 – LECTURE 22
JENS FORSGÅRD
http://www.math.tamu.edu/~jensf/
This week:
M: review
W: Midterm 2
Next week: 14.1–4
webAssign: 14.1–3, opens 3/28 12 a.m.
Help Sessions:
Sun–Thu 6–8 p.m. in BLOC 149
Office Hours:
BLOC 641C
M 12:30–2:30 p.m.
W 2–3 p.m.
or by appointment.
Review
13.1–3
13.4–5
13.6
13.8
13.9–10
Double integrals, areas, volumes, iterated integrals,
reversing the order of integration
Polar coordinates, change of variables to polar coordinates
Applications: total mass, center of mass
Triple integrals, volumes, iterated integrals,
Cylindrical coordinates, Spherical coordinates.
Domains
Exercise 1. Let D denote the type I domain {−5 ≤ x ≤ 5, 0 ≤ y ≤
domain. Express D in polar coordinates.
√
25 − x2}. Express D as a type II
Domains
Exercise 2. Let D denote the domain {x ≥ 0, y ≥ 0, z ≥ 0, 2x + 2y + z ≤ 2}. Express D in spherical
coordinates.
Domains
Exercise 3. Let D denote the domain {x ≥ 2y 2 + 2z 2, x ≤ 2}. Express D in cylindrical coordinates.
Domains
Exercise 4. Let D denote the domain {0 ≤ x ≤ 10, 0 ≤ y ≤
Express D in spherical coordinates.
√
100 −
x2 ,
p
x2
+
y2
p
≤ z ≤ 200 − x2 − y 2}.
Domains
Exercise 5. Let D denote the domain {x2 + y 2 + z 2 ≤ 4, x ≥ 2}. Sketch D. Express D in cylindrical
coordinates. Express D in spherical coordinates.
Domains
Exercise 5. Let D denote the domain {x2 + y 2 + z 2 ≤ 4, x ≥ 2}. Sketch D. Express D in cylindrical
coordinates. Express D in spherical coordinates.