4. Week: 10/1610/20

Regular+Biochem  Physics 
pgs 115118 number 4,12
pg 124127 number 4 (no technology),
14,18,20,22
pgs 134136 number 2,8,12,16

pgs 263264 number 2,6,8
pgs 124127 number 2,4,14,18
Also do:

1) Let F=(2 x y ^{2} + 3 x^{2}, 2 y x^{2}). Compute
the line integral of F along from (0,0) to (1,1) along the following curves:
a) The diagonal x=y
b) Along the x axis from x=0 to x=1, then from (1,0) to (1,1) along the line x=1
c) Along the y axis from y=0 to y=1, then from (0,1) to (1,1) along the line y=1
d) Exhibit a potential function for F and use the fundamental theorem for line integrals.

2) For each of the following, find values for the constants a,b which make the given vector
field conservative:
a) F=(a x^{3} y + b y ^{2},x^{4}+y x)
b) F=(sin(y) + b y cos(x),a x cos(y) + sin(x))
c) F=(a y e^{(xy)} + y ^{2},x e^{(xy)} + 2 y x^{b})
d) F=(3 x^{a} y^{b},4 x^{3} y^{3})


Solutions Regular/Bio ,
Solutions Phys ,
Solutions: Physics additional problems 
5. Week: 10/2310/27

Regular/Biochem  Physics 
pgs. 136 number 14
pgs. 140 number 2
pgs. 146 number 6
pgs. 156159 number 2,8,10,16,20,26a,c
pgs. 245248 number 2,4,6

pg 127 number 20,22
pgs 134136 number 2,8,10,12,14,16
pg 140 number 2
pg 146 number 6
pg 395 number 2,4,8
pg 93 number 28


Solutions Reg/Bio ,
Solutions Phys

6. Week: 10/3011/3

Regular/Biochem  Physics 
pgs 247248 #8
pgs 168169 $4,8,12,14
pgs 179182 #4a,c,10
pgs 191193 #4
Also do:
1) Find the minimum distance from the surface x^{2}+y^{2}z^{2}=1 to the origin.
2) Find the maximum and minimum values of x+y2z on the sphere x^{2}+y^{2}+z^{2}=1.
3) Find the local extreme points of f(x,y,z)=xyz on the surface x+y+4 z=1.
4) Model the earth as the sphere x^{2}+y^{2}+z^{2}=1. Suppose that the temperature
at a point (x,y,z) on the surface is T(x,y,z)=x^{2}y^{2}+z+1
in appropriate units. Find the points with the highest and lowest temperatures.
5) Suppose that the profit from Scooter sales is a function N of variables (x,y,z) that is given
by N(x,y,z) = 4 x^{2}+2xyz^{2}.
Suppose as well that the values of (x,y,z) are
not independent, but constrained by x+y+2z=1. What values of (x,y,z) should be used to maximize the profit?

pgs 179182 #4a,c,10
pags 191193 #4,8,10,12


Solutions Reg/Bio
Solutions Phys

7. Week: 11/511/10 (Due Thursday 11/16, rsp. Friday 11/17)

Regular/Biochem  Physics 
pgs. 192193, number 8,10,12
pgs. 199200, number 2,6
page 385, number 10,14

pgs. 179182, number 4a,c 10
pgs. 191193, number 4,8,10,12


Solutions Reg/Bio
Solutions Phys

8. Week: 11/1311/17 (Due Tue 11/28 rsp. Wed 11/29 after Thanksgiving)

Regular 
Physics 
Biochem 
pgs 207208 number 2 (no tech), 10, 12
pgs 254255 number 2, pages 263364 number 2 (no tech), 6, 8
Also do:
1) Let F=(2 x y ^{2} + 3 x^{2}, 2 y x^{2}). Compute
the line integral of F along from (0,0) to (1,1) along the following curves:
a) The diagonal x=y
b) Along the x axis from x=0 to x=1, then from (1,0) to (1,1) along the line x=1
c) Along the y axis from y=0 to y=1, then from (0,1) to (1,1) along the line y=1
d) Exhibit a potential function for F and use the fundamental theorem for line integrals.
2) For each of the following, find values for the constants a,b which make the given vector
field obey the necessary condition stated as the fact on page 262 of the text to be
a gradient:
a) F=(a x^{3} y + b y ^{2},x^{4}+y x)
b) F=(sin(y) + b y cos(x),a x cos(y) + sin(x))
c) F=(a y e^{(xy)} + y ^{2},x e^{(xy)} + 2 y x^{b})

pgs 199200, number 2,6, pg 385 number 10,14, pgs 207208 number 2 (no tech) 10,12

pgs 207208 number 2 (no tech),10,12
Rosner, p.4044 number 2.1,2.2,2.8,2.9,2.10,2.18


Solutions Solutions book problems (Reg) , and
additional problems (Reg) = Week 4 (Phys)
Solutions Phys .
Solutions Bio:
2.1) 215/25 = 8.6 days, median 8 days
2.2) variance 32.67, stand. dev 5.72, Range 27 Days
2.8) variance 0.39 diopters
2.9) variance 0.395, stand. dev 0.63 diopters
2.18) arithmetic mean: 8.8 mmHg rsp. 0.9 mmHg
median: 8 mmHg rsp. 1 mmHg

10. Week: 11/2712/1

Regular/Physics 
Biochem 
pgs. 273275 # 2,8,10, pgs 279280, # 2 4
pgs 286287 #2 (skip plotting task), 4,6, pgs 292293 #2,4
Also do:
1) Take a parameterized curve C: (f(u),g(u)), where g(u)>0 in the xy plane and
revolve it about the xaxis in space to create a surface (called a 'surface of
revolution').
a) Show that X(u,v) = (f(u), g(u) cos(v), g(u) sin(v)) parameterizes the
surface where v is in the interval [0,2 pi).
b) Sketch the surface of revolution in the case, where f(u)=u and g(u)=1
and also in the case, where f(u)=cos(u) and g(u)=sin(u)+2.
2) Find a parameterization for the surface obtained by revolving the curve
y=exp(x) about the xaxis.
3) Find a parameterization for the surface, where xy^{2}+z^{4} y^{4}=0.
4) Find a parameterization for the y>0 part of the surface, where
y^{2}((x^{4}+z^{4})^{8}+1)=0.
5) Find the area of the part of the plane x+y+z=1, where x,y,z are all
between 0 and 1.
6) Integrate the function f(x,y,z)=xy over the part of the plane
x+2y+3z=6, where x,y, and z all lie between 0 and 1.

Rosner: pgs 6773, # 3.12, 3.15, 3.16, 3.17, 3 24, 3.25, 3.28, 3.76, 3.77, 3.78, 3.83, 3.89
pgs 108110, #4.10, 4.14, 4.15, 4.20


Solutions Reg/Phys
Solutions Bio

11. Week: 12/412/8

Regular 
Physics 
Biochem 
Week 11 (GIF)

Week 11 (GIF)

Rosner: pgs 109110, #4.734.74, 4.814.83,
pgs 147149, #5.6, 5.7, 5.41, 5.42, 5.44, 5.53, 5.61, 5.70


Solutions

12. Week: 12/1112/15

The problems are on the
Differential equations handout.

Solutions
