Lecture Notes 4/3/19 through 4/17/19

Lecture Notes 4/3/19

Lecture Notes 4/5/19

Lecture Notes 4/8/19

Lecture Notes 4/10/19

Lecture Notes 4/17/19

PracticeTest3 #2

Hello professor,
I was working on the Exam 3 practice ( https://math.asu.edu/sites/default/files/mat_267-post_exam3_solutions_0.pdf ) and I was confused on question #2 of the multiple choice. For the limits of integration of phi I got found them to be from 0 to pi. However, the correct answer says its from 0 to pi/2. Why is that?

Thank you

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In Cartesian (xyz) coordinates, your integration dz integration runs from z=0 to z=√(4-x^2-y^2); i.e. from the xy-plane UP to the top half of the sphere x^2+y^2+z^2=4, specifically there's nothing below the xy-plane. But the xy-plane is at 90 degrees or π/2 radians from the positive z-axis, hence π/2 has to be the upper limit.  If you went all the way to π your domain would have to include the negative z axis. 

Lecture Notes 3-27-19 through 4-1-19 (to be updated)

Lecture Notes 3/27/19

Lecture Notes 3/29/19

Lecture Notes 4/1/19

Section 12.3: Problem 8

Hi Professor,
I'm not sure why my approach is incorrect. I appreciate the direction in advance!

Thanks,

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Well, the positive direction in theta is counter clockwise, but limits of integration going from π/2 to -π/2 is backwards, so your your limits of integration mean that you're going backwards in the right half plane 

Lecture Notes 2/25/19 through 3/25/19

Lecture Notes 2/25/19

Lecture Notes 2/27/19

Lecture Notes 3/20/19

Lecture Notes 3/22/19

Lecture Notes 3/25/19

Scores and estimated final grade as of 3/24/19

Worksheet

(for those of you who couldn't attend today's field trip)
The link below includes a topo map of Camelback Mountain.  Get out your ruler to estimate horizontal (i.e. non vertical) distances, and your protractor to estimate angles.
1) estimate the magnitude and direction of the gradient vector at the red "x"s, direction in degrees from the right hand x-axis.
2) locate the local max's (hint: there are a lot of them) on the map, as well as the saddle points.
I'll be asking questions on the Monday after Spring Break.

Worksheet

PS: those who went on the field trip can also benefit from this work sheet.