Math151, Spring 2001

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Section
Example

content outline (for linked Picture Tour)

suggested Homework

9.1
Missouri Farmland:

- Data plot
- Cross-sectional models from data
- Formula for entire Surface
- Cross-sectional models from surface formula
in Text pp. 565-569
# 1,3,5,7,9,12,19,11+20,14+18

9.2

Farmland Map
Monthly Paytments
on 9% Loans
Sausage
- What are contour lines?
- What are contour lines?
- Playing with a function of two variables...
- How to find formulas for contour lines
HW set 1: #4,8,11,13,14,15,16,20
Hand in #7 and #15 after break

9.3

Mom and Pop store

Sausage 2
dutch cheese
- Intro to slopes of a surface in x and y direction
(Intro to partial derivatives)
- Finding slopes in coordinate directions
- formulas for partial derivatives
# 1,3,7,9,11,13,17,18,21

Section
Example

content outline (for linked Picture Tour)

suggested Homework

10.1
&
10.2

critical points
in
Missouri Farmland
review critical points, extrema, etc.
for functions of one variable (y = f (x))
Functions of two variables:
critical points, local extrema, saddles
What they are, and what they look like...
How do we find them?
(1) critical points (both partials = 0)
(2) The D-test...
Sec. 10.1: # 1,4,5,6,9,13,14,18
Sec. 10.2: # 7-10, 16
(first: find all critical pts.)
(for 7,8: How can you tell if
you have a local max or min
or neither? Be creative!)
Sec. 10.2: # 7-16
(for graphs click here)
Hand in #15 after Easter Break.

10.3
Cobb Douglas Example Optimizing under a constraint:
- using the constraint to eliminate one variable What is the optimal allocation of
$98,000 when we pay $10 per hour?
Sec. 10.3 # 1,3

- the method of Lagrange multipliers Sec. 10.3 # 9,11,13

What we still have to do:
Work at least one more exercise
(One for each method, if possible)
When do we use which method?
What is the advantage of the Lagrange method?

Section	Example	content outline (for linked Picture Tour)	suggested Homework
9.1	Missouri Farmland:	- Data plot - Cross-sectional models from data - Formula for entire Surface - Cross-sectional models from surface formula	in Text pp. 565-569 # 1,3,5,7,9,12,19,11+20,14+18
9.2	Farmland Map Monthly Paytments on 9% Loans Sausage	- What are contour lines? - What are contour lines? - Playing with a function of two variables... - How to find formulas for contour lines	HW set 1: #4,8,11,13,14,15,16,20 Hand in #7 and #15 after break
9.3	Mom and Pop store Sausage 2 dutch cheese	- Intro to slopes of a surface in x and y direction (Intro to partial derivatives) - Finding slopes in coordinate directions - formulas for partial derivatives	# 1,3,7,9,11,13,17,18,21
Section	Example	content outline (for linked Picture Tour)	suggested Homework
10.1 & 10.2	critical points in Missouri Farmland	review critical points, extrema, etc. for functions of one variable (y = f (x)) Functions of two variables: critical points, local extrema, saddles What they are, and what they look like... How do we find them? (1) critical points (both partials = 0) (2) The D-test...	Sec. 10.1: # 1,4,5,6,9,13,14,18 Sec. 10.2: # 7-10, 16 (first: find all critical pts.) (for 7,8: How can you tell if you have a local max or min or neither? Be creative!) Sec. 10.2: # 7-16 (for graphs click here) Hand in #15 after Easter Break.
10.3	Cobb Douglas Example	Optimizing under a constraint: - using the constraint to eliminate one variable	What is the optimal allocation of $98,000 when we pay $10 per hour? Sec. 10.3 # 1,3
		- the method of Lagrange multipliers	Sec. 10.3 # 9,11,13
		What we still have to do: Work at least one more exercise (One for each method, if possible) When do we use which method? What is the advantage of the Lagrange method?