MATH151, Spring 2003
On this page we will
 - keep track of what we do in class
 - list homework assignments
 - place links to relevant web pages

e-mail rossa@xavier.xu.edu

WEEK 7

T 2-25		Return Test 1 Continue discussion of Section 9.1 Cross Sectional Models:      from data // from formula (Examples: MO Farmland and Wind Chill) Then we discussed Exercise 14, 20		Missouri Farmland		Homework: From last time: Sec. 9.1#11,14,19,20 Now also: #7,9,16,23 Prepare (read) Section 9.2.: "Contour Graphs"
R 2-27		Discuss Homework Sec. 9.1 Section 9.2: "Contour Graphs"  - what is a contour line?  - how do we find contour lines from     - data     - formula "Reading" a Contour Graph		Contours for Mis souri Farmland		Homework: Sec.9.2.#3,7,13,14,15

WEEK 8

T 3-4		Spring Break
R 3-6		Spring Break

WEEK 9

T 3-11		Review Contour lines:        Missouri Farmland (see link) - discuss #15 and #7 or 13 of Sec. 9.2 - contour maps for different contexts    "reading"/"interpreting" contour maps - matching contour maps and surfaces				HW: Sec. 9.2 # 16,17,18,19,20,23,24 $ finish hand-outs No class on Thursday (Rossa out of town) Settle remaining questions about Sec. 9.1, 9.2 in Math Lab Prepare (i.e. read and think about) Sec. 9.3
R 3-13		No Class

WEEK 10

T 3-18		Section 9.3.: Partial Derivatives slope of a surface in x-direction (at a point) slope of a surface in y-direction (at a point)  - How to estimate it from contour map of surface  - How to calculate it from formula for surface     (Example: Missouri Farmland)				HW: Calculate the slope of the Missouri Farmland in x-direction at the points (.5,.5),(.5,1),(1,.5) and (1,1). Then calculate the slope in y-direction at these points. Use the method from class.
R 3-20		Section 9.3.: Partial derivatives A detailed discussion using the Mom and Pop store example...		Mom 'n Pop store		HW: Sec. 9.3 # 7,9,10,11,15,17ab,19,24

WEEK 11

T 3-25		Section 9.3. Discussion of several HW problems review for test By popular demand: Test 2 is moved to next Tuesday				HW: Take a look at "second partial derivatives" in section 9.3. Read section 10.1: Multivariable Critical Points
R 3-27		Review Optimization for functions of one variable (MATH150, Chapter five) Terminology (local/absolute max/min, saddle, critical point) and connections: How can we tell that/if we have a loc. max, loc. min, or saddle at a critical point ... ?  - check if derivative changes sign  - via concavity (2nd derivative) Intro to optimization of functions with two inputs Terminology (how do we characterize a loc max., ...)  - What do these things look like in a contour map?  - finding local extrema and saddle points in a map. How to locate potential local extrema from the formula for the surface f(x,y)... ?  - slope in all directions must = zero, so, in particular,    both partial derivatives must equal zero ...    (Example: Missouri Farmland)				Sec. 10.1.:#2,5,7,13,17,18 Take a look ahead at section 10.2.

WEEK 12

T 4-1		Test 2 (Sections 9.1-9.3)
R 4-3		The role of critical points in optimizing functions of two (or more) variables. Finding critical points: Theory and practice  - Missouri Farmland  - Removing peptides from crayfish processing byproducts (#16)				HW: # 13, 15, 17: Find all critical points

WEEK 13
  e-mail rossa@xavier.xu.edu 

T 4-8		determining if we have local max. / local min. / saddle point at critical point. The D test.		a function which is concave down in x and y direction at a critical point, but does not have a local maximum...		HW: finish # 13,15,17 in Section 10.2 hand in: #10 of Sec. 10.2 (in new text!) Begin to read Section 10.3.
R 4-10		Sec. 10.3: Optimizing under Constraints  - paths through the Missouri Farmland    (and checking for high and low points      along the path...)  - the matress production example...    optimize under constraint by    (1) "follow your nose" trial and error    (2) Substituting K=98-8L into          productivity formula... (see Cobb          Dougl. html on right for summary)		Cobb-Douglas Example (html) Cobb-Douglas Example (mws)		HW: Maximize productivity under our constraint using Math150 methods on P = 48.1 . L0.6 . K1-0.6 after substituting the constraint K + 8L = 98. also Sec. 10.3. #1,3

WEEK 14

T 4-15		Sec. 10.3: Optimizing under Constraints Finish (2) from above The Lagrange Multiplier Method: The rationale (why it works) and an example...				HW Sec. 10.3 # 9, 11 I recommend to use both methods:      (1) use constraint to eliminate one of the variables      (2) Lagrange multiplier method Also: optimize the function h(w,z) = .6w2 + 1.3z3 - 4.7wz under the constraint that z = .6w - 4 and that z must be between 2 and 6.
R 4-17		Easter Holiday -- No Class

WEEK 15

T 4-22		Discussion of Section 10.3 homework open floor for general questions (chapter 10)				In preparation for the test, I recommend to work the exercises through #4b of the review test in our text. (not: #4c,d, #5)
R 4-24		Test 3 (chapter 10)

WEEK 16

T 4-29		student presentations
R 5-1		student presentations

Final Exam: Tuesday, May 6th, 4:00-6:00 p.m.