Week 1 

9/2  write a short report on the Math Labs we did in class today.  Include any observations or comments.  Hand in results on Thursday

9/4  Please download for next class:  Areas-K, Functions-K, and rate of change-K

Hand in only the starred problems:

  Do:  *speed on a hill problem - pg 5  lines-K

          *John and Mary run a race problem - pg 5 Lines-K

          *Terminal velocity problem - pg 6 Lines-K

          pg 4 Lines-K/ do all odd problems

purchase some graph paper

Week 2

9/9

Lines-K  page 6/linear depreciation problem

Functions-K  page 2/ 1b,c,d  For each of these try to find the result when h--> 0

Today's handout  page d/ problem 1 and 2.   If you understood what I did in class today, find the area under the function y = 1/x from problem 2 between x = 1 and x = 5

Read Forum-K Sections 1 and 2

Read Areas-K Section 1

Print out Rate of Change-K

9/11

hand in only the starred problems

*Lines-K  page 6/linear depreciation problem

*Functions-K  page 2/ 1b,c,d  For each of these try to find the result when h--> 0 (the result will depend on the value of a)

*Areas-K  page 4 problem a and b at the bottom of page

Read areas-K   For additional information about signed areas under curves you can download areas-AN

Bring rate of change -K to class tomorrow.

9/12

* means hand in,   ** means extra credit

We will have a fifteen minute quiz on Tuesday covering lines, functions, areas and rate of change

Download:  rate of change -AN, areas -A, and Accumulated rate of change -K

Read Functions-K Sections 6,7,8 on pages 9-11

*Functions-K page 10- problems 1 a,b,c at top of page (composite functions) and problem 1a,b,c at the bottom of the page (inverse functions)

**Do the problem on page 11

Areas -K  page 8 problems 4-7, 9, 12-15

*Use the trapezoid formula on page 4 to find T⁽⁴⁾  for f(x) = 4x(1-x)  on the interval [0,1]

** Use the trapezoid formula to find  T⁽⁴⁾ for f(x) = sqrt(1-x²) on the interval [0,1].  The answer should approximate pi (why?)

Week 3

Rate of change - K page 6 problems 9,11,12,13

9/18

Read Section 2 and 3 in Functions - K

Do:

Functions - K problems on page 5

Functions - K   Exercise on the bottom of page 7*  a,b,c,d,e,f  applied to problem i on the next page.  Use graph paper to do this problem.

Also find the formula for the function in problem i *   (i is enough for tomorrow.  Save ii for next time)

Download areas - AN and do page 254  problems 16, 21 a, b (express answer in terms of A), 22 *(use any one method of approximation left, right , middle or trapezoid), and  23* (use three trapezoids,

Please download for tomorrow and bring to class:  accumulated rate of change - K

Makeup quiz in room 611 Cullimore at 4 PM

9/19

Read Accumulated rate of change - K

Do:  page 5/ 1,2*,3,4,5*,6,7*,9,10*, 11** (extra credit)

Do the Mary problem on page3

Functions - K do problem ii on page 8

Download Lesson 1 in the class notes on the web and bring it to class on Monday.  You will also need a piece of graph paper.

Week 4

9/22

Do the three problems from the handout.

Download Lesson 2 and bring it to class

I would like to have a short quiz on Friday on rate of change, area, accumulated rate of change and graphing of functions.

9/25

Now that we went over problem 'a' on the handout sheet today, you are invited to do b,c and d over again.

For extra credit you can try to do the problem that I set up in class today where a hinge was placed in the corner of the structure and it was analyzed in two pieces with two hinges, one with forces R1 and R2 acting on it and the other with forces R3 and R4 acting.  Good luck.

9/26

Do the three beam problems on the handout

Make sure that you download Lesson 2.  You can also try reading it to get a head start on our next lesson and see if it makes sense to you.

We will have our first exam on Tuesday Oct. 7

Week 5

9/29

Do the beam problem on page 7 of Lesson 2.  Solve for the shear force, V, and then use the three methods that we talked about in class today to find the bending moment, M.  That is find M by the mechanics method (sum of vertical, horizontal , and moments equal 0), the area method, and the slope method.  If you read Lesson 2 it will tell you how to do this.

I am postponing the exam until next Thursday so we can have another review session next Tuesday (I will not be able to come to a review session this Friday)

Please note that there is another Technology and Society Forum tomorrow (Oct. 1) at 3 PM in the Campus Center Ballroom.  Miquela Craytor, the Executive Director of a group named Sustainability South Bronx is coming to talk.  She will describe how her organization had been able to turn a devastated area like the South Bronx into a great place to live with lots of green architecture, jobs, gardens and industries.  I hope that you can make it. 

10/2

Do the problem that you were working on in class today which is problem 2 on page 9 of Lesson 2.  We found the V today.  Use the area method and the slope method to find M.

Solve the cantilever problem that I drew on the board today.  To do this you will first have to first find the values of V and M due to the wall acting on the beam.  Find M for the beam by all three methods.

Good luck.

Week 6

10/7

Do the first problem on Lesson 3 page 3 by using either the area method or the mechanics method (you don't know how to use the slope method yet).  If you succeeded in doing this problem for hw last time then do problem 2 on page 3.

Find the center of gravity of an irregular pentagon by the string method and by the 1/2, 1/3, 1/4 , 1/5 method

Download Lesson 4 on the derivative

There will be one beam problem on Thursday's exam.  The problem will have only concentrated forces like in Lesson 2 not distributed force like in Lesson 3.  There will be a problem on finding areas, rate of change, a word problem with lines, and a problem to sketch curves, and also a problem about Mary's trip to the lake

Note:  Since M(x2) - M(x1) = sign area under V curve, if x2 is at the right end of the beam and x1 is at the left end of the beam then M(x2) = M(x1) = 0 when the beam is free standing.  That means that the signed area under the V curve of a free standing beam is always equal to 0.  This is a nice check on your answer. .

10/10

Do Lesson 3 page 3 problem 2 by either the area method or the mechanics method (extra credit if you use both).

Use the derivative machine to find the derivatives of:

    a)  f(x) = 2x + 3

    b) f(x) = x^3

    c) f(x) = sqrt x

Download Lesson 5

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