-*---* A. Iarrobino, Math U141, Fall 08 Classnotes

Math U141 class notes, Fall 2008

Prof. A. Iarrobino



Section A meeting MWTh at 9:15 AM in 308 Hurtig (Key #18759).
Section B meeting MWTh at 10:30 AM in 140 Dodge (Key #18770)


Look here for specific assignments and brief comments on what we did (or will do) in class. This will be updated usually by 9 PM each class day. TBA = "to be announced"


Course-wide Spring 08 syllabus (assignments: your instructor will pick a subset): Math U141 course wide Syllabus C (List of topics, assignments) (pdf) (the instructor will assign HW problems, usually from this list.

Information sheet (grading, etc. for Prof. Iarrobino's sections) Math U141 Information for Prof. Iarrobino section Syllabus A (pdf file)

Course home page (you probably already know this information): Math U141 home page (html)

Course outline (broad strokes) Course Outline



First day of classes: Wednesday September 10: Take placement quiz.
Go over syllabus, information, introductions.
Review the equations of a line, both slope-intercept y=mx+b form and point slope form. (Text section 10.2)
Find points a fraction - as two thirds - along the line segment between two points. (Worksheet #1A).

Second day of classes: Thursday, September 11: Return placements, discuss interpretation (see below).
Find points along a line seqment, more practice.
Deciding when a function given in table form is linear function, finding lines to match data in table.
Emphasis on units of measure, as: the slope of a line has units the quotient: y units/x-units.

HW for Monday September 15: Worksheet #1A (hand out in class), #1A-E. Text Section 1.2 p. 11 # 2,7,9 or 10.

For more information on linear functions, read Text Section 1.2.

Placement quiz Interpretation: : 7 or higher out of 11 algebra skills appear to be stong enough for Calculus 1, perhaps you have some material to review; 5-6 plan to attend algebra review sessions, or obtain tutoring, or do a thorugh review for algebra; 3-4 less: consider switching to Math U121 Precalculus, or Math 110 algebra, or plan a rather more extensive review of algebra, as pre-calculus algebra skills appear to be too weak to pass Math U141. 2 or less: not enough algebra skilss to pass Math U141.

Note: Class packets Available at Reprographics as of September 15, Monday after class (corridor behind Campus Bookstore, about $7). We will use from the packet worksheet 1B for Wednesday HW, and practice quiz 1 for Thursday's quiz.

Week of September 15: Linear functions and units, change of units and slope. Average slope of a function. Quiz 1.

Monday September 15 Questions. We went over WS 1A #1A,B,D,E.
Further questions on finding a point a fractional distance olong a line. Change of units in slope, and in equations of a line (continued).
Average slope between points x=1, 1+h on y=3x^2, or y=5x^2.
Instantaneous slope at a point, as limit of average slope.

Homweork for Wednesday Sept. 17. Read Text p. 135-139 (limits), Begin p. 139 #1 (We will discuss it in class).
Do WS 1A #2a,b,c (but 9:15 AM class please use y=5x^2 in place of 3x^2, done in class). [Added Tues AM online].

Wednesday September 17 Average slope of a function from a given point and instantaneous slope at a point.
We went over an example WS 1A #2 (or variation for 9:15 class, y=5x^2).
Here y=3x^2, P(1,3) and Q(1+h,3(1+h)^2).
We wrote the The Difference quotient rise/run for m_{PQ}
Here m_{PQ}=6+3h, after simplification of the expression.
The instantaneous rate of change (slope) of a function at a point P is the limit of average slopes from P to Q, as Q approaches P.
In the example, m_P= 6.
This is the definition of derivative of f(x)=3x^2 at x=1, as a limit, a key concept in calculus.

Then each class went over text p. 139 #1 (from HW), identifying line segments related to the slope m_{PQ} of the secant line PQ, for f(x) given as a graph.

We also went over the example f(x)=2^x, at P(0,1). The difference quotient is (2^h-1)/h and we took very small h to approximate the limit as 0.6931... (the actual slope of 2^x at P is ln(2) but we can't tell that from approximating this way.) See p. 136 Example 2 of text (which begins from (2^h-1)/h. s

HW for Thursday Sept 17 Do Quiz 1a from Class Packet. Also text p. 140 #2,4,5

Thursday, September 18 Questions; Quiz 1 (second half of class)

Math U141 F08 Quiz1 (pdf)

Math U141 F08 Quiz1-Solutions (pdf)

Homework for Monday, September 22 Read Text Section 2.1 ``Instantaneous Rate of Change''
Do p. 103 #1-4,6,7,9,14,21,23.

Week of September 22 Insantaneous rate of change, slope functions, continued, Worksheet 2B (polywog), and text.

Monday, September 22: Quiz 1 back (solutions on web). Questions on HW from section 2.1: we went over #2,3,7, 9 or 14, 21 on p. 103.
Instantaneous rate of change, continued.
Derivative function (Section 2.2)
Interpreting the derivative function of y=3x^2, (here y'=6x). Using y,y' to find equations of tangent lines to y=f(x). (Section 2.2).
[9:15 AM section: Using the definition of derivative to find the derivative function for y=3x^2.]

Homework for Wednesday September 24 (Plan)
Section 2.2 p. 109 #1-8, 9-12,14, 27,29 (mostly graphical derivative function)
Read Section 2.3 through Example 6 p. 114. Do p. 116 #1-5 (units of derivative function).
[9:15 AM section: Also do Worksheet 2A #1D. (reference, Quiz 1A p. 35, #1D and solution in back)] (this will be on HW for Thursday Sept 25 in 10:30 AM class).

Wednesday September 24 Check HW. Questions on HW.
Graphing the derivative, intro to concavity, inflection points
Local linear approximation (text p. 114-115 in Section 2.3)

Partial homework for Monday September 29 (see below for rest)
Section 2.3 p. 116 #9-13,15,18 (units of derivative, interpret); 23, 25, 27 (local linear approximation)

Thursday September 25. Derivative function, continued, graphing the derivative function, concavity. Maximum problem.
Questions from 1 minute feedback: graphing, local linear approximation - when to use it? What is f'(x)?
Worksheet 2B #1, (pollywog, interpret f'=0 as max depth for a quadratic function f.
Begin derivative formulas for powers x^n.

Homework for Monday, September 29 (continued from above)
(assigned Wed): Read "Local linear approximation" p. 114-115. Do Section 2.3 p. 117 #23,25,27
Class Pac: Quiz 2a p. 38 #3.

Week of September 29 Power rule (section 3.1), exponential functions (sections 1.5-1.6), their derivatives (Section 3.2), exponential functions (sections 1.5-1.6), their derivatives (Section 3.2). Composite functions and chain rule (Section 1.8 and 3.3). Quiz 2 Wednesday or Thursday.

Monday September 29: Questions.
Power rule - (x^n)'=nx^{n-1}. Obtaining power rule from definition of derivative, The expansion of (x+h)^n using Pascal's triangle
      1
     1 1
    1 2 1
   1 3 3 1
-----
1 n ..........

Difference quotient done in class for x^2, and x^3, then indicated for x^n.
Using formula to differentiate powers and roots (WS 2B #3A,3B, Section 3.1).

Homework for Wednesday, October 1
Text "Composite functions" p. 55 #3,9,11,30.
Quiz 2A p. 37 of packet - do problems up to #4B (the rest is chain rule, we'll discuss Wednesday).
Text Section 3.1 p. 147 #5-7,9-19,23,27,
(assigned from web ) WS 2B#3A,3B.

Wednesday October 1 Questions.
Chain rule, extended power rule. WS 3A.

Homework for Thursday, October 2
Worksheet 3B #5 only (we did most of it in class)
P. 157 chain rule #1-33 odd (you may omit problemw with sinx, cos x)

Thursday October 2 Questions.
(if time) Concavity (Section 2.4).
Section 2.3 #37 interpret "compliance" (students to do this, together in class).
Quiz 2 (see below, allow at least 40 minutes)

Homework for Monday October 6
WS 2B #3
Read Section 2.4, Do p. 122 #1-9.

Week of October 6 Concavity, logarithm, exponential functions and derivatives, product rule.

Monday, October 6
Quiz 2 and solutions back. Go over.
Chain rule, WS 3B #5.
Second derivative and concavity: Section 2.4.

HW for Wednesday, Oct 8
Text p. 122 #8,9,11,12, 15, 16.
WS 3A #3 (graph using calculus, by graphing first the max, min, and inflection points.

Wednesday, Oct 8 Questions: p. 122 #16: using slope f' information to graph f" then f.

10:30 AM class #8: comment after class by Meaghan O.: w is concave up!
Product, quotient rule, WS #3B #4, also #6B
Graphing B(x)=xe^{-x/3} using calculus: finding max: set B'(x)=0, find P(3,3/e).

HW for Thursday Oct 9: WS 3B #6,7
HW for Wednesday Oct 15: see above, also text Section 3.4 p. 162 #2, 3-15 odd, 34,41.

Thursday, October 9 Product rule, continued; graphing using calculus (we used #41 p. 162, and WS 3A #3 as examples).
For further discussion, read text Chapter 4.1 "Local maxima and minima".

Homework for Wednesday, October 15
See above for Section 3.4 HW
Class Packet Quiz 2.5 p. 39 (solutions later)

Week of October 13 Exponentials and logarithm functions, trigonometric functions, graphing using calculus, half quiz.

Monday October 13 Columbus Day holiday, no classes.

Wednesday October 15 Questions. Graphing using calculus. Exponential functions (section 1.5).

Homework for Thursday, October 16
Read text chapter 4.1,4.2 (graphing using calculus)
Do p. 180 #1-5;
Do Section 4.2. p. 186 # 12,13, 17.
(Optional) For more practice graphing, to prepare for quiz, choose problems from #11-20 p. 186 of text.

Thursday October 16 Questions, exponential functions, Quiz 2.5.

Homwwork for Monday, October 20.
A. Read sections 1.5,1.6,1.7 of text.
Do Section 1.5 p. 38 #1,2
Section 1.6 p. 43 #1,3,5
Section 1.6 p. 50 #15 (9:15 AM; 10:30 AM try is, we'll discuss in class).

B. Exam 1a F03 p. 45 of classpac: do Section 1 (all p. 45).

Week of October 20 Exponential functions, global max-min, review for Exam 1, Exam 1 Thursday.

Monday, October 20 HQuiz 2.5 back with solutions. Go over.
Exponential functions (Section 1.5, 1.7.). Percent growth and Exp functions. Formulas A=A_0(r)^{x/t_0}, with t_0 the time period for ratio r.
A= A_0 (R)^x with R growth ratio per unit time.
Exponential standard form A= A_0 e^{kx}. Finding A_0, k, given two data points. Converting the others to standard form.
[ Remark: in continuously compounded interest at rate k, the decimal k is the coefficient of x in the A_0 e^{kx}).].

Global max-min (section 4.3), given an interval of x. Step 1, find critical points in interval. Step 2, write a table with the x, y values of those critical points and the endpoints. The global max is (x,y) in table with y biggest; the global min the point with y smallest.
p. 191 Problem #15 (begun in class)

Homweork for Wednesday, October 22 Section 1.5 p. 38 1-3,6,16,18.
Section 1.7 p. 50 #15,16.
Section 4.3 p. 192 #5-8,15.17,30.
Complete Exam 1a F03 from Class Pac (p. 45-46).

Wednesday October 22 Questions, review problems

Thursday October 23 Exam 1 (see below).

Homework for Monday October 27
Worksheet 5 p. 27 of packet #1-3 (exponential functions).
Read Section 1.10 Periodic functions, Do p. 68 #1,2.
Read Section 4.8. Surge function (this is just f= axe^{bx}), do p. 225 #1a,b.

Week of October 27 Periodic functions (includes trig), surge function, antiderivative and motion.

Monday, October 27 Exam 1 back. Went over graph, exponential problems.
Periodic functions (Text section 1.10): trig functions, radian measure, amplitude, period, y = Asin(Bx)+C as model.
Surge function (Section 4.8) y-axe^{-bx}, used to model drug concentration.
MathU141 Fall O8 Exam 1a Sols (9:15 AM) (pdf)
MathU141 Fall O8 Exam 1b Sols (10:30 AM)


Homework for Wednesday, October 28
Text p. 68 #1-5, 8, 12,13.
p. 225 #1-4, 6,9.

Wednesday, October 29 Questions, p. 68, p. 225 #3,8 or 9.
Antiderivatives and IVP (initial value problems) (Section 7.1 of text).
Motion word problems - begun: see WS #4A, in class packet p. 13 for a worked example.

Homework for Thursday, October 30
Section 7.1 of text, p. 303 #1-17 odd, #27,29.
Packet p 24 (A1 page), #1-11.

Thursday, October 30 Questions. Review antiderivative.
9:15 class: review of surge function problems. Began motion WS 4A example.
10:30 class: go over antiderivative examples; motion problems
In motion problems we use s position, v velocity, and a acceleration are related by differentiation (s to v to a) or antiderivative (a to v to s).

Homework for Monday, November 3 Worksheet 4A p. 13 of classpack: Ex 1-2 at bottom.
Class packet p. 25 (A2) #1, 10.
Worksheet 4B #1. (Use the relation between s,v, and a).

(Optional): Read text p. 170-172. Do p. 172 #7,11.
(Optional, to prepare for max-min word problems: Read WS 4C page 15 of packet).

Week of November 3 Motion, max-min word problems. Begin integral (if time).

Monday November 3 Questions. Motion problems, continued.

Homework for Wednesday November 5
WS #4B #2, p. 14 of packet Packet p. 21 (MM#1), #1-6,8-9,10.

Wednesday November 5 Motion questions: We went over WS 4B#2, p. 21 #8. Students put a few others p. 21 on board, or we went over them.
Max-min word problems (begun) :
A. Maximize area of two rectangular side-by side pens, if one has 900 linear feet of fence.
Step 1: maximize A=xy, given 2x+3y=900. Step 2, sub y=(900-2x)/3 into A. Step 3. Set A'=0. Ans. x=225, y=150., A_max=(225)(150).

B. p. 21 #8. Step 1. Write cost C=2(x+2y)+1(y)=2x+3y, to minimize, side 25000=xy, solve latter for y and sub in cost, then set C'=0 .

HW for Thursday November 6
Read p. 15-20 of class packet. [Note, it is simpler to let x be the whole length of fence, as we did in class, slightly different from p. 15. But the broad step by step approach I gave is that on p. 15, and carries over to different types of Max-min word problems. An important step is choosing which function F is maximized or minimized, and which is the side condition! Another key step is finding the critical point of F.
Complete the max-min word problems assigned p. 25.
WS 4C #1,2.
P. 21 of packet (labelled MM#1), #1-6,8.

Thursday Nov. 6 Max-min word problems, continued. Students put problems on board. Discussion of range, and the two paradigms for fence/perimeter or cost and area problems
Revenue, ticket, orchard problems. Text p. 201 #20 (ice cream revenue), Packet p. 21 #18 (peaches), These involve finding a linear function N(x), and maximizing the prodcut x N, where x is either price per unit (so N is number of units sold), or x is number of peach trees per acre (and N is bushels of peaches per tree).

Homework for Monday, November 10 Packet p. 22 #18-23 (ticket, etc), #24,25 (a little different).
Quiz 3 p. 40 of packet, (solutions p. 91, but I suggest you work the quiz first before looking at solutions, in order to practice for Quiz 3 Wednesday).

Week of November 10 Max-Min, Quiz 3 Wednesday, Integral.

Monday November 10 Questions
Integral (9:15 AM only)
Practice for Quiz 3 (one page, passed out)
MathU141 Practice Quiz 3 (pdf) (passed out in class).
MathU141 Practice Quiz 3 solutions (pdf)

Homweork for Wednesday, November 12
Practice for Quiz 3 (do practice sheet)
Read Section 5.1 Integral.
(9:15 AM only; Worksheet 6A, #1,2.

Wednesday November 12
Questions.
Integral.
Quiz 3 (45 min).
MathU141 F08 Quiz 3 solutions (pdf)

Thursday, November 13. Quiz 3 back.
Integral as area (Section 5.3, WS 6)
Approximating distance from a table of velocity using left and right sums, and trapezoid sums (5.1)
Begin Riemann sums Section 5.2

Homework for Monday November 17
Read Section 5.1. Do p. 240-1 #2-7,9
Do WS 6B #2,3
Quiz 4 p. 42 #1A,B.
(optional) Do Exam 2 practice from packet (only the problems we have dicussed to now)

Week of November 17 Integral, continued; practice for Exam 2, Exam 2.

Monday November 17 Questions. Integral: as area, Riemann sums
Properties of integral: additivity, linearity (see text p. 172).
Change in amount = integral of rate (section 5.2)
FTC: integral from a to b of f = F(b)-F(a), F any antiderivative of f

Homework for Wednesday November 19
Amount from rate: Section 5.4 p. 258 #1,3-7 odd, 10-14 all, 30.
FTC: Section 5.5 p. 265 #11. Section 7.3 p. 312 #1-11 odd, 18.
Integral and area: Section 5.3 p. 253 #8-10,16.
Packet Exam 2 (solutions later in packet): Omit #4,6, 7A,C. #8iii. Note #8A uses p. 272 of text and geometric area (8A).
Good Practice for Exam 2: See Fall 07 Exam 2 posted below.

Wednesday, November 19 Questions on Integral (p. 258 #12,13,...). Area between two curves (text p. 252). Practice for Exam 2.

HW for Thursday Practice for Exam 2.

Wednesday, November 19 Office Hour 1:30 PM-3:30 PM)

Thursday November 20 Exam 2. (see below)
Solutions to MathU141 F08 Exam 2 (pdf)

HW for Monday, November 24
Read Section 5.3 esp. p. 251-2, area between curves.
9:15 AM section: Do Section 5.3 p. 253 #25,30,32. Also Classpac,p. 48 Exam 2 F03 #4.
10:30 AM: may try the #4 (see solutions).

Monday November 24 Exam 2 back, reviewed #2,4A,C.
(9:15 AM) Question #32 p. 253 area between curves.
(10:30 AM) Area between curves (example y=x^3, y=4x, first quadrant)
(All) Begin ODE (chapter 10): Interpreting problem as an ODE (Section 10.1).
Checking whether a given function y=f(x) is a solution to a given ODE. (Section 10.2).
Exponential growth: ODE y'=ky with solution y=A_0 e^{kx}. Section 10.4

HW for Monday, Dec 1. Read Sections 10.1,10.3,10.4
Section 10.1 p. 400 #1-3,5-7,9,13-15.
Section 10,2 p. 404 # 1-3,5,13-15.
(9:15 AM) Section 10.4 p. 416 #1,5,7,9. (10:30 AM begin these): exponential growth
(10:30 AM) Section 5.3 p. 253 #25,30,32; Packet p. 48 #4. (area between curves)

Wednesday-Thursday Nov. 26-27 no class, NU closed for Thanksgiving. Have a safe and enjoyable break!

Week of December 1 ODE, equilibrium, Newton's law of cooling. Quiz 4 Thursday.

Monday December 1 Questions: we discussed assigned problems from each section<, including Section 10.1 p, 400 #2,6,7,14,15; Section 10.2 p. 404 #1,5,13-15; Section 10.4 #1.
10:30 AM questions on p. 253 #30,32 (area between curves.
Equilibrium solutions: Solve y'=0: discussed for NLC, logistic equation (p. 400). Stable, unstable equilibrium (9:15 AM class)
Newton's Law of Cooling y'=k(L-y) with solution y=L+Ce^{-ky} (Section 10.5). Properties of solutions. Note: for temperature problems k>0 when NLC is written this way.

HW for Wednesday, December 3
Section 10.5 p. 424 #1,3,5,8,13,16-18. [Note change #8 for #6
Note also, In #1,3,5,6 p. 424 the constant k is negative when the ODE equation is written in the above standard form y'=k (L-y).
10:30 AM: Do exponential growth Section 10.4 p. 416 #1,5,7,9.
(Optional) Prepare for Thursday quiz: Do Quiz 5 p. 43 in packet. Also Quiz 4 #2.

Partial make up for Exam 2 to a maximum 72 C by making an 85 on a MU outside of class: I plan to announce this in class Wednesday.

Wednesday, December 3 Questions. Practice ODE. NLC again.

Thursday, December 4 Questions; Quiz 4.

Homework for Monday, December 8 Do Final Exam Fall 2003 p. 58 and FE Fall 2006 p. 64 ff in class packet. I suggest that you do Fall 06 under exam conditions (no notes, 2 hour limit), then compare your solutions with answers later in packet. (Both have solutions in packet).

Monday December 8 Quiz 4 back, Solutions handed out.
- Practice -students did Fall 07 FE in small groups, and put solutions on board.

HW for Wednesday December 10 and later Continue preparing for FE: Sample problems for Fall 2003 FE (p. 53ff) and Final Exam Review Fall 2007 (p. 73). Note that all FE problems and FE have solutions later in packet except Fall 2007. I plan to post solutions to Fall 2007 by Monday Dec. 15.

Wednesday December 10 Questions. Continued practice for FE.

Extra Credit HW If you wish, bring ECHW to Final exam. Either separate or in notebook (could be with your class notes) with headers for section (or page of classnotes). I will sample this to determine an ECHW grade.
A level counts 4 points in HW-Quiz grade, and I use ECHW on occasion in course grade decisions. Please pick you ECHW up before leaving the final exam!

Course wide review Wednesday Dec 17 at 2;30-4 PM In 325 Shillman (this deliberately overlaps a half hour with two FE periods, so most students should be able to make at least an hour of the review). Bring questions.

Office Hours:
Wednesday Dec 10: 4-4:30 PM
Thursday Dec 11: 3-4 PM
Monday Dec 15: 2:30-3:30 PM
Wedmesday Dec 17: 8:30-10 AM; and 2-2:30 PM. (course wide review 2:30-4 PM 325 Shillman).


Forthcoming featured events

Final Exam Friday December 19, 10:30 AM (two hour) at 300 Richards.
Make your travel plans so you can take the final, required of all. Bring graphing calculator and Extra Credit HW (see information sheet of syllabus).
MathU141 F08 FE formula sheet (pdf) (this is the formula sheet that will be on the Final Exam.)
Answers to Fall 07 FE (pdf)

Archived events

Quiz 4 Thursday, December 4. See Quiz 4 #2 (area between curves), Quiz 5 (ODE) in class packet for sample.

Exam 2 Thursday November 20. See practice Exam 2 in packet and Exam 2 Fall 07 below. The exam will cover the course since Exam 1. The focus is on the material on the practice for Quiz 3 (see above), and also the integral (Thursday Nov. 13, Mon. Nov. 17).
Further practice: MathU141 F07 Exam 2 (pdf) (note, #3 area between curves, to be discussed Wed Nov 19 - see text p. 252).
A good way to prepare is to try to solve a practice exam under exam-like conditions (timed, no notes), then check your answers. Solutions to MathU141 F07 Exam 2 (corrected 11/19/08 pdf)

Quiz 3 Wednesday Nov. 12. Sample: See Class Packet p. 40 Quiz 3 F03, and practice quiz passed out Monday Nov. 10. Also be prepared for a max-min "ticket" problem (see #18-23 p. 22 of ClassPac. There may also be a surge function problem (Section 4.8)
For further practice: MathU141 Fall O7 Quiz 3 (pdf)
A good way to practice is to do the Quiz 3 Fall 07 in quiz conditions (as if you were taking it),
and then check your solutions with other students or/and the solutions set below
. MathU141 Fall O7 Quiz 3 Solutions (pdf)

The following, is a solution to a different Q3 . You can try to solve the problems on it first (without looking at solutions) then look. MathU141 another old Quiz 3 solutions (pdf)

Exam 1 Thursday October 23. See sample Exam 1 in class packet p. 45-46 and also previous classnotes. It is cumulative and will include exponential functions and global max-min (sections 1.5-1.7, 4.3).
For further practice,
MathU141 Fall O6 Exam 1

The best way to prepare for an exam is
a. to practice doing problems in near exam conditions
b. Work in a study group to practice problems,
You may wish to delay downloading solutions!

MathU141 Fall O6 Exam 1 Solutions

> Half quiz 2.5 Thursday October 16. See sample quiz 2.5a p. 39 in class packet. Also, text sections 4.1,4.2, p. 186 #12,13,17.
MathU141 Fall O7 Quiz 2.5
MathU141 Fall O8 Quiz 2.5
MathU141 Fall O8 Quiz 2.5 Solutions

Quiz 2 Thursday October 2. See Sample Quiz 2a, in ClassPac p. 37, solutions later in ClassPac. We will have chain rule but no trig functions. Exponentials with chain rule possible. Expect a problem on linear approximation along the tangent line (see p. 115 ff in Section 2.3, and the problem 3 on the Fall 07 Quiz 2 below.)
Math U141 F07 Quiz 2 (pdf)
Math U141 F07 Quiz 2 Solutions (pdf)

Math U141 F08 Quiz 2 (pdf)
Math U141 F08 Quiz 2 Solutions (pdf)

Quiz 1 Thursday Sept 18: see sample quiz 1 in class packet.
Expect also a problem part on finding points a fraction along a line segment, or beyond (find the point 2/3 between PQ, or the point 2/5 beyond Q along the line through PQ).
Expect two problems #1,2 resembling #1,2 of the Sample Quiz, but with no #1D extra credit. Then one extra credit problem 3: part A is like #4 on Sample quiz; part B like Example 2 p. 136 as outlined above.

Reminder: attendance policy The attendance policy (announced in Syllabus: information sheet):
Briefly, more than four unexcused absences affects your grade, or may result in a W or F in the course.


Questions or comments: e-mail to a.iarrobino@neu.edu.  This is the quickest way to reach me, or come by 526 NI, MWTh.

Math U141 home page (html)

Math U141 Fall 2007 Classnotes (may give an idea of timing of future material, quizzes, exams).

Math Tutoring  Free, at NU, available to Math U141 students. Begins Sept. 22.



Links  to other calculus resources on the web:

Visual Calculus (U. Tenn)


Prof. Anthony Iarrobino
Department of Mathematics
Northeastern University
Boston, MA, 02115
Office:526 NI
Phone: (617) 373-5524
Email: a.iarrobino@neu.edu


Created: September 14, 2008. Last modified: December 15, 2008. URL:http://www.math.neu.edu/~iarrobino/AIMathU141Spr08classnotes.html