-*---* A. Iarrobino, Math U141, Fall 06 Classnotes

Math U141 class notes, Fall 2006

Prof. A. Iarrobino


For Section


meeting MWTh at 10:30 AM in 159 Ryder.


Look here for specific assignments and brief comments on what we did (or will do) in class. This will be updated at least weekly and usually by 4:30 PM each class day. TBA = "to be announced"


Course-wide Spring 06 syllabus info (Prof. A. Iarrobino coordinator): Math U141 Course wide info (Syllabus A) (pdf)

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

Syllabus (goals, assignments) for A. Iarrobino section Math U141 Detailed assignments: syllabus C (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 6 Go over syllabus, information, take placement quiz (for student info only). Review the equations of a line, both slope-intercept y=mx+b form and point slope form. Finding points a fraction - as two thirds - along the line segment between two points.

HW for Thursday September 7: Worksheet #1A (handed out in class), #1A-E.

Thursday, September 7 We went over WS#1A, problem #1. We emphasized the role of units in equations: using #balloons, minutes vs. #balloons, hours led to different equations.
Then we studied average rate and instantaneous rate of change for y=5x^2 (giving height of ballon in feet x minutes after start) between x=1,x=3 (obtaining 20 ft/min) then (x=1, x=1+h), obtaining 10+5h, and between (x=3, x=3+h), obtaining (30+5h), and we discussed the limits as h goes to zero, as instantaneous rate of change.

Note for more information on limits, see p. 135-139, especially examples with quadratic functions (not exponential yet).

HW for Monday: Worksheet #1A, #2.3
Also Text Section 1.2 p. 11 #2,7,9,15,20-21,24,26-29.

Week of September 11 Continue discussion of average, instantaneous rate of change. Derivative function. Quiz #1 Thursday.

Monday September 11 We went over Text Section 1.2 #24,29. Also WS #1A .
We continued discussion of average, instaneous slope.
We introduced derivative function, and found the derivative function of y=3x^2, using the definition: we first found the slope m_{PQ} between P(x,3x^2) and Q(x+h,3(x+h)^2), namely
m_{PQ}= 6x+3h, then we found the limit
  m_P=lim_{h to 0) m_{PQ}=6x.
Interpretation of derivative function as slope of f(x) at any point.
Finding the equation of tangent line at a particular point. Example, y=3x^2, y'=6x: when x=-5, slope f'(5)=6(-5)=-30, eqn of TL: y-75=-30(x+5).
Approximating a slope at P by using m_{PQ}, Q a nearby point. We did this for y=5e^{sin x}, slope at x=0, using P=(0,5), Q=(0.0001, 5e^{sin(0.0001)}), finding an estimated slope 5.00025, close to 5 (the actual slope, from chain rule we study later).
Passed out WS #1B, and part of Spring 06 Quiz #1.

HW for Wednesday, Sept 13 WS #1B all, Quiz #1 Spring 06 (p. 1 only).

Math Tutoring at Math Dept 540B NI this week: Mon: 10 AM-1PM, Tues 10 AM-9PM, Wed 11-12 AM.

Wednesday, September 13 (Plan) Continue discussion of derivative function. Meaning of derivative function (worksheet #2A)

Thursday, September 14 (Prof. Krikorian substituting for this class only) Questions on derivative. Quiz #1 (35 min).

HW for Monday, September 18 Read p. 135-139 of text. Do p. 139 #1,5,6 (use calculator),19,20, 25,26.
Worksheet #2B, class pack: #1A-C. For part C use the quick formula, slope of ax^2+bx+c is f'=2ax+b.

Week of September 18 Interpretation of derivative. Slopes of polynomials (Section 2.1-2.3, worksheet #2B, possibly Section 3.1)

Monday September 18 Passed Quiz #1 back, we went over problems 2-3.
Reminder of math tutoring hours at 540B Nightingale, forthose who want extra help. (see class info sheet in packet for website with hours).
Formulas for derivative of a degree-2 polynomial.
Use of derivative to obtain maximum point (worksheet #2B, polywog problem #1, all parts.
Approximating derivative from table information (Section 2.1 #7) using average slopes.

Homework for Wednesday Sept 20 Complete the HW above for p. 135-139 on limits.
Section 2.1 p. 103 #3,7,11,10,21,23,26.

Wednesday Sept 20 Derivative function, and interpretating the derivative (Section 2.2, text. Graphing a derivative function from a graph of f(x). Inverse problem of interpreting derivative as Section 2.2 #30 balloon problem.

Homework for Thursday Section 2.2, #2-7,9-12,14,19-26, 30 (done in class).

Thursday Sept 21 Questions answered on Section 2.2.
We continued interpreting the derivative function (section 2.3).
Concavity of a functioin and recognizing it from graph or table of f'(x) (see Section 2.3 and 2.4).
Local linear approximation to a function, or/and using the tangent line at a point P (section 2.3).
Formulas for derivative function of power functions x^n is nx^{n-1}: we derived these using the Pascal triangle to expand Delta y = (x+h)^n- x^n. (Section 3.1).

Homwwork for Monday Section 2.3, #9,10, 23,25,30,37,38
Section 3.1 #5-7, 9-19.

Announcement Due to a family need, I will not have office hours Monday afternoon, Sept 25, but will resume regular hours Wed Sept 27, before Quiz #2.
There is a chance I will make it back for an office hour Monday 4-5 PM, feel free to phone x5524 or drop by to check if I'm back.
In any case you have excellent tutoring Monday till 9 PM around the corner (see below)

Tutoring Note the extensive Mon-Wed Math tutoring hours (from 10 AM to 9 PM) in 540B Nightingale. There is a designated Lead tutor for Math U141, Elizabeth Doovan, who has taught Math U141, and is currently teaching the sequel course, Math U142. The tutoring is well monitored, and likely to be helpful. One can sign up in advance (many slots for next week were open today).

Week of September 25 Exponential and logarithm functions and their derivatives. Composite functions and chain rule Section 1.8, 3.3. Quiz #2 Thursday.

Monday Sept 25 Exponential functions (section 1.5), overview of ln (section 1.6), their derivatives (section 3.2). Composite functions (Section 1.8).
Emphasis on exponential functions, and concept of equal ratios in equal times (for an exponential function of time).
Two ways of writing an exponential function F = A_0 e^{kt), and F=A_0 b^t, use of each to model a problem, conversion from one to the other.

Homework for Wednesday, Sept 27
Section 1.5 p. 38, #1-4,6,9,11,13,17,25-26.
Section 1.6 p. 43 #1,3,5,21.
Section 1.8 p. 55 #3-5,9,30.
Section 3.2 p. 152, #1-11 odd.

Wednesday September 27 Chain rule (Section 3.3).

Homework for Thursday, Sept. 28.
Section 3.3 p. 157 #1-8 all, #19-23 odd, 33, 36,44.
Worksheet #3B, #5 (chain rule)
Quiz 2A in Class Packet (p. 37-38), in preparation for Quiz 2.

Next office hours:
Wednesday Sept 27: 2:30-4:30+ PM
Thursday, Sept 28 12-1:30, 2:30-3 PM.

Tutoring The Math Workshop, 540B Nightingale, is open 10 AM till 9 PM on Wednesdays (as well as Mon,Tues).

Thursday Sept 28 Questions. Product rule (if time), followed by Quiz #2 (See below for further information on the quiz).
About 25 minutes for questions and product rule (briefly, if time), 40 minutes for quiz. (No product rule on quiz).

Homework for Monday, Oct 2
Section 3.4 p. 161 #2,3-15 odd, 39,41.
WS #3B #4,6B,7.

Week of Oct. 2 Product, quotient rule (Section 3.4), continued;
Local and global max-min using calculus to graph functions (Chapter 4 and packet);
Begin Max-min word problems (Class packet).

Monday October 2 First work groups set. Quiz 2 back, we went over Problems #3,4.
Product & Quotient rule: volunteers presented HW on board (see above).
Worksheet #3B (p. 12 packet), #6B, 7 began in class.

Next Office hours Monday Oct 2 1-4 PM.
Tutoring: Math Workshop, 540B NI, 10AM-9 PM Mon-Wed. Note, they have Quiz 2 and solutions on hand.

HW for Wednesday
Worksheet #3B (p. 12, packet), #4-6,7.
Read Section 1.10 (trig functions), begin p. 68 #1-5, 13,31,34.

Extra Office Hour
Tuesday October 3, 10:40-11, 12-12:30.

Wednesday October 4 Trig functions and their derivatives (Section 1.10, 3.5). Half Quiz 3A (see below).

HW for Thursday, October 5. Section 1.10 p. 68 #1-5,13,31,34.
Section 3.5 Odd #1-11, 15,26.

Thursday October 5. Pass back half quiz 3A. Local maxima and minima (Section 4.1). Three methods to check a critical point for max-min; second-derivative test. Inflection point. Graphing using calculus. (Sections 4.1,4.2)

Homework for Wednesday, October 11.
Local Max, Min: Section 4.1 p. 180 #1-5,8-10,14-15,21,27,28.
Class Packet: WS 3A (p. 11), #3. Exam 1 (p. 45) #2.

Week of October 9. Graphing using calculus. Local, global max,min.

Monday October 9. Holiday, no class.

Wednesday October 11. Check HW. Graphing using calculus, inflections, (Sections 4.1-4.2)

Homework for Thursday, October 12.
Section 4.2 syllabus HW: p. 186 #1-6,8-10,11-15 odd, 26,27-31,33.

Thursday October 12. Questions on Graphing, Section 4.2. Global max-min. (Section 4.3)

Homework for Monday, October 16.
Section 4.3 p. 191 #1-3,5-9,11-20,28-30.
Exam 1a from Class Packet (p. 45-46, solutions later in packet).
Note correction to class packet solution to Graphing problem: "local min", "local max" conclusion should be switched, with same work for SDT.

Week of October 16 Global Max-Min questons, applications to max-min word problems, Practice for exam 1, Exam 1 Thursday.

Monday October 16 Questions on Section 4.3 HW. Max-min word problems (Worksheet 4C, p. 11 of Class Packet).

Homework for Wednesday, October 18: Class Packet p. 21 (MM #1 written at top): Do #1-5, using worksheet #4C as quide.

Wednesday October 18 Max min work problem, practice for Exam 1.

Thursday October 19. Exam 1 (for more info see below).

Week of October 23 Max-min word problems. Logistic Growth (Section 4.7), Surge function (Section 4.8), if time.

Monday October 23 Pass back Exam 1 and solutions. Go over graph related problems. Announce partial make up (see below). Max-Min word problems MM #1 first problems on board, Cost related problems.

Homework for Wednesday, October 25 MM #1 (p. 21, class packet): # 9,10. Also #7, 17.

Wednesday October 25 Fence max-min problems (again) from HW, students put some on board. Fare, cost, profit problems. (Class pack MM #1, and part of Section 4.4.

Homework for Thursday, October 26 MM #2 p. 22 #18-22.

Thursday October 26 Fare problems from HW in class. #36 from Section 4.3(crow problems). Max of surge function (Section 4.8)

Homework for Monday, October 30
Class Pack, MM#2,3 p. 22-23, #23-25 (on #23, replace .002 % by .02%).
Text Section 4.3 #30-33,36 (done in class), 44.
Section 4.4 #20-22 (similar to fare problems above).
Read Text section 4.8, especially p. 420 to 422.
Do Text Section 4.8 p. 225 #1-3,6.

Note opportunity Monday (For those planning to take the partial make up for Exam 1). If you choose the old problems analogous to those you wish to do (see directions) show them to me Monday sometime in person (with old exam), then you may go to the front of any line (so sno wait) when you come in Wednesday or Thursday for the make up.

Next office hours: Thurs Oct 26 till 3 PM, then 4:30-5 PM.
Monday Oct 30: 12:30-3 PM.

Week of October 30 (Retrospective posting) Antiderivative (Section 7.1), Motion & work problems (Packet)

Homework for week
Antiderivatives: Section 7.1 p. 303: #1-18 odd, 27, 33.
Class packet p. 24 (A1) #1-10.
Motion word problems: Class Packet WS 4A, p. 13 #1-3.
p. 25-26 #1-13.
Packet WS 4B, p. 14 #1,2.

Week of November 6 Integral: accumulated change, definite integral and Riemann left-right sums, definition of integral as signed area (chapter 5.1-5.3).

Monday November 6 Questions about motion problems. Begin integral (as area, left sum, right sum).

HW for Wednesday
Text Section 5.1 p. 540 #1-4.
Class Packet WS 6A p. 29 #1.

Wednesday November 8 Integral and left, right sums, continued.

HW for Thursday
Class packet WS 6A p. 29 #2,3.
Text Section 5.1: 7-8,10-11, 14-16.
Text Section 5.2: p. 247 #1,2,7-8


Thursday November 9 Integral, continued. Riemann sums (Left, right, trapezoid sums with n subdivisions, for definite integral. Checked HW.

Week of November 13 Integral and applications. Flow to amount. Fundamental Theorem (integral and antiderivative) (Chapter 5, classpacket). Half Quiz B on Monday.

HW for Monday, November 13
WS 6B packet p. 30: #2A-D, #3A.
Section 5.2 #1,2,7, 11,13,15.
Section 5.3 #1-2 (use n=3).

Monday November 13 Check new HW for those who hadn't completed HW for Thursday).
Definite integral and Riemann sums. Fundamental Theorem. Half quiz A (see below for topics).

HW for Wednesday Nov 15
Section 5.3 #5-9, 10-12,17-18,22.
Section 5.4 #1-3,5-7,9,12-14.

Wednesday November 15. Fundamental Theorem. (Sections 5.4, 7.3).

HW for Thursday Nov 16
Text 5.3 #23-30
Section 5.4 #23-33
Section 7,3 #1-12,26-33.
Section 5.5 #11.

HW for Monday Nov 20
(Class Packet) Read WS #7A, do WS #7B.
(Packet, prepare for Half Quiz): Quiz 3.5 p. 41, Quiz 4 p. 42, Quiz 4.5 p. 43 #1 only.
Section 5.5 #16-18,25-27,38,41.

Monday November 20 Questions from assignment. Half quiz 3.5 (see below).

HW for Monday November 27
Chapter 5 review p. 266 #1-2,4-5,15,17,21,26,28,30,33.
Read Section 10.1 (Differential equations): Try #1,2,5-7
Read Section 10.4 (exponential growth again): #1,10,13.
You may wish to prepare for Exam 2 (see below).

Wednesday November 22 Individual questions, introduction to differential equations.

Note: Day before Thanksgiving. I will teach Wednesday Nov. 22, the day before Thanksgiving, but there will be no quiz that day. Typically students attending that day have time for individual questions. I will not count an absence on that one day toward the attendance policy; but attendance will cancel another absence for the policy.

Week of November 27: Differential equations (selection from chapter 10), Prepare for Exam 2, Thursday (see below ).

Monday November 27. Differential equations - setting up from word problem. Equilibrium solutions.

Homework for week of Nov. 27
Section 10.1 #1-11,14-15
Section 10.2 #1,3,5,9,10,13-15
Section 10.4 #1,10,13.

Wednesday November 29. Questions on ODE. Prepare for Exam 2.

Thursday November 30. Exam 2. (see below)

Homework for Monday December 4
Read Section 10.2. Do #11,12 (see also HW above) (text)
Worksheet #5 p. 27 of packet (exponential growth)

Practice for final exam: (Do at least one item for Monday December 4):
Math 1107 final p. 57- 61 except #6 [not all topics of Math U141)
Sample problems for final p. 62ff
Final Exam Fall 2003 p. 67 ff.
Final Exam Fall 2005 p. 109-116 except #3.

Note: Solutions for the first 3 items are in the packet.

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.

Forthcoming featured events

Final Exam Wednesday Dec. 13 at 10:30 AM. See HW for Monday Dec 4 for practice exams, problems.

Archived events

Exam 2 Thursday November 27.
Cumulative on material since Exam 1, Chapter 4.8,5,7,10, and packet (Max-min, motion, ticket-orchard word problems, flow to amount).
To prepare, Exam 2 in packet p. 47-49 (except #6),
Half quiz 4 (p. 43, this is on new material of Monday Nov. 27, HW assigned for Monday Nov. 27.
Sample integration problems p. 51 of packet except #3C T(50); #5 is on edge of what we have discussed. (Answers are later in packet).

Half Quiz 3.5 A November 20: Integral, Fundamental theorem, area between curves, flow to amount (as integral, also from table of rate of flow). For preparation see Quiz 3.5, 4, and problem #1 of Quiz 4.5, p. 41-43 of packet (answers later).

Half Quiz A November 13. Max-min word problems, antiderivative, motion word problems. For a sample, see Quiz 3 p. 40 of Classpack, but no antiderivative of exponenential or trig functions, and I may omit fence problems in favor of integral. See also Quiz 3.5 #1,3. answers later in packet.

Partial Make up for Exam 1 Wednesday afternoon Nov. 1, Thursday afternoon Nov. 2. (if you have a score below 90 on Exam 1).
Do 1.5(89-score) points from problems on similar exam, like the problems you missed on Exam 1. Get (2/3)(new points) added to old score: so max total score is 89 = B++ for those eligible for the partial make up. See handout with more detail.

Exam 1. Thursday, Oct. 19.
Covers in Text most of Chapters 1-4.3.
In particular Chapter 1: 1.2-1.3,1.5-1.10, and Limits p. 92ff.<\br> Chapter 2: 2.1-2.4.
Chapter 3 all
Chapter 4: 4.1-4.3
And all homework from Class Packet due before the day of the exam.
For a sample, see Exam 1a, F 2003 p. 45-46 of class packet. The Solutions are on p. 81-83, but note correction mentioned above in "HW for Monday, October 16".

Half quiz #2B Wednesday Oct 4: On problems like Q2 #2C,D, 3A,B, 4, also product rule. About 25 minutes. Possible 8 pts to add to Q2 grade (max 20 total).

Quiz #2. Thursday Sept 28. Interpreting the derivative, derivative formulas. Sections 2.1-2.4, 3.1, 1.5, 1.6, 3.2, composite functions and chain rule (Sections 1.8, 3.3, WS 3B #5)
For practice, see Quiz #2A p 37-38 in packet (solutions p. 75-76).
I may replace #1 there (sample quiz in packet) by an exponential growth problem(s) like the word problems assigned in Section 1.5 (gone over Wed. Sept 27), or/and Section 1.6.
Also, section 1.8 (composite functions) may very well appear, and you should expect the Chain rule, as on the sample quiz, and on the HW for Thursday.

Quiz #1. Thursday Sept 14: For guidance, see sample quiz passed out (Spring 06) and gone over today in class, and Quiz 1 from Fall 03 in class pack (p. 35, solutions p. 73). There may be also some problem similar to the HW in Section 1.2. (interpreting data for a linear function, units of linear function).


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

Math U141 Fall 2006 Prof. Iarrobino section Information Information, Office hours, grading, etc for Prof. Iarrobino section

Math U141 home page (html)

Math U141 Spring 2006 Classnotes (may give an idea of timing of future material, quizzes, exams).

Math U141 Fall 2005 Classnotes (may give an idea of timing of future material, quizzes, exams).

Math U141 Spring 2006 Classnotes (may give an idea of timing of future material, quizzes, exams).

Math Tutoring  Free, at NU, available to Math U141 students.



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: iarrobin@neu.edu


Created: August 11, 2006. Last modified: December 1, 2006. URL:http://www.math.neu.edu/~iarrobino/AIMathU141.F06.classnotes