MTH 1108 Basic Calculus 2 - Graphing Calculator Section

Winter 2001

Course Description

Review of Differential Calculus, and extension to trig functions.

Integral calculus including antiderivative, Fundamental Theorem of Integral Calculus, and approximation of integrals by Riemann, trapezoid, and Simpson's sums.

Applications of Integral Calculus to

Some Differential Equations important in applications to health sciences, population growth. Concept of mathematical modelling.

Course Information

Course: MTH 1108, Basic Calculus 2
Instructor: Professor Anthony Iarrobino, Office: 526 NI, phone: 373-5524; e-mail iarrobin@neu.edu
Time and Place: Section 1: M-W-Th at 8:00 AM to 9:05 AM in Room To Be Announced,   (Key #)
Textbook: Ostabee & Zorn, Calculus from Graphical, Numerical, and Symbolic Points of View, Volume 2, Harcourt Brace & Co. (1997),
ISBN 0-03-016977-1
Note: this is a different text than that used by other sections.
Also, Solutions Manual (packaged with text at the bookstore, share if you buy used).
Office hours: Mon, Wed, Thurs: 9:30-10AM; Wed 12-1 PM, Thurs. 1-2 PM, or by appointment.
Class Notes: Brief notes about what was done in class, HW assignments.
Final Exam: Time TBA. See main info sheet for MTH 1108 for more info.

Graphing Calculator: You are required to have, or to have access to a graphing calculator (GC) for this section. The preference is for a TI-85 or TI-86; also TI-83 or TI-82 (I may have trouble getting you the programs for the TI-82) may be used. These are chiefly used to help understand the integral as a limit of Riemann sums, and approximations to an integral, beginning in the second week of classes. There are some GC programs that I will supply for the TI GC's, that do these sums. If you have another make GC and know it well (and can program Riemann sums on it), you may prefer to use it, but I will not be able to help you. The TI-85 and TI-86 also can be useful in the differential equations section, as well as in graphing curves, as in MTH 1107. Most students in the GC section already have or purchase a GC; they cost about $90-$120. I don't have extras, but you may be able to borrow one, or share.

Why is there a GC section with a different text and syllabus?. There is discussion within the mathematics department about whether a GC should be required in the Math 1107-1108 sequence. I have been a proponent of requiring it, and students who have used it generally report that they have found the GC useful in understanding the course, and many expect to continue to use it. The Ostabee-Zorn text is oriented to GC use, and also has a more careful treatment of Riemann sums than in the textbook for other sections; also there are some optional sections in the Ostabee-Zorn text that are useful applications (as probability distributions, used in psychology, geology, and underlying statistics that are important in the health sciences). The two textbooks are similar in philosophy, but the Ostabee-Zorn is more detailed, and suitable as a reference. It costs a little more, and it is not perfect: I have added worksheets with applications keyed to our course.

Is the GC section more difficult than other sections? I don't think so. I do believe there can be a deeper exploration of the concepts, especially in the added attention to Riemann sums. The GC sections have been taught for several years. Overall course grades in the GC sections are similar to those in other sections. See my teaching philosopy

Is use of the GC taught? Yes, for the GC calculators listed above, you will learn how to do basic graphing, and use the Riemann sum programs in the class. In the past, some students have already been familiar, so have taught others. I am also available in office hours or by appointment to answer questions.

Study groups: We usually divide into study groups of three or four persons for work in class such as worksheets. These will be assigned, and will change from time to time. It is possible that one quiz will be done in groups, if the class so wishes. All exams are individual.

Attendance policy: Your regular attendance is expected, and is particularly needed when we work in groups. You are responsible for knowing assignments and other class information even if you should miss a class. If you are noted absent more than four times, your final grade may be W (withdraw). If absent 0 or 1 time, with good participation, bonus of 2%.
Homework: I will sometimes collect weekly homework and mark it done/not done, possibly +/-. I will also collect and grade some worksheets.
Extra Credit Homework Grade: At the end of the course, at beginning of the final exam, you may pass in your collected homework for an extra credit grade, based on amount completed, I will pass it back as you leave.
Optional portfolio (extra credit) A summary you write of your work to date, with commentary on what you have learned. You may wish to prepare for the portfolio by writing a weekly commentary.

Reading assignments: You will be asked to read chapters in advance of our class discussion of them - please prepare questions for discussion. The weekly quiz will include questions about the reading.

Grading will be based on several half-hour quizzes, collected homeworks and worksheets (20-25%), two exams (35-40%), and the final exam (40%). Homework and worksheets will be regularly assigned and discussed in class. Quizzes will normally be material from homework and worksheets, so doing the homework is very important.


Assignments

WS = Worksheet, *=harder, EC = Extra Credit, R&OL=Read and outline. Note: I may change these assignments, or assign a portion. Your responsibility is to try those assigned, and to come in with any questions to class. Some require more thought than just routine applying formulas you've seen, as the point is to check understanding. We will choose at most several of the optional sections.

Derivatives:Review of differentiation- especially chain rule. Product and quotient rule, derivatives of trig functions. Work Sheet #1A (2p), 1C (1p.)
- Graphing the derivative function f'(x) given the graph of f(x). WS #1B.

Integral and signed area
Properties of area, what is an integral? Read and outline § 5.1; Do § #1,2,4a,b,5,6,*28. EC:#7,10,23,34.
Area function A_f(x) = integral from a to x of f(x), R&OL § 5.2. Do WS #2A #1-3. § 5.2 #2,*4,5,6; then (2nd assignment) *10,11, 13, EC #7,*15,*20a.

Fundamental Theorem of Calculus R&OL § 5.3. Do #1a,2, 3a,b,d,e,f (Hint: you need to know antiderivatives of each integrand). Begin WS #2B.
Graphing the integral A_f(x) and f(x). Using the antiderivative. (2nd assignment): § 5.3 #1b, rest of #3, 4,*7,11,15. EC #12,13.

Graphing Calculator skillsGraphing functions, adjusting range, finding extreme values Ð max-min, finding zeroes. Use of Riemann sum program. Finding integrals. Graphing indefinite integral. (In class practice).

Approximating sums for the integral Read and outline §5.4. Do #1,3,14a,b. (in #3,14 use GC Riemann sum program to obtain left, right and trapezoid sums). (2nd assignment) #2,*10,15. EC #17.

Applications via approximating sums: distance from speed, amount from flow, area between curves. R&OL §5.5. Do § 5.5 #1,2,5,6,7. EC. *4,9,13,14. WS #2A rest.

Antiderivatives by formula§ 6.1. Do #1-8, 24. EC #9-15, 23,27,29.

Substitution method Read and outline § 6.2. Do #1-10. Also, WS #3. (2nd Assignment) § 6.1 #11-14,35,*37,39,41,70-72. EC #61,36,40,42,*80.

Reduction formulas § 6.3 #4,5,7-9,11,15,17. Also, find integral of cos^3(2x) from 0 to pi/4, same for sin^4(2x). (see also § 9.3 #2-5. EC 9.3 #17,18,25, *34).

Applications to volume Read and outline § 8.2. Do § 8.2 #1-4, 7,9. *11, *12, 17,19, 22.

Applications to flow & amount of water, or of dissolved substance, or to flow & amount of electricity.
KEY IDEA: the integral of rate of change = amount. WS #3.

Approximating the integral (Most sections optional, except intro to Simpson's rule)
Error bound for left sums of monotone functions Read and outline § 7.1. Do #1,3,19,*26.
Error bound for left, right sums, using derivative. Read and outline §7.2. Do #3,6,13.
Error bound for trapezoid sum Read and outline § 7.3. Do trapezoid sum portions of #1,2,10,11. EC #14.
Simpson's rule Read and outline § 7.4. Do #3,6,15. EC. #14, WS #5.
                                                           Exam 1

Application: Work (Optional) Read and outline §8.4. Do #1-3,8, 9. EC #7.

Application: present value of an income stream (Optional) Read and Outline § 8.5 Do #1,3,5,8. EC #7,9.

Fourier polynomials and approximation of functions (Optional). Read and outline § 8.6. Do # 1,7,9,10.

Integrals involving infinities . (Optional) § 10.1 #9,10,12. EC #15,24-27.

Application to probability density functions. (Optional, but likely) Read and outline § 10.3 Do #1,2,7,14,19, 20, 24. EC. #4, *5, 15, 20, 23.

Differential equations.
Initial value problems (IVP). Newton's law of cooling. Read and outline § 4.1 p. 743. Do #1,2,11,15, 19. EC #14, 17,18, 20. WS. #6 (or sample exam #2).
Exponential Growth (review) and logistic equation. § 4.2 p. 751. Do #1, 5 (logistic equation), 6, 9. EC #13. WS or/and Sample exam.
Meaning of Differential Equations. §12.1 Do #1,2,5. EC #6.
Mathematical Modelling (Handout). Do problems #1-3.
                                                            Exam #2.
Slope or direction fields (Optional) Read and outline § 12.2. Do #1,2,7 and slope field for y' = 4y(2-y) (logistic equation). EC #3,8,9.
Separable ODE's, and logistic equation (again) § 12.4. #1,*3,4,7, 15, 22 EC #19,21,23,25.

Review. Sample final. Final Exam.


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

Class Notes  Winter, 2001.

Old Class Notes, from Spring 2000 Math 1108 GC sections:

Old Class Notes, from Winter 2000 Math 1108 GC section:

Back to Math 1108 home page.


Created: December 29, 1999. Last modified: Jan 4, 2001. URL:http://www.math.neu.edu/~iarrobino/AIMath1108.