Math 246: Calculus for the Biological Sciences I, Winter 2008

Course information

CRN:	23093
Location:	301 Deady
Time:	Monday–Thursday
	4:00–4:50 p.m.
Office hours:	See schedule
Text:	Calculus for Biology and Medicine, 2nd ed., by Claudia Neuhauser
Prerequisites:	Math 112 or satisfactory placement test score
Supervisor:	Wendy Sullivan, assistant department head

Class log

Some online versions of handouts are in the Portable Document File format and require a special reader. You probably already have a PDF viewer installed on your system. If not, some PDF viewers include GSView and Adobe Reader (previously known as Acrobat Reader).

Thursday, 13 March

• Final exam review packet: Part I, Part II
• Optional final exam review session: Tuesday, 18 March, 4:00 p.m., Deady 208. Please come with questions!

Tuesday, 11 March

• Homework update:
  1. You may have until Thursday to turn in the homework that was originally due today.
  2. I didn’t mean to assign Section 5.6. I meant to assign Section 5.8. Either way, I’m not going to cover enough by Wednesday to collect either.
  3. If you already started working on Section 5.6 (or 5.8), turn in what you did Thursday for extra credit.

• Remember to log onto DuckWeb and fill out your course evaluations this week. If you don’t want to fill out the course eval, you can scroll to the bottom and decline. If you don’t either fill out course evals or officially decline, then you will not be able to see your grades until March 28, the Friday of spring break! I think we’d all agree that would be rather unfortunate.

  Course evals, especially the written comments, help me improve as a teacher. I won’t see what you’ve written until grades are assigned. So, please fill out your course evals.

  If you have any more questions about the course eval system, please see the registrar’s web site.

Friday, 7 March

• The folks at the UO Libraries asked me to remind you that the Knight Library will be open 24 hours a day from Tuesday morning of dead week until Friday night of finals week.

Wednesday, 5 March

• Handout about homework.

Tuesday, 4 March

• Homework (due Tuesday, 11 March Thursday, 13 March):
  • Read Section 5.3. Then do exercises 2, 6, 12, 16, 20, 22, 24, 26, 36, 38, 44.
  • Read Section 5.4. Then do exercises 2, 5, 12, 20, 22, 23.
• Last homework (due Thursday, 13 March):
  • Read Section 5.5. Then do exercises 2, 6, 10, 16, 24, 40, 44, 48.
  • SEE UPDATE ABOVE! Read Section 5.6. Then do exercises 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 32.

Thursday, 28 February

• Monotonicity and convexity worksheet.

Wednesday, 27 February

• Homework (due Tuesday, 4 March):
  • Read Section 5.1. Then do exercises 6, 16, 18, 22, 24, 34, 36, 38, 40, 44, 48, 50, 52, 54, 56 (Hint: I did 56 in class!)
  • Read Section 5.2: Then do exercises 2, 4, 6, 9, 10, 12, 16, 20, 26, 28, 30, 32, 34, 36, 38, 39, 40, 41, 42, 44.

Monday, 25 February

• Quiz Wednesday, up through end of Chapter 4.
• I handed out a copy of an article (Rajapakse, et. al., Hardy’s “Small” Discovery Remembered, Notices of the American Mathematical Society, vol. 55, no. 3 (March 2008), 384–386) describing a contribution that the mathematician G. H. Hardy made to the field of population genetics. I thought it might interest some of you. (The article is available for free download from the AMS; follow the link.)

Sunday, 24 February

• Midterm II solutions.

Tuesday, 19 February

• Differentiation practice (solutions).
• Solutions to “Trigonometric derivatives”
• Solutions to Quiz #3.
• Differentiation rules so far. (Ignore the part on the bottom about the “Focus on Practice”. If you want to “focus on practice”, do odd problems in your book.)
• Homework (due Tuesday, 26 February):
  • Read Section 4.5. Then do: 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 66, 73.
  • Read Section 4.6. Then do: 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 60, 64, 66, 70.
  • Read Section 4.7. Then do: 8, 10, 12, 14, 20, 24, 26, 28, 30, 32, 34, 38, 40, 46, 64, 74, 76.
  Really, you should be doing as many differentiation problems as you can. Do odd ones for practice!

Saturday, 16 February

• Midterm 2 review.

Wednesday, 13 February

• Trigonometric derivatives (solutions).

Tuesday, 12 February

• Homework (due Tuesday, 19 February):
  • Read Section 4.4. Then do: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 38, 46, 50, 52, 56, 58a, 60a, 64, 66, 68, 70, 72, 74, 78, 80, 86. Hints:
    1. A right-circular cone (in exercise 70) is what you’d probably think of if they had just said “cone”:
       
    2. The symbol ∝ in exercise 72 means “is proportional to”. See example 7 on p. 26.

Wednesday, 6 February

• Derivatives review worksheet (solutions).

Tuesday, 5 February

• Homework (due Tuesday, 12 February):
  • More from Section 4.2: 42, 44, 48, 50, 52, 56, 60, 66 (Hint: look for f'(x) = 0.), 68, 74.
  • Read Section 4.3. Then do: 2, 6, 10, 14, 18, 22, 24, 26, 30,, 32, 34, 46, 38, 40, 46, 48, 50, 52, 54, 58, 66, 70, 72, 78, 84, 46, 94. (Really, you should do as many differentiation problems as you can, so that way you can become more adept at taking derivatives.)

Monday, 4 February

• Sum, difference, and constant multiple rule worksheet (solutions).
• Midterm I solutions.

Tuesday, 29 January

• I handed out a three-paragraph excerpt of an article (Miller, et. al., A Critical Review of Twenty Years’ Use of the Resource-Ratio Theory, American Naturalist, vol. 165, no. 4 (April 2005), 439–448) on Tilman’s resource-competition model. The excerpt began “Tillman (1980, 1982) used the resource-ratio theory to make a number of predictions, [...]”.
• Homework (due Tuesday, 5 February):
  • Read Section 4.1. (The handout is related the the section labeled “Tilman’s Model for Resource Competition”.) Then do exercises: 2, 4, 6, 14, 22, 24, 32, 34, 35, 36, 37, 38, 39, 40, 42.
  • Read Section 4.2. Here we learn some rules for differentiation. The best way to remember these rules—and yes, we do want to have them memorized—is to practice taking derivatives. After much practice, you’ll be able to take derivatives very quickly.
    • Doing (and turning in) exercises 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 will be good practice.
    • (For better practice, you should do some, maybe all the, odd problems as well, but you needn’t turn those in.)
    • After those, please do exercises 42, 48, 56, 58, 64, and 70.

Saturday, 26 January

• Solutions to Quiz #1
• Solutions to Quiz #2
• Solutions to “Practice with limits”
• Solutions to “Using the limit laws”

Friday, 25 January

• Redacted version of the first midterm

Tuesday, 22 January

• Review session for the first midterm: Friday, 3:00–3:50 p.m., 301 Deady (our usual room).
• Homework (due Tuesday, 29 January—please don’t wait until the night before!):
  • Read Sections 3.2, 3.3, 3.4, and 3.5.
  • Section 3.2: 2, 6, 8, 16, 20, 24 (Hint: exp(x) means the same thing as e^x), 26, 28, 30, 34, 38.
  • Section 3.3: 2, 8, 10, 26, 28.
  • Section 3.4: 2bc, 4c, 6, 8, 10, 12.
  • Section 3.5: 2, 4, 6.
• The quiz tomorrow will cover material up to Section 3.1.

Wednesday, 16 January

• Using the limit laws (solutions)

Tuesday, 15 January

• Homework (due Tuesday, 22 January):
  • Read Section 2.3. Don’t worry about memorizing all the details (I’ll never ask you to recite the formula for, say, the discrete logistic equation) of this section, but focus on getting the flavor of the section. Mainly, I want you to see how slightly changing the different parameters can radically change the outcome of the system.
  • Here is a picture that shows the chaotic behavior of the discrete logistic equation x_t+1 = r x_t(1 - x_t):
    
    (This image taken from Wikipedia.)
    When 1 < r < 3, the system will stabilize to one value. As r increases to just over 3, the system oscillates between 2 values, then between 4 values, and so on. After r is slightly above 3.6, the system becomes chaotic.
  • From Section 2.3, do exercises 14, 16, 18, 36, 38, 40.
  • Read Section 3.1. (Do pay attention to the details here.) Then do exercises 2, 4, 6, 8, 10, 16, 20, 22, 24, 26, 30, 32, 34, 40, 42, 44, 46, 48, 50, 52, 54.

Thursday, 10 January

• Homework (due Tuesday, 15 January):
  • pp. 99–103: 2, 4, 8, 12, 14, 16, 20, 24, 26, 30, 32, 36, 40, 42, 72, 76, 80, 82.
• Practice with limits (solutions).

Tuesday, 8 January

• Syllabus.
• Getting to know you.
• Homework standards.
• Homework (due Thursday, 10 January): Read Sections 2.1–2.2. Then do these exercises:
  • pp. 87–89: 3, 6, 10, 14, 18, 24, 28, 32, 36, 40, 44, 48, 50, 52, 54, 56, 58, 60, 62, 64, 68, 72, 74, 75, 76, 77.
  Be sure to follow the homework standards handout.

Monday, 7 January

• Class this day will be conducted by Chad Giusti.

Last updated: 13 March 2008