Math 222: Calculus for the Life Sciences
Fall 2006, 4 credits, MRC 346, MWF1:10-2:00, R 12:00-12:50
Instructor: Rich Maresh, Associate Professor, Mathematics Department
Office: MRC 521, Phone: 796-3655, Hours: MWF 9-10, 12-1, R 9-10
Final Exam: Friday, 15 Dec 2006, 12:50-2:50 pm
Catalog Description: This course is intended to be a one-semester survey of Calculus topics specifically for Biology majors. Topics include limits, derivatives, integration, and their applications, particularly to problems related to the life sciences. The emphasis throughout is more on practical applications and less on theory. Pre-requisite: grade of C in Math 180, or suitable placement score. This course qualifies as a General Education course, G9.
Text: Calculus for the Life Sciences, by Bittinger, Brand, and Quintanilla (Pearson-Addison-Wesley, 2006).
Note: I have chosen a text that includes a nice collection of problems that are oriented toward applications of calculus to the life sciences. So this course really has two characteristics: (1) it is something of a “Calculus lite”, a little less emphasis on theory and proof that the traditional course, and (2) it has a particular emphasis on applications in the life sciences.
General Education Core Skill Objectives
1. Thinking Skills: Students engage in the process of inquiry and problem solving, which involves both critical and creative thinking.
(a) The student understands the “big problems” in the development of differential calculus, the tangent problem and the area under the curve problem.
(b) The student understands the mathematical concept of Limit.
(c) The student explores differentiation and works with differentiation formulas for a variety of functions, including exponential and logarithmic functions, and the applications of these methods, especially to problems from the realm of life sciences
(d) The student explores integration and a variety of integration techniques, and applications of these techniques to a variety of problems, especially those related to the life sciences.
2. Communication Skills: Students communicate effectively orally and in writing in an appropriate manner both personally and professionally.
(a) The student does group work (labs and practice exams) throughout the course, involving both written and oral communication.
(b) The student uses technology - graphing calculators and DERIVE in the computer labs - to solve problems and to be able to communicate solutions and explore options.
(c) The student will use the language of mathematics accurately and appropriately.
(d) The student will present mathematical content and argument in written form.
3. Life Values: Students analyze, evaluate, and respond to ethical issues from informed personal, professional, and social value systems.
(a) The student develops an appreciation for the intellectual honesty of deductive reasoning.
(b) The student understands the need to do one’s own work, to honestly challenge oneself to master the material.
4. Cultural Skills: Students understand their own and other cultural traditions and demonstrate a respect for the diversity of the human experience.
(a) The student develops an appreciation of the history of calculus and the role it has played in mathematics and in other disciplines.
(b) The student learns to use the language of mathematics - symbolic notation - correctly and appropriately.
(a) The student will demonstrate the basic ability to perform computational and algebraic procedures using a calculator or computer.
(b) The student will demonstrate the ability to efficiently and accurately graph functions using a calculator or computer.
(c) The student will demonstrate the knowledge of the limitations of technological tools.
(d) The student will demonstrate the ability to work effectively with a CAS, such as DERIVE, to do a variety of mathematical work.
1. Functions (Pre-Calculus Review)
a. Linear functions
b. Polynomial functions
c. Rational functions
d. Trigonometric functions
a. Limits and continuity
b. The derivative
c. Techniques for finding derivatives
d. Derivatives of products and quotients
e. The chain rule
3. Applications of the Derivative
a. Maximum/Minimum values of functions
b. Using the derivative to find max/min
c. Differentials and linear approximation
d. Implicit differentiation
e. Related rates
4. Exponential and Logarithmic Functions
a. Derivates of exponential and logarithmic functions
b. Exponential growth
c. Exponential decay
a. Definition of integration
b. Areas and accumulations
c. The Fundamental Theorem of Calculus
d. Definite integrals
e. Techniques: Substitution, Integration by parts
f. Tables and technology
g. Volumes, solids of rotation
Required Course Work
Your basic work in this course is to learn the material and develop your problem-solving kills so that you can apply the concepts and methods of the calculus to problems you will encounter along the way. It is important that you attend class regularly and especially that you do the homework. The homework may seem “hidden” to you since it will not be graded, but it precisely in that outside-of-class practice that you learn the material. There is a rule of thumb that says college courses require roughly 2 hours outside of class for every hour in class and I think this is not at all an overstatement. It takes discipline to leave class on a Wednesday or Thursday, knowing that you have class again the very next day, and still find a couple hours to practice your calculus, but it is exactly that sort of discipline that is required for success in the course. In short: DO YOUR HOMEWORK!
Your grade will be based on two primary factors: (1) Exams; and (2) Group work. There will be a quiz following the review chapter, an exam following each of chapters 2 , 3, and 4, and then a final cumulative exam at the end of the course, following chapter 5. These exams will be done in class subject to the 50 minute time limit (except for the final, of course), but you can use a set of notes you prepare for the exam and you may use a graphing calculator as well. I see exams as a way to see if you as an individual can actually do what the course asks of you.
Secondly, there will be two types of group assignments: (a) Labs; and (b) practice exams. Every so often, roughly once a chapter, I will take a day and have you work in small groups of 2 or 3 students on a set of problems. I will refer to these problem sets as “labs”, in the sense that you will be exploring the concepts and trying to apply them to the problems. I like the idea of asking you to occasionally work in groups – I think the opportunity to discuss the mathematical ideas is extremely valuable. After all, mathematics is a language as well as a way of thinking about things.
I will also have you take a “practice exam” during the class period just prior to each individual exam. These practice exams will be done in groups like the labs, and must be turned in by the end of the period, as do the labs. This is an attempt on my part to give you an idea of what to expect on the exam.
I am also going to try a sort of “oral exam” this semester – let’s call it an “interview”. After the third exam I will meet individually with each of you and ask a few questions to test your understanding of the material we have been covering.
It is also worth mentioning here that because one of our goals is to develop some skills with technological tools, I will be asking you to use DERIVE on a few problems along the way. DERIVE is a computer program created by Texas Instrument, the calculator people, to perform a very wide variety of mathematical procedures. It is a CSA (Computer Algebra System), which means it can perform algebraic manipulations like solving equations or factoring polynomials, as well as graphing functions in 2 or 3 dimensions. It can also perform calculus procedures and we will have a chance to see some of this power.
My general “lecture” style is more of a give-and-take discussion than simply a rote presentation of material. I like to try to see that the class is following what I am doing and so I want feedback along the way. I often will ask a leading question to see that you are ready for what is about to come.
One specific strategy I will use is called Think-Pair-Share. In this case I will ask a question and have each of you think about it for a bit, then pair up with a “neighbor” and finally share the answer with the rest of the class. Not every pair will share with the class each time, but I hope as we do this on a regular basis most of you will have an opportunity to speak.
I have already mentioned the “Labs” we will do on occasion. I will randomly assign you to a group and give each of you rotating roles within the process; I’ll explain the details when we do that first lab on Wednesday, 7 September. I will try to keep the labs reasonably short so that the group can turn in the work at the end of the period.
The main outcomes I want to see in each of you can basically be listed briefly as: (1) thinking, or problem solving; (2) communicating your mathematical ideas and solutions; and (3) using technology to do some of the work. I will be assessing your ability to do these things throughout the course by grading the labs, the technology assignments, and the exams. I will also be noting your participation in the class room, both in your group work and in general class discussion.
I expect, in sum, that we will have the following possible points during the semester:
Quiz 50 Points (on chapter 1 review material)
Exams 300 Points (three exams)
Final exam 150 Points (25 pts on practice exam, 125 on individual part)
Group Labs 160 Points (eight labs, 20 points each)
DERIVE problems 50 Points (this is an estimate, 5 assignments 10 points each)
Interview 25 Points (week of Nov 13-17)
Attendance 55 Points (one point per day)
Total: 790 Points
I will then assign letter grades as follows: 90% of possible points for “A”, 80% for a “B”, 70% for a “C”, and 60% for a “D”. By the way, I am aware that the biology program requires a grade of at least a “C” in its support courses, so you needn’t tell me that if the going gets “close” later on in the course. I wish this wasn’t the case, since it is sometimes stressful on me as well as on you, and I don’t like “losing” the possibility of giving a “D” grade – sometimes people pass a course but “just barely”.
One final note about grading: I will “guarantee” the grade you earn on your final exam! What I mean by this is, regardless of the grade you have earned based on the percentage of total points, if you score a higher grade on the final I will accept this demonstration that you have learned the material at this higher level and will give that grade. Please don’t depend on this as a means of getting through the course – most people do not show better performance on the final exam, but it does give you one last chance to improve things.
I think that regular attendance is of paramount importance in any course, but perhaps a mathematics course more than most. There may be the occasional exception, a student who is so mathematically talented that she or he can get the material by just reading the text and doing some problems, but for most students it is important to be in class every day. To encourage this I am going to include attendance in the grading scheme in a simple way: 1 point for each day you are there. I’m not going to engage in deciding whether absence is “excused” – too many subtleties and degrees there - just a point a day when you are there.
If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and/or Wayne Wojciechowski, the campus ADA coordinator (MC 320, 796-3085), within ten days to discuss your needs. I want to include taking exams in the learning center under this category; you will need a written request from Wayne Wojciechowski before I will allow you to take exams there.
Fall 2006 MATH 222 Tentative Course Schedule
28 Aug <1.1> Slope and Linear Functions p 16 # 1-35 odd, 57-67 odd
30 Aug <1.2> Polynomial Functions p 29 # 1-37 odd
31 Aug <1.3> Rational and Radical Functions p 38 # 1-51 odd, 55, 57
1 Sep <1.4> Trigonometric Functions p 46 # 1-63 odd
6 Sep <1.5> Trigonometric Functions, the Unit Circle p 58 # 1-53 odd, 59-65 odd
7 Sep Lab #1
8 Sep Quiz: Chapter 1 [50 points]
11 Sep <2.1> Limits and Continuity p 80 # 1-29 odd
13 Sep <2.2> Limits, Algebraically p 91 # 1-39 odd
14 Sep <2.3> Average Rates of Change p 98 # 1-21 odd
15 Sep <2.4> Derivatives as Limits p 112 # 1-35 odd
18 Sep Lab #2
20 Sep <2.5> Differentiation Techniques p 123 # 1-41 odd
21 Sep <2.6> Instantaneous Rates of Change p 130 # 1-19 odd
22 Sep <2.7> Product and Quotient Rules p 139 # 1-41 odd, 95-101 odd
25 Sep <2.8> The Chain Rule p 147 # 3-53 odd, 71, 73
27 Sep Lab #3
28 Sep <2.9> Higher Order Derivatives p 153 # 1-41 odd
29 Sep Review …
2 Oct Group/Practice Exam #1 (20 Points)
4 Oct EXAM #1 (80 Points)
5 Oct <3.1> Max and Min Values of Functions p 176 # 1-23 odd, 37-45 odd
6 Oct <3.2> The Second Derivative Test p 193 # 1-47 odd, 105-109 odd
9 Oct <3.3> Graph Sketching, Asymptotes p 210 # 1-49 odd
11 Oct <3.4> Absolute Max/Min p 224 # 1-53 odd, 71, 73
12 Oct <3.5> Applications: Max/Min Problems p 234 # 1-23 odd, 29, 37, 39
13 Oct Lab #4
16 Oct <3.6> Approximation Techniques p 246 # 1-31 odd, 37-41 odd
18 Oct <3.7> Implicit Differentiation, Related Rates p 253 # 1-39 odd
19 Oct Review…
23 Oct Group/Practice Exam #2 (20 Points)
25 Oct EXAM #2 (80 Points)
26 Oct <4.1> Exponential Functions p 275 # 1-51 odd, 77, 95, 99
27 Oct <4.2> Logarithmic Functions p 292 # 1-61 odd, 91-95 odd
30 Oct <4.3> Applications: Exponential Growth p 308 # 1-11 odd, 25-29 odd
1 Nov Lab #5
2 Nov <4.4> Applications: Exponential Decay p 320 # 1-23 odd, 29, 31, 35
3 Nov <4.5> Derivatives of ax and loga(x) p 328 # 1-39 odd
6 Nov Review …
8 Nov Group/Practice Exam #3 (20 Points)
9 Nov EXAM #3 (80 Points, covering chapters 2-4)
10 Nov <5.1> Integration p 345 # 1-59 odd
13 Nov <5.2> Areas and Accumulations p 359 # 1-23 odd
15 Nov <5.3> Fundamental Theorem of Calculus p 369 # 1-83 odd
16 Nov <5.4> Definite Integrals p 378 # 1-35 odd
17 Nov <5.5> Integration Techniques p 385 # 1-73 odd
20 Nov Lab #6
27 Nov <5.6> Integration by Parts p 393 # 1-41 odd
29 Nov Lab #7
30 Nov <5.7> Integration Techniques: Tables,Technology p 404 # 1-55 odd
1 Dec <5.8> Volumes p 411 # 1-33 odd
4 Dec Lab #8
6 Dec Integration Quiz (50 Points)
7 Dec Review …
8 Dec Group/Practice Final Exam (25 Points)
15 Dec (Fri) Final Exam: Comprehensive, 125 Points (12:50-2:50 pm)