Math 222: Calculus for the Life Sciences
Fall 2005, 4 credits, MRC 378, MWF 9:00-9:50, R 8:00-8:50
Instructor: Rich Maresh, Associate Professor, Mathematics Department
Office: MC 521, Phone: 796-3655, Hours: MWF 12-1, R 1-2
Final Exam: Tuesday, 13 Dec 2005, 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 with Applications for the Life Sciences, by Greenwell, Ritchey, and Lial (Addison-Wesley, 2003).
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.
a. Linear functions
b. Least squares line
c. Properties of functions
d. Quadratic functions
e. Polynomial and rational functions
2. Exponential and Logarithmic Functions
a. Exponential functions
b. Logarithmic functions
c. Applications: growth and decay
3. The Derivative
c. Rates of change
d. Definition of the derivative
e. Derivatives and graphs
4. Calculating the Derivative
a. Techniques for finding derivatives
b. Derivatives of products and quotients
c. The chain rule
d. Derivatives of exponential functions
e. Derivatives of logarithmic functions
5. Graphs and the Derivatives
a. Increasing and decreasing functions
b. Relative extrema
c. Higher derivatives, concavity, the 2nd derivative test
d. Curve sketching
6. Applications of the Derivative
a. Absolute extrema
b. Applications of extrema
c. Implicit differentiation
d. Related rates
e. Differentials and linear approximation
b. Substitution technique
c. Area and the definite integral
d. The Fundamental Theorem of Calculus
e. Area between curves
8. Further Techniques and Applications of Integration
a. Numerical integration
b. Integration by parts
c. Volume and average value
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 an exam following chapters 1 and 2, chapters 3 and 4, chapters 5 and 6, and then a final cumulative exam at the end of the course, following chapters 7 and 8. These exams will be done in class subject to the 50 minute time limit, 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 3 or 4 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. After each of these labs I will ask you to write up a brief reflection paper about the lab you just did. These will be due the next class period and should comment on the basic idea you were supposed to learn from the lab problems.
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.
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 – this is required. I am also requiring each of you to write up a brief reflection paper on each of the labs, due the next class meeting, in which you reflect on what you learned from the lab, or what you think you were supposed to have learned – this will be more or less a “journal”.
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.
Because this is the first time this course has been taught we are all serving as guinea pigs, and there may very well need to be some adjustments made along the way. But I need to put something down on paper at the start, so here it is.
Exams 350 Points (three exams, each 25 pts on practice exam, 75 pts on individual part; a quiz on integration, 50 points)
Final exam 150 Points (25 pts on practice exam, 125 on individual part)
Group Labs 140 Points (eight labs, 20 points each, but one missing allowed)
Reflection papers 40 Points (one after each lab, 5 points each)
DERIVE problems 50 Points (this is an estimate, 5 assignments 10 points each)
Class participation 25 Points
Attendance 55 Points (one point per day)
Total: 810 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”.
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 335, 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.
I think that regular attendance in 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 whether absence is “excused” – too many subtleties and degrees there - just a point a day when you are there.
One other note about the labs: because I want to collect them all at the end of class and grade them for the next class meeting, there will be no opportunity to “make them up”. You either do it or you don’t. But I am making a bit of an allowance here; the total value of the labs is 140, but it is possible to earn 160 points in total – basically I have one lab as a “freebie”.
Fall 2005 MATH 222 Tentative Course Schedule
29 Aug <1.1> Lines and Linear Functions p 15 # 1-33 odd, 45-55 odd, 65, 67, 71, 75
31 Aug <1.2> The Least-Squares Line p 27 # 3, 5, 9, 11
1 Sep <1.3> Function properties, Domain, Range, Composition p 40 # 1-43 odd, 55-63 odd, 69, 71
2 Sep <1.4> Quadratic Functions p 50 # 3-31 odd, 43, 47, 49, 55
7 Sep Lab #1
8 Sep <1.5> Polynomial and Rational Functions p 61 # 3-39 odd, 47, 49, 51
9 Sep Chapter 1 Review p 69 # 37, 39, 43, 53, 59, 61, 63, 65, 67
12 Sep <2.1> Exponential Functions p 85 # 1-25 odd, 31, 35, 37
14 Sep <2.2> Logarithmic Functions p 99 # 1-53 odd, 65, 67, 75, 77
15 Sep <2.3> Applications: Growth and Decay p 107 # 7, 9, 11, 15
16 Sep Lab #2
19 Sep Group/Practice Exam #1 (25 Points)
21 Sep EXAM #1 (75 Points)
22 Sep <3.1> Limits p 148 # 1-49 odd, 61, 65, 69
23 Sep <3.2> Continuity p 159 # 1-23 odd, 31, 37
26 Sep <3.3> Rates of Change p 169 # 1-19 odd, 23, 25, 27
28 Sep <3.4> Definition of the Derivative p 186 # 3-37 odd, 43, 47
29 Sep Lab #3
30 Sep <3.5> Derivatives and Graphs p 194 # 3-15 odd
3 Oct <4.1> Techniques for Finding Derivatives p 212 # 1-23 odd, 27-47 odd, 53
5 Oct <4.2> Derivatives of Products and Quotients p 221 # 1-31 odd, 37, 39
6 Oct <4.3> The Chain Rule p 231 # 1-13 odd, 17-41 odd, 53, 55, 59
7 Oct Lab #4
10 Oct <4.4> Derivatives of Exponential Functions p 238 # 1-25 odd, 33, 35
12 Oct <4.5> Derivatives of Logarithmic Functions p 247 # 1-35 odd, 47, 49
13 Oct Review … p 261 # 69, 73, 75
14 Oct Group/Practice Exam #2 (25 Points)
17 Oct EXAM #2 (75 Points)
19 Oct <5.1> Increasing and Decreasing Functions p 274 # 1-31 odd, 37, 39
20 Oct <5.2> Relative Max and Min Points p 287 # 1-31 odd, 37, 39, 41
24 Oct <5.3> Higher Order Deriv, Concavity, 2nd Derivative Test p 300 # 1-37 odd, 61, 63, 67, 77
26 Oct <5.4> Curve Sketching p 313 # 1-23 odd, 43, 45
27 Oct Lab #5
28 Oct <6.1> Absolute Extrema p 327 # 1-27 odd, 37, 41, 45
31 Oct <6.2> Applications of Extrema p 338 # 5-19 odd, 29, 39
2 Nov <6.3> Implicit Differentiation p 347 # 1-37 odd
3 Nov <6.4> Related Rates p 353 # 1-19 odd, 25, 27
4 Nov <6.5> Differentials: Linear Approximation p 361 # 1-25 odd
7 Nov Lab #6
9 Nov Review …
10 Nov Group/Practice Exam #3 (25 Points)
11 Nov EXAM #3 (75 Points)
14 Nov <7.1> Antiderivatives p 378 # 5-35 odd, 45, 47, 49
16 Nov <7.2> Substitution p 388 # 3-33 odd, 37
17 Nov <7.3> Area and the Definite Derivative p 398 # 7-25 odd
18 Nov <7.4> Fundamental Theorem of Calculus p 409 # 1-43 odd, 53, 55, 59
21 Nov Lab #7 (Thanksgiving week)
28 Nov <7.6> Areas Between Two Curves p 424 # 1-29 odd
30 Nov <8.1> Numerical Integration p 443 # 1-13 odd, 23, 25
1 Dec <8.2> Integration by Parts p 454 # 1-33 odd, 43
2 Dec <8.3> Volume and Average Value p 1-27 odd, 39
5 Dec Lab #8
7 Dec Integration Quiz (50 Points)
8 Dec Review …
9 Dec Group/Practice Final Exam (25 Points)
13 Dec Final Exam: Comprehensive, 125 Points (12:50-2:50 pm)