Biocalculus I

MATH 220A and C- Fall 2009

Benedictine University


Basic Information


Academic Honesty

Course Description


Academic Accommodations For Religious Obligations (AAFRO)

Course Objectives


Electronic Devices Policy

Core Goals

In-Class Work

Other Information

Learner Outcomes

Daily Questions

Homework Assignments



Dr. Tim Comar's Homepage 

Technology Requirement

Attendance and Tardiness


Basic Information:

Instructor: Dr. Timothy D. Comar

Location:  Monday, Wednesday, Friday:

A: BK 025, C: KN 135

Office: Birck 128

Phone: (630) 829 - 6555


A: MWF: 9:30 a.m.- 10:40 a.m.

C: MWF: 12:20 p.m. - 1:25 p.m.


Web Site:

Blackboard login:

Office Hours:


10:45 a.m.-12:05 p.m.



10:45 a.m.-12:05 p.m.


10:45 a.m.-12:05 p.m.


by appointment


T. Comar, et al., Calculus and Mathematical Models for the Biological Sciences, (preprints of chapters)

C. Neuhauser, Calculus for Biology and Medicine, 2e, Prentice Hall, 2004


Calculator: TI-83 or TI-84 series strongly recommended. Calculators with computer algebra systems are not permitted on exams,

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Course Description:

This is the first course in a two-semester sequence in calculus with biological applications. There is a strong emphasis on biological models using real biological data. Topics include semi-log and log-log plots, sequences, basic difference equations, discrete time models, limits, continuity, differentiation and antidifferentiation of algebraic, trigonometric, and transcendental functions, applied problems on maxima and minima, equilibria and stability, basic differential equations, and the fundamental theorem of calculus. The course uses the computer algebra system Derive, Excel, and modeling program Berkeley Madonna to explore calculus concepts and biological models

We will approach material using the Rule of Four: Symbolically, Graphically, Numerically, and Verbally. We will emphasize the technical aspects of the course material as well as effective communication of the mathematics. We will use technology including graphing calculators, the computer algebra system, Derive, Excel, and the modeling program Berkeley Madonna to solve problems when appropriate.

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Course Objectives:

We would like to develop proficient understanding of the course material and the ability to use the course material in further course work as well as outside the classroom. To serve these ends, we will emphasize critical thinking and effective communication skills, both verbal and written. Success in this course will be dependent upon your ability to communicate your technical understanding of course material to your peers as well as to the instructor.  You will also be expected to successfully work collaboratively with others.

This biocalculus course is different from a traditional calculus course is that mathematical, biological, and compuational content is integrated throughout the course. You will be expected to think about problems and issues from each of these three perspectives.

Basic skills include: (ISBE Math Content Area Standards in bold)

  1. Using regression and creating semi-log, and log-log plots from data sets.
  2. Understanding Limits in sequences and continuous functions (8C4, 8C5, 8G1)
  3. Differentiation (8C5, 8C6)
  4. Computing Basic Definite Integrals (8C5, 8C6)
  5. Using Calculus and Computational Methods to Solve Biologicallly Oriented Problems (2A, 2C, 3A, 3B, 3C, 4A, 4B, 4D, 4E, 7A3, 7A5, 7B5, 7C7, 8C6, 8E9, 8E10, 8F5, 8G2, 8G3, 9E6, 10A3, 10A4)
  6. Understanding discrete time populations models expressed as difference equations.
  7. Using calculus to analyze equilibria and stability of difference equations.
  8. Understanding how to use the differential to determine error and relative error
  9. Communicating Mathematics Accurately and Effectively (1C)
  10. Using Computational Software to Investigate and Solve Biologically Oriented Problems (2A, 2B, 2C, 3B, 5A, 5B, 7C8, 10E4; Core Technolgy: 5G)
  11. Working Collaboratively with Peers

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Core Goals:

This course contributes to the science component of the core. The course is intended to enable students to continue to meet the following core goals:

1.      Demonstrate an effective level of cognitive, communicative, and research skills;

2.      Achieve a college level of computational skills and an ability to understand and interpret numerical data;

3.      Acquire a knowledge of the history and heritage of western civilization to include: c) scientific literacy through a knowledge of the history, the methods, and the impact of science on the individual, society, and the environment;

5.      Apply liberal learning in problem solving contexts as preparation for active participation in society;

6.      Make informed ethical decisions that promote personal integrity, the legitimate rights and aspirations of individuals and groups, and the common good.

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Learner Outcomes:

To successfully complete this course, the student will:

  1. Demonstrate ability to successfully approach mathematics problems four different ways: geometrically, algebraically, numerically, and verbally (oral and written forms); this will be achieved through homework exercises, projects, and exams.
  2. Evidence understanding of geometric, numerical, and symbolic interpretations limits and computational mastery of limits through homework exercises, projects, and exams.
  3. Evidence mastery of the geometric viewpoints of differentiation and integration through homework exercises, projects, and exams.
  4. Evidence mastery of differentiation and antidifferentiation rules through homework assignments and exams.
  5. Evidence understanding of many applications of differentiation and applications of integration, particularly those related to biology, through problem solving in laboratory projects, homework exercises, projects, and exams.
  6. Evidence the ability to read, represent, and interpret data in numerical and graphical formats through homework exercises, projects, and exams.
  7. Evidence the ability to interpret and apply biological models expressed as basic difference and differential equations through homework exercises, projects, and exams.
  8. Evidence the ability to analyze quantitative biological data using sophisticated mathematical computational software through projects.
  9. Evidence the ability to apply the concepts of rate of change and total change to biological problems through homework exercises, projects, and exams.
  10. Evidence the ability to interpret biological mathematical models and the ability to formulate a biological mathematical model from a verbal description through homework exercises, laboratory assignments, projects, and exams.
  11. Evidence the ability to work collaboratively through collaborative homework and collaborative projects.

IDEA Objectives:

    1. Gaining factual knowledge (terminology, classifications, methods, trends). (Essential)
    2. Learning fundamental principles, generalizations, or theories. (Essential)
    3. Learning to apply course material (to improve thinking, problem solving, and decisions). (Important)

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This course is fast-paced and demanding.  It is expected that you will study at least two hours for each class hour.  You should devote at least ten hours of study to this class per week.    You are expected to read the required section in the text and attempt the assigned problems from the section before the material is either summarized or expanded upon in class.  Your notes from studying should include the following: the title of the section, a list of key concepts from the section, a brief summary of the ideas and techniques presented, solutions to the problems you have solved and a list of questions and problems you have not solved.  Ask questions!  If there is material with which you are not fully comfortable, you are expected to ask questions either during class, online, or during office hours. 

We are a community of learners working together to achieve our course goals. As such, it is incumbent upon all class members to show appropriate respect for each other. Each class member has something important to contribute to the class and should feel comfortable sharing with the class.

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Technology Requirement:

Students are expected to use Blackboard for all course communications, accessing notes and course information, and the completion of certain assignments as indicated in this syllabus. Students are expected to be familar with graphing calculuators and are expected to learn how to use the computer algebra system Maple in the concurrent MATH 207 course. In this course, students will learn how to use MS Excel to represent data graphically and to work with basic discrete dynamically systems. Students may also learn how work with basic discrete and continuous dynamically systems using Berkeley Madonna. The computer algebra system Maple may be introduced. Portions of quizzes and exams may require or prohibt the use of calculators and/or computers.

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Quizzes/In-Class Work


Daily Questions


Group Homework and Projects


Exam 1


Exam 2


Final Exam



The grading scale is 90% for A, 80% for B, 70% for C, and 60% for a D.  It is the student’s responsibility to seek clarification of the course requirements and evaluation policy.

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The homework assignment sheet lists the sections that will be covered in each class and suggested homework problems for you to use to reinforce the text's concepts. It is recommended that you attempt at least seventy percent of the suggested problems listed. These problems may be the content of quizzes. It is your responsibility either to know how to solve all assigned problems or to ask for assistance.  Your homework assignments also require daily questions. (Read on.)

There will be ten or elevenl Group Homework assignments throughout the term. These assignments will be a primary medium for you to experiment and learn the course material. These assignments are designed to help deepen your understanding of the course material through basic problem solving, writing, and applications. In particular, you will work with Excel, Maple, and Berkeley Madonna to analyze problems arising from biological models. You will have the opportunity to re-think, re-organize, and build upon ideas that have been discussed in class. Moreover, you will be to learn computational techniques that can be transfered into other academic and research environments. You will collaboratively with 2-3 other class members and submit one solution set for a grade. Any of the group homework problems may appear on pop quizzes or on exams. Group Homework will count for 35% of the semester grade. No late work will be accepted.

Studying mathematics is a social process. Much benefit can be gained by sharing insights and by struggling through problems with your peers.  You are strongly encouraged to study and work with other class members.  You are also strongly encouraged to consult Dr. Comar outside of the class periods either during office hours or via e-mail at or via the Blackboard site for the course.

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There may be unannounced quizzes based on homework assignments, readings, and classroom activities.  You should be prepared for quizzes daily.  Be prepared!

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In-Class Work:

Cooperative-learning exercises will take place on a regular basis. Learn to work with each other and learn from each other. Some activities may require follow-up work and re-writing outside of class. Some exercises will be graded for accuracy, and others will be granted credit for participation. Additionally, you will be required to write one-page summaries of talks by in-class speakers. The summaries will be included in this grade component. Each summary will count up to one percent of the total semester grade.

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Daily Questions:

Reading a mathematics textbook is very different from reading a novel and is often difficult.  To help you gain practice reading mathematics, you will be required to read the assigned sections, answer a question based on the reading, and submit at least two important questions of your own related to each assigned section.  The questions you pose may be significant questions that the text answers for you.  (In this case, provide a brief answer.)  Other important questions may arise from concepts that are unclear to you or from issues or extensions of concepts that the text does not discuss.

Questions should be significant and should indicate that you have thought carefully about what you have read.  Questions should not be of the form "What was Section 7.3 about?", "Does anybody really care about Section 7.3", "Can you do problem 46?", or "What does "homeomorphism" mean?" You still encouraged to ask about specific homework problems or examples in the text as long as you clearly indicate your issue with such problems or examples.  You may find that by identifying your difficultly and looking back in the text may enable you to answer your own question--a job well done!  All questions will be answered either in class, outside of class, or in written form.  Moral: ask questions!

Many of the basic concepts in the text will not be addressed explicitly in class.  Your questions will help direct discussion to important, yet difficult, issues and leave time for applied or exploratory activities.

Your questions and responses are required prior to each non-lab session and should be submitted to Dr. Comar via WebCT in the following manner.

Responses to Instructor’s Study Questions:  Mail tool

Your Questions:                                            Discussion tool

These are due by to 7:00 a.m. prior to the next class meeting.  Questions not submitted in by this time will not receive credit and may not be addressed in the next day’s class. Your postings will be graded as a participation grade.  Credit is earned by submitting your questions and by seriously attempting to answer to the study questions--right or wrong.  Extra credit of one half a participation score may be earned (once each submission day) by correctly responding to a fellow’s student question before class discussion of the question.  The instructor reserves the right to post questions with responses to the class discussion board on WebCT

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There will two in-class exams and a two-hour comprehensive final exam. The in-class exam dates are 9/28/09 and 11/16/09.  The comprehensive final exam will take place on 12/11/07, 3:15 p.m. – 5:15 p.m.  Exams and quizzes cannot be made up or retaken.  If you miss an exam, your total exam score will be based on your performance on the other exams including the final.  Use of graphing calculators is strongly recommended on tests and quizzes.  Calculators with computer algebra systems including the TI-89, TI-92, and the TI-92+ are not permitted on exams.  The instructor reserves the right to delete all calculator memory prior to an exam. Note that the common MATH 207 exam will be given to all students enrolled in MATH 210 and MATH 220 at 10:15 a.m. - 12:15 p.m. on 12/18/09.

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Absence and Tardiness:

Absence due to documented illness, participation in Benedictine University athletic activities, religious observance, or other extenuating circumstances will be excused.  It is your responsibility to inform Dr. Comar in the event of such absences.  Class attendance is very important.  Others will depend on you to be to participate in group exercises.  It is incumbent upon you to obtain class notes and updated assignments for missed classes. Tardiness will interfere with your time to complete homework quizzes and exams.  No student shall be admitted fifteen minutes after the scheduled classtime.

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Academic Honesty:

The search for truth and the dissemination of knowledge are the central missions of a university. Benedictine University pursues these missions in an environment guided by our Roman Catholic tradition and our Benedictine heritage. Integrity and honesty are therefore expected of all members of the University community, including students, faculty members, administration, and staff. Actions such as cheating, plagiarism, collusion, fabrication, forgery, falsification, destruction, multiple submission, solicitation, and misrepresentation, are violations of these expectations and constitute unacceptable behavior in the University community. The penalties for such actions can range from a private verbal warning, all the way to expulsion from the University. The University's Academic Honesty Policy is available at , and students are expected to read it. Acts of any sort of academic dishonesty will not be tolerated.  All instances will be pursued.  The first case of any academic dishonesty will result in a grade of zero for the assignment.  A second case will result in failure of the course. Any incident of academic honesty on the final exam will result in failure of the course.

Your name should appear on all of your submissions of your work.  If collaboration is allowed, you must state with whom you have collaborated.  You are responsible for understanding any authorized collaboriation policies on specific assignments. You must also properly reference any other print, electronic, or human resource that you consult.

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Academic Accommodations For Religious Obligations (AAFRO)

A student whose religious obligation conflicts with a course requirement may request an academic accommodation from the instructor. Students must make such requests in writing by the end of the first week of the class.

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Electronic Devices Policy

One aspect of being a member of a community of scholars is to show respect for others by the way you behave. One way of showing respect for others in the educational community is to do your part to create or maintain an environment that is conducive to learning. That being said, allowing your cell phone to ring in class is completely inappropriate because it distracts your classmates and thus degrades their overall classroom experience. For the sake of your classmates, you are expected to turn off your cell phone or set it to mute/silence BEFORE you enter class-every class. Furthermore, if you use your cell phone in any manner during class (e.g. text messaging, games, etc.), you will be dismissed from class and will forfeit any points you might have earned in the remainder of the period. If you use your cell phone in any manner during a test or quiz, you will receive a zero for that test or quiz. (This policy also applies to pagers, iPODs, BlackBerrys, PDAs, Treos, MP3 players and all other electronic communication and/or data storage devices.)

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Other Information:

Americans with Disabilities Act (ADA):

If you have a documented learning, psychological, or physical disability, you may be eligible for reasonable academic accommodations or services.  To request accommodations or services, contact Tina Sonderby in the the Student Success Center, Krasa 012, 630-829-6512.  All students are expected to fulfill essential course requirements.  The University will not waive any essential skill or requirement of a course or degree program.

Final Drop Date:

November 22, 2009

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This syllabus is subject to change.  Any changes will be communicated to all class members electronically.

Contact Dr. Comar:

 Dr. Tim Comar's Homepage 

Benedictine University Homepage | Department of Mathematics | Faculty Profiles


 This page was last modified on August 30, 2009.