Calculus for the Life Sciences I

MATH 220B- Fall 2016

Benedictine University


Basic Information


Attendance and Tardiness

Course Description


Academic Honesty

Course Objectives


Academic Accommodations For Religious Obligations (AAFRO)

Course Goals/Core Goals

In-Class Work

Electronic Devices Policy

Learner Outcomes

Entry Questions

Other Information



Homework Assignments

Technology Requirement


Dr. Tim Comar's Homepage 

Basic Information:

Instructor: Dr. Timothy D. Comar

Location:  Monday, Tuessday: BK 236; Wednesday, Friday: KN 244

Office: Birck 128

Phone: (630) 829 - 6555

Time: MTWF: 1:30 p.m. - 2:45 p.m.


Web Site:

D2L login:

Office Hours:

Monday, Tuesday, Wednesday, Friday:

9:30 a.m.-10:30 a.m.


3:00 p.m.-4:00 p.m.


2:00 p.m.-3:00 p.m.


by appointment


T. Comar, et al., Calculus and Mathematical Models for the Biological Sciences, (draft preprints of chapters will be available through D2L) to be published by Kendall Hunt


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 Maple and Excel 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, Maple, Excel to analyze and 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:

  1. Using regression and creating semi-log, and log-log plots from data sets.
  2. Understanding Limits in sequences and continuous functions
  3. Differentiation
  4. Computing Basic Definite Integrals
  5. Using Calculus and Computational Methods to Solve Biologically Oriented Problems
  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
  10. Using Computational Software to Investigate and Solve Biologically Oriented Problems
  11. Working Collaboratively with Peers

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Course Goals/ Core Goals:

Core Goals (for students using the 2013-2014 catalog or earlier catalog):

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.

Course Goals (QCM) (for students using the 2014-2015 catalog or later catalog):

This course satisfies the Computational, Mathematical, and Analytical Mode of Inquiry requirement (QCM).  This mode of inquiry introduces students to methods for analyzing and logically organizing information; formulating algorithmic solutions to problems; and utilizing data abstraction, modeling, interpretation and analysis.  Courses in this area should foster understanding of these techniques to levels that would enable students to generalize solutions and think abstractly beyond specific examples covered.


All QCM courses are designed to enable students to continue to meet the following student learning goals:


1a.  Demonstrate critical thinking and analysis  In this course, students will learn how to interpret problems and solutions in four different contexts, being able to work equally well in each context:  graphically, symbolically, numerically, and verbally. (Homework exercises, labs, and exams).


1b.  Identify, study, and solve problems  In this course, students will not only learn methods for solving problems, but why they work, when they are appropriate to use, and how to apply them to new settings. (Homework exercises, labs, and exams).


1c.  Achieve computational skills and an ability to understand and interpret numerical data  In this course, students will use both the computer algebra software Maple and the spreadsheet Excel to solve problems and how to check whether their answer is reasonable or not. (Homework exercises, quizzes, labs, and exams).


6a.  Develop intellectual curiosity and a desire for lifelong learning  In this course, students will be asked to consider why the techniques they are learning are important and will build a foundation of skills that future courses will build upon. (Homework exercises, Career Day assignment, labs, and exams).


7a.  Use knowledge, theories, and methods from the arts, humanities, natural sciences, and social sciences to raise and address questions germane to those areas of study  Self-explanatory. (Homework exercises, labs, and exams).


7d.  Explore connections between classroom and real-world experiences  In this course, students will learn applications of the material to solve real-world problems, particularly those of a biological nature, both by hand and by use of computational software, which is how many problems in industry are solved. (Homework exercises, Career Day assignment, labs, and exams).

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Learner Outcomes:

Student Learning Objectives:

This course is designed to meet the following Department of Mathematics Student Learning Objectives:

2. Communicate mathematical concepts, both orally and in writing.

6. Use technology to solve problems and communicate mathematics.

Specific Learning 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. (1a, 1b)
  2. Evidence understanding of geometric, numerical, and symbolic interpretations limits and computational mastery of limits through homework exercises, projects, and exams. (1c)
  3. Evidence mastery of the geometric viewpoints of differentiation and integration through homework exercises, projects, and exams. (1a, 1b, 1c)
  4. Evidence mastery of differentiation and antidifferentiation rules through homework assignments and exams. (1c)
  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. (1a, 1b, 6a, 7a, 7d)
  6. Evidence the ability to read, represent, and interpret data in numerical and graphical formats through homework exercises, projects, and exams. (1c)
  7. Evidence the ability to interpret and apply biological models expressed as basic difference and differential equations through homework exercises, projects, and exams. (1a, 1b, 6a, 7a, 7d)
  8. Evidence the ability to analyze quantitative biological data using sophisticated mathematical computational software through projects. (1a, 1b, 1c, 6a, 7a, 7d)
  9. Evidence the ability to apply the concepts of rate of change and total change to biological problems through homework exercises, projects, and exams. (1a, 1b, 1c, 6a, 7a, 7d)
  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. (1a, 1b, 1c, 6a, 7a, 7d)
  11. Evidence the ability to work collaboratively through collaborative homework and collaborative projects. (6a)
  12. Evidence the ability to implement basic biological models using computer software through homework and projects. (1a, 1b, 6a, 7a, 7d)
  13. Evidence the ability to read basic literature in mathematical biology through homework. (1a, 1b, 6a, 7a, 7d)


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 Desire to Learn 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 . In this course, students will learn how to use Maple to perform to use MS Excel to represent data graphically and to work with basic discrete dynamically systems. Additional Maple content will introduced in the this course. Portions of quizzes and exams may require or prohibt the use of calculators and/or computers and/or D2L.

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Entry Questions


Quizzes/In-Class Work


Group Homework




Exam 1


Exam 2


Exam 3


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.

The College of Science is committed to giving regular and timely feedback to students to aid their progress toward achieving course learning goals. Normally, in class assignments, homework assignments and quizzes will be graded and returned within one week, and larger assignments such as exams will be graded within two weeks, following their submission. Per College of Science policy, students may not invoke an instructor's failure to meet the above schedule for grading and providing feedback as the basis for a grade appeal.


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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. 

There will be ten or eleven 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 and Maple 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. There may be additional reading and writing assignments in group homework assignments, which will be submitted individually. Group Homework will count for 15% 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 Desire to Learn (D2L) site for the course.

Learning in this course will take place both in the classroom and outside of the classroom. Some learning will be completed independently and some will be done collaboratively. As much of the classroom time it devoted to active learning, it is imperative that you follow this proceedure for completing the various components of homework for this course.

Proceedure for Completing nightly homework:

1. Look on the schedule of the section or sections that will be addressed in the next class.

2. Read the section in the text and the corresponding lecture notes posted in D2L.

3. Print out and answer the corresponding Entry Questions. (These questions must be written in your own handwritting and be submitted to the instructor at the beginning of class for entry into class on the given day.)

4. Post your questions in the appropriate Discussion in D2L for the given section by 10:30 a.m. of the class day.

4. There are practice problems listed for each section of the text. These will not be collected. Some of these will be addressed in class. It is imperative that you attempt all problems as you read and re-read each section. See what you can do before class discussion, and then try some more after class discussion. If there are problems you cannot do after thinking about them, please be sure to ask for assistance.

5. There are collected homework sets approximately each week. These are listed in bold type in the syllabus. These assignments are collaborative and will be graded.

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There may be unannounced quizzes based on homework assignments, readings, and classroom activities.  You should be prepared for quizzes daily, but expect at least one per week.  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. You may also have to respond to online quizzes on D2L. 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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Entry 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 class session and should be submitted to Dr. Comar via Desire to Learn in the following manner. For each class, the appropriate Entry Questions must be printed and answered in your own handwriting and submitted to the instructor at the beginning of class in order to be admitted to class.

Responses to Instructor’s Entry Questions:  Paper to instructor in class.

Your Questions:  Discussion tool in Desire to Learn

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.  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 D2L. 

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There will be eight to nine computer lab projects, typicailly on Wednesdays, throughout the course. These projects will introduce you to the computer algebra system Maple and the spreadsheet Excel for mathematical computation and analyzing problems. We will explore both mathematical concepts and biological models using these platforms. One of the lab assignments will be a Career Day assignment, which supports the College of Science's Careers in Science initiative. This particular assignment will require you to fill out a survery in the Careers in Science D2L course, attend a panel session, and make a Career Day presentation in class.


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There will two in-class exams and a two-hour comprehensive final exam. The in-class exam dates are 9/28/16, 10/25/16 and 11/22/16.  The comprehensive final exam will take place on Wednesday, 12/14/15, 1 p.m. - 3 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.

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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. 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 collaboration 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.)

To diminish disturbance, cell phones will be silenced and left at the front of the class before class begins.

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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, please contact Michelle Schaefer in the Academic & Career Enrichment (ACE) Center in Goodwin Hall Rm 214, (630) 829-6041. 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: Sunday, November 20, 2016

Policy for switching from 210 or 220 to 170 (Fall only):

If you feel that the pace of this course is too fast for you, the department offers a slower-paced version of Calculus I, MATH-170, which includes a more extensive review of precalculus.  (MATH-170 followed by MATH-200, which is offered in the spring, is equivalent to taking MATH-210 or MATH-220.)  So, if you need MATH-210 or MATH-220 for your major, then passing MATH-200 with a 'C' or higher satisfies this requirement.  Students interested in this option should make the change by then end of the second week. This option will not be allowed after 4:00 p.m. on Friday, September 2, 2016.  To make this change please contact me and the MATH-170 instructors (see me for contact information) by this time.  In addition you must obtain all appropriate documentation to officially make the course change from MATH-210 or MATH-220 to MATH-170 in a timely fashion.  You should start attending MATH-170 as soon as you are given permission.   Students who switch classes after the add drop date may have to pay a late registration fee.  Also this option will be offered to students as long as seats are available.

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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


This page was last modified on August 26, 2016