Biocalculus II Laboratory

MATH 208A- Spring 2007

Benedictine University


Basic Information

Technology Requirement Academic Honesty

Course Description

Evaluation Academic Accommodations For Religious Obligations (AAFRO)

Course Objectives


Other Information

Learner Outcomes

Final Exam

Homework Assignments


Attendance and Tardiness

Dr. Tim Comar's Homepage 




Basic Information:

Instructor: Dr. Timothy D. Comar

Location: KN 227

Office: Birck 128

Phone: 829 - 6555

Time: Thursday: 8:30 a.m.- 10:30 a.m.


Web Site:

Blackboard (WebCT) login:

Office Hours:


12:30 p.m. - 2:30 p.m.


12:30 p.m. - 2:30 p.m.


10:30 a.m. - 11:30 a.m.

Also: by appointment

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

deVries, et al., A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods, SIAM, 2006



Back to Top

Course Description:

This is laboratory course to accompany MATH 221, Biocalculus II, which is the second course in a two-semester sequence in calculus with biological applications. There is a strong emphasis on biological models and examples using real biological data. In this course, we will apply the mathematical of topics of methods of integration, differential equations, systems of linear equations, matrices, eigenvalues and eigenvectors, analytic geometry, functions of several variables, partial derivatives, differentiability, tangent planes and linearization, systems of difference equations, systems of linear and nonlinear differential equations, equilibria and stability, and an introduction to probability to biologically oriented mathematical models. Applications may include allometric growth, age-structured population matrix models, epidemic models, competition models, host-parasitoid models, and models for neuron activity. The course uses the computer algebra system MATLAB and the modeling program Berkeley Madonna to investigate biological models and solve problems.

Back to Top

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.

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

  1. Techniques of Integration (Substitution, Integration by Parts, Partial Fractions) and Improper Integrals (8C5, 8C6)

  2. Applications of Integration to Biological Problems (4A, 4B, 4D, 4E, 6C6, 8C5, 8C6, 8G2, 8G3, 9E3)

  3. Analyzing basic biologically significant differential equations using computational software

  4. Using multivariable calculuus and linear algebra to analyze biologically significant systems of difference and differential equations (linearization, equilibria, and stability)
  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. Using Computational Software to Investigate and Solve Biologically Oriented Problems (2A, 2B, 2C, 3B, 5A, 5B, 7C8, 10E4; Core Technolgy: 5G)
  7. Working Collaboratively with Peers

Back to Top

Learner Outcomes: (ISBE Math Content Area Standards in bold)

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 laboratory activities and projects and a final exam.
  2. Evidence understanding of geometric, numerical, and symbolic interpretations limits and computational mastery of limits through laboratory activities and projects and a final exam.
  3. Evidence understanding of applications of integration related to biology, through laboratory activities and projects and a final exam.
  4. Evidence the ability to analyze quantitative biological data using sophisticated mathematical computational software through projects.
  5. Evidence the ability to interpret biological mathematical models and the ability to formulate a biological mathematical model from a verbal description through laboratory activities and projects and a final exam.
  6. Evidence the ability to interpret and apply biological models expressed as systems of difference equations, systems of differential equations, and matrix models through laboratory activities and projects and a final exam.
  7. Evidence the ability to apply basic concepts and techniques in linear algebra and multivariable calculus to biological models expressed as systems of difference equations or systems of differential equations laboratory activities and projects and a final exam..
  8. Evidence the ability to compute probabilities and expectations of continuous random variables through exams.
  9. Evidence the ability to work collaboratively through laboratory activities and projects and a final exam.

Back to Top


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 2 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. Cell phones and pagers must be turned off. Inappropriate and disrespectful behavior including cell phone usage will result in dismissal from the class for the remainder of the class period.

Back to Top

Technology Requirement:

Students are expected to use WebCT 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 calculuator and are expected to know how to use the computer algebra system Derive from the MATH 207 course. Derive will not be taught in this class. In this course, Berkeley Madonna, MS Excel, and MATLAB will be the primary software tools.

Back to Top


Lab Activities




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.

Back to Top


These assignments aredesigned to help deepen your understanding of the course material through writing and applications. In particular, you will work with MATLAB, MS Excel, 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 MATH 221. No late projects will be accepted.  Your lowest project score will be dropped from project grade. Questions for a particular assignment will not be addressed on the due date of the assignment.

Back to Top

Final Exam:

The comprehensive final exam will take place on 5/8/08, 8:00 a.m. – 10:00 a.m.  This exam cannot be made up or retaken. This exam will be a collaborative effort using the software to solve several problems.

Back to Top

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.

Back to Top 

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. Cheating and plagiarism of any sort 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.

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.

Back to Top

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.

Back to Top 


Other Information:

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 Academic Resource Center, 249 Kindlon Hall, 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: April 13, 2007

Back to Top

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