Math 110.107, Calculus II (Biological and Social Sciences)

Fall 2010 Course Syllabus

http://www.mathematics.jhu.edu/brown/courses/f10/107.htm

 

 

 

 

Text:  C. Neuhauser, Calculus for Biology and Medicine,3^rd edition.

 

Current Recitation Sections:

 

 

Course Material: The core of the course will center on the text material, and will basically cover the material detailed in the schedule below.  Note that the course will actually start with Section 7.4 Improper Integrals.  Sections 7.1 through 7.3 are a part of the previous course 110.106 Calculus I.  If you are not familiar with this material, you will have to acquaint yourself with it outside of this course.  I will do a very brief review of this material, both in lecture and in recitation.

 

Grade Policy:    There will be weekly homework sets (20%), 2 in-lecture exams (40%) and a final (40%).  The schedule of these exams is given with the homework problems below. There will be no make-ups on homework or exams.  If you miss an exam, you will have to be cleared by me to be excused from the exam, a process that will include documentation and a valid excuse.  In this case the ultimate grade for that exam will be calculated based on your performance on future exams and the final. 

 

Homework:    Homework based on the week’s lectures will be posted as official on the course web site sometime on Friday (Homework may be posted earlier, but may change as the lectures evolve for the week). That assignment will be due in lecture at the end of the following week.  See below for the due dates.  You are encouraged to do your homework in groups. You are required, however, to write up your homework on your own. Homework is an essential educational part of the course. You will be graded mostly on your ability to work problems on exams. You cannot work problems on exams if you have not practiced the techniques within the homework problems. If you misuse homework by not doing it yourself, or not checking that you can solve a problem on your own after having been shown how to do it, then your exam scores and corresponding grade will reflect this. Talk to your section Teaching Assistant about how to turn in a homework if you cannot go to class.  The link here is a brief idea of how one should construct homework problems for submission:

How to construct homework problem solutions

 

Course Policy: You are responsible for lecture notes, any course material handed out, and attendance in class.  While I will not formally record your attendance, I will get to know you and your rate of presence over time.  The lectures will be conducted as if you have already read the material and attempted some homework problems.  In this manner, you can focus mainly on those parts of the lectures that cover the areas of your reading you found difficult to understand. My teaching style is that of interactive discussion and I will rely on your input in developing the material.  Active participation in the classroom is a great way to generate the discussion necessary to fully grasp the material.

 

Help Room:      213 Kreiger Hall.  The hours are 9am  9pm on Monday through Thursday, and 9am  5pm on Friday.  This free service is a very valuable way to get one-on-one help on the current material of a class from other students outside the course.  It is staffed by graduate students and advanced undergraduates.

 

Ethics Statement:  The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful.  Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies.

Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the Internet and electronic devices unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.

In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged.  Your ability to talk mathematics is of particular importance to your general understanding of mathematics.

You should collaborate with other students in this course on the general construction of homework assignment problems.  However, you must write up the solutions to these homework problems individually and separately.  If there is any question as to what this statement means, please see the professor or the recitation instructor.

For more information, see the guide on "Academic Ethics for Undergraduates" and the Ethics Board web site (http://ethics.jhu.edu).

Students with Disabilities:  Students with documented disabilities or other special needs that require accommodation must register with the Office of Academic Advising. After that, remind me of your needs at least 5 days prior to each exam; we will need to have received confirmation from Academic Advising.

Math 110.107 Calculus II (Biological and Social Sciences)

Fall 2010 (VERY) Tentative Schedule

 

The details of this material will be updated and reformed as the semester progresses.

 

How to construct homework problem solutions

 

The Java applet JODE for producing slope fields of  linear systems

 

*These problems are listed by Chapter and Section number.  For example, so that 3.4.2 is Chapter 3, Section 4, Problem number 2.  For the rest of the semester, problems will be listed directly according to the Section.  Hence they will not carry the Chapter and Section number with each problem.

**I neglected to describe the Stability Criterion (p. 410) for equilibrium solutions in class.  You will find it useful for this homework, and I will describe it on Monday, September 20.

*** I did not spend time on the definition and use of the Hessian of a function .  However, you need it for the exercises in Section 10.6.  It is ONLY the second derivative matrix of , and it is in page 551.  A restatement of the 2^nd derivative test for local extrema using the Hessian is on page 553 (bottom).  I will talk about this on Monday, November 1. 

Extra Problems:  Challenges for practice.

EP1:             For the function , calculate  and .               EP2:             Find an antiderivative of  using Integration by Parts.               EP3:             Determine if the improper integral  exists or not.  If it exists, determine its value. (Be careful here.  Look for asymptotes of the integrand which may be hidden.)               EP4:             Find a stable equilibrium solution to the autonomous differential equation  and show that it is stable.               EP5:             Determine all equilibrium solutions to the differential equation .  Describe the stability of each equilibrium.               EP6:             For the Logistic Equation  , do the following: ·      Show that by using a change of variable , you can rewrite the differential equation as .  (Note:  This is a form one sees a lot when studying the Logistic Equation.  It is only a rescaling of the population, and does not affect how the solutions behave.) ·      Use the partial fraction method to solve . ·      Suppose the model in Part b were used to model a lake recently restocked with fish, where  is measured in thousands of fish.  What is the long term population size for the lake if the initial restocking used 200 fish?                EP7:             Solve the system of equations                 EP8:             For , its inverse, if it exists, is .  Verify that .               EP9:             Graph the domain of , from Problem 10.2.28, in the  -plane.  Graph also the  -level sets corresponding to  0, 1, and 2.