Welcome to Math 1323!   This is a second semester course in
calculus designed by Professor Edward Spitznagel for students with interests in the biological and health sciences   It shares about two-thirds of its material with our standard Calculus II course, Math 132.  The remaining one-third is statistics with a small amount of pharmacokinetics to “glue” the two subjects together. To allow time for statistics and pharmacokinetics, most of the topics in Math 132 which are geared to geometry and the physical sciences are either glossed over or omitted altogether in Math 1323. Other key differences between Math 1323 and Math 132 are as follows:
    ***Math 132 uses multiple choice, machine graded, exams putting a high degree of stress on accuracy.  Math 1323 uses essay style,hand graded exams which are more tolerant of small mistakes.
    ***Math 1323 emphasizes empirical understanding of calculus ideas by examing the extent to which data sets are consistent with theoretical models and by developing techniques for approximation from data of various constants employed by models.

         All of you have had some calculus before, so you know what that subject is about.  You also have been exposed to statistics in newspapers and magazines, so you have at least a basic knowledge of it as well. However, you probably are unfamiliar with pharmacokinetics. The word itself is a hybrid of the Greek word for drug and the Greek word for motion. Pharmacokinetics is a study of how drugs travel through the body, from the moment they are
introduced until the time that so little is left they can no longer be detected by chemical assay. All major pharmaceutical companies employ pharmacokineticists, at excellent salaries.  In addition, all physicians, nurses, and pharmacists need to know at least the rudiments of the subject.  Oncologists and infectious disease specialists need to know it very well. Pharmacokinetics combines the calculus ideas of definite integrals (areas under curves) and
compartment models with statistical methods for estimating these things from data.  It is an excellent example of how calculus and statistics can be combined. For the most part, the kind of pharmacokinetics we will study deals with government approval of
generic drugs.  We will look at data sets reflecting blood concentrations at various times after drug administration of two forms of a drug, one from the company that orignally developed the drug and one from a company developing a generic version.  For the generic version to be approved by the FDA (or its Canadian equivalent, the HPB), the generic company must use pharmacokinetics to establish that the differences in concentration levels between the two forms of a drug are too small to be of
importance.

        Following is a rough schedule of topics to be covered during the semester.  Numbers refer to the calculus book chapters, S refers to statistics, and P refers to pharmacokinetics.  See the Lesson Schedule for details on daily assignments.

January:      (5)   Integration
February:     (6)   Applications of Integration
              (S)   Mean & Standard Deviation
              (P)   AUCt
March         (7)   Differential Equations
              (P)   Compartment Models
              (S)   Regression and Correlation
              (P)   Terminal Elimination: AUCi
April         (S)   Tests and Confidence limits
              (P)   Bioequivalence
              (8)   Infinite Sequences and Series
 

            EXPECTATIONS AND ADVICE
 

         1. Read the text. Your instructor can't possibly say everything that's there. An hour's lecture wouldn't be enough even to read the day's assignment aloud, let alone try to highlight or clarify. Your instructor's job is to complement the text so that you can learn from it.  Simply relying on your lecture notes will only give you the highlights of the material.  To ignore the text is to start out looking for a minimal understanding.

      Read with scratch paper at hand and fill in missing steps. When the author simply asserts  "...this expression simplifies to...", simplify it!  When you read "you should check that...", check it!  Try to work some of the examples in the text before reading them.  Play with the material: ask yourself  "what if I changed the problem to...?".  Write down questions that come to mind.  If you can't answer them, ask your friends. Try to understand why the assertions in the text are true.
 

         2. Read ahead.  The lectures will be much more valuable if you have tried to digest some of the material already.  Also, you'll be able to judge that some things on the board needn't be written down.  For example, you'll know that those formulas the instructor is writing on the board are just the ones listed in the text.  That frees you to think about what's being said and not be always frantically transcribing material from the board.

         If you choose to ignore the advice about reading ahead, then at least read the material in the text before trying to do related homework problems.  Some students start out with the problems and when they get stuck, they page back through the text looking for a formula or example to help.  This puts the focus in the wrong place.  Simply being able to "do the problems"  represents at best a minimal strategy for the course. You do have to do problems, and you do want to have certain technical skills that the problems sets can help develop, but you also want to understand the material.  Carefully reading the text is essential for that.

         3. Don't be passive. You can't learn mathematics by watching someone else do problems. You need to do as many problems as you can realistically find time to do: the more, the better.  It's useful to work with other people on homework as long as you're involved as an active partner. Compare solutions; ask each other questions; make up quizzes for each other; agree on some extra problems to try together--such as the review problems at the end of each chapter.  Prod each other to do the assignments!  Do whatever helps!  But all of this is to improve your understanding: your study group isn't there at quizzes, tests, or when you need your math in another course.

         4. Stay on top.  Sometimes it's hard to keep up with everything, but it's important not to fall behind in the course.  A lot of the material we cover is interdependent, and if you're not comfortable with the material from two days ago, today's lecture might be totally incomprehensible.  It's better to be a bit ahead--the lectures will mean more and you've got a buffer when an emergency strikes.

         Also, there's a limit to how fast you can digest material and learn to use it in your thinking.  Avoid cramming just before tests by staying on top of things.  It makes life much more pleasant.

         5. Make use of your instructor.  Office hours are set aside specifically to see students; those times are for you!  Most instructors are also willing to set up special meetings with students as time permits. Your responsibility is not to waste these times.  Try to solve your own problems first, together with your friends. What you learn that way will be more valuable than the same answer "given" by your instructor. Come to office hours with specific questions.  Bring questions to your instructor quickly, as soon as you realize there's some difficulty you can't resolve.  (It's hard for any instructor to cope with  "I haven't understood anything for three weeks"; we aren't magicians.)