Page 37 - Essentials of physical chemistry

Introduction: Mathematics and Physics Review xxxv

PREVIEW OF COMING ATTRACTIONS WITH REASSURANCE!

That concludes our brief but intensive review of the mathematics and physics needed for the
remainder of the text, although we may need some special formulas from time to time. In our
experience, this initial review is the secret to being able to make a full treatment of selected topics
without diluting the coverage, although we will still make use of the simplest correct derivation of
other relationships. The student should realize we are attempting to do a ‘‘university level’’
treatment of physical chemistry while being helpful to students with only one semester of calculus.
A concurrent second semester of calculus or other mathematics elective is encouraged in the second
semester. The student should be aware that even with this helpful approach, the use of scratch paper
and working examples is highly encouraged! What follows is a set of homework problems and our
experience has shown that a flurry of activity to review and extend calculus skill at the beginning of
the course really pays off in student confidence for later topics.
While it is difficult to give broad treatment of many topics in one semester, we can do selected
topics at a university level to form a foundation for other science fields such as physics, forensic
science, biochemistry, inorganic chemistry, and a possible second semester with some quantum
chemistry. Students should be reassured that this text is based on a course that has been presented to
a group where on average about one-third of the class only has one semester of calculus and yet the
success rate is very high! The secret is that we give examples in the text of specific problems and the
homework problems are like the examples. The organization of this text in the mind of the author is
to link each chapter topic to a ‘‘calculus nugget’’ as a way to master details of that topic. A hint to
understanding each chapter is to look for the ‘‘calculus nugget.’’ It is hoped that we can develop
calculus skill as we go along so that the reader=student will be able to treat new topics as they may
be encountered. We have avoided the encyclopedic coverage of every possible topic and selected a
lesser group of ‘‘essential’’ topics. Old tests are provided to show what is expected and a few key
topics are treated in detail.
In a possible second semester, more modern material is covered from the twentieth century. Our
strategy in the second semester is to instruct students to assimilate as much of the difficult
derivations, but pay special attention to the conclusions, the final formulas! Yes, we cover some
very complicated details for the few who might be interested but a wise student will focus on the
conclusions! Again a few key topics are treated in detail but old tests are provided to indicate what is
expected. The second semester may end at Chapter 15 or 16 but additional material is provided for
special projects or by the preference of the teacher. If this material is studied with a positive attitude
and use of pencil and paper, a very high rate of success can be expected in terms of real learning by
students. Now let’s get going!

CALCULUS REVIEW PROBLEMS

d 3 3
1. 4x þ 2x þ ¼ ?
dx x 2
d 4x 2x 2 2 3x
2. 2e þ e þ x e ¼ ?
dx
4
d x
3. ¼ ?
3
dx (x þ 2x)
d 2
2 ax
4. x e ¼ ?
dx
d 2 npx
5. sin ¼ ?
dx 2 l

qP
6. PV ¼ nRT, ¼ ?
qT
V, n