The critical issue of life sciences majors taking college physics courses has come to the fore in a recent article ('Reinventing physics for life -sciences majors' ) in Physics Today (July, p. 38)
As the authors note, given quantitative measurements and modeling are emerging as key biological tools, it makes sense biology/pre-med and other life sciences majors would take at least one proper physics course. And ideally, that course needs to be calculus -based (as opposed to stripping calculus from older physics text books and recycling them, while adding a few biology applications.) However, if needed, a more basic "algebra-based" physics course is a reasonable alternative.
As the authors observe:
"Those applications are not recognized as relevant by biologists themselves and they fail to address biologists' real concerns. The traditional calculus-based courses cover the same subjects, which implies that all those customary topics are worth the intense intellectual effort by biology students."
The authors in this regard also bring up IPLS Physics, i.e. http://phys.gwu.edu/iplswiki/index.php/Competency_E3:_Teaching_IPLS_Physics_Content,_session_B
and the need to enhance such courses for "greater biological relevance" given this single course or one like it may be the only exposure most of these students ever have to physics. Further, "without giving suitable instruction, how can we expect a novice in both physics and biology to make connections across disciplines?"
Of key importance also is the point that "instructors of ILPS courses need to do more than draw examples from a life sciences context. They also need to help their students understand that the underlying physics leads to a deeper understanding of biology." (It's not enough to skip relativity and sneak in a little fluid dynamics.)
Teaching proper physics courses for life science students also means appreciating the basic differences between those with a physics mindset and those geared more to living things. Thus, physics stresses reasoning from a few fundamental principles, and generally expresses those principles in terms of mathematical laws, i.e. Newton's Second law of motion, F = ma. Biologists, meanwhile, focus on structure- function relationships and rarely stress quantitative reasoning. There is also an enormous amount of memorization which students also think they can bring to physics - but are sadly mistaken.
When I taught calculus-based physics at Harrison College, the students having the most difficulty were invariably those on life science tracks, say for pre-med, biology or environmental science. Often, these students needed extra tutoring, and the way I dealt with it was via problem solving exercises.
There were also ample integration or connection paths in the syllabus. For example, radioactive decay. For reference, the fundamental law of radioactive decay, based on some original number of N(o) atoms decaying with an activity a over time t to a number N atoms, is:
N = N(o) exp (-at)
The ‘half-life’ is the time for half of the original (N(o)) atoms to disintegrate, or for
N(o) -> N(o)/2
N(o)/ 2 = N(o) exp(-a T ½)
After canceling N(o) from both sides of the above equation, and taking natural logarithms one fids:
a T ½ = ln 2 = 0.693
or T ½ = 0.693/ a
Using this basis, any sample or fossil, with even a minuscule amount of radioactive element, can be dated. All we need to know is that over the period T ½, half of the number of remaining atoms decay and the current activity in Becquerels. Thus, if T ½ = 15,000 yrs. for a = 200 Bq, then if a = 50 Bq now, we may deduce the sample is ~ 45,000 yrs. old. (E.g. three half-lives decaying) Thus, there is a direct connection to evolutionary biology, paleontology.
The chief problem for most of the biology, pre-med track students doing physics was the calculus, and let's face it - to fully appreciate and comprehend modern physics, one needs calculus! I was prepared, however, to accommodate bio students up to a point, so if I found a physics class had more than its sure of bio -track kids, I would do what the authors of the Physics Today article suggested, i.e. omit detailed treatments of EM induction and oscilloscopes, as well as projectile motion, rotations with constant acceleration. The authors also indicate shelving Newton's law of universal gravitation, but I believe that would be an error. This law is the cornerstone of much of astronomy, not to mention orbital mechanics-physics, and to deprive bio students of this would be unacceptable. (It could, however, be taught in its algebraic format with little or no calculus.)
On the other hand, there can't be any compromise when it comes to entropy in terms of the 2nd law of thermodynamics. As the authors note:
"Cell biologists need to understand entropy because free energy measures how much useful work can be done."
Pre-biotic cell or protenoids are also of interest. One could view the transition from non-reproductive- non-growth to replicating-growing states as a ‘symmetry breaking’ in the organic molecules that yield a very primitive living cell. Thus, my own students investigated (in one of several special projects using simulations) the evolution of monomers to stable polymers that could enable protenoid emergence. In general, -d F/ d(kT) = S/k where (dF) is the free energy difference. We can write, therefore: F2 – F1 = - kT[(L + ℓ)ln (z)- ℓln (z)] = -kT L ln (z), which is the free energy difference between polymers of length L and those of lengths L + ℓ.
This sort of phenomenon, can apply in a real world sense to the alpha-beta transition in fibrous proteins or the helix random coil transition evident in solutions of nucleic acids and proteins.
My point is that a good physics course, with solid calculus support, is feasible for life science students if the effort is properly made. With suitable adjustments and some extra math tutoring, all my biology-based students fared very well and all passed the course with at least a B.
Even if the calculus is diluted, what essential skills should the bio-track student learn in a college physics course? The authors provide the following:
1) Drawing inferences from equation. For example, one implication of the kinetic energy equation, K = 1/2 mv2 is that the energy can be minimized in a running vertebrate by minimizing the mass of its legs.
2) Building simple quantitative models. Example: create an equation for the pressure drag after learning that the force is due to collisions with fluid molecules.
3) Connect equations to physical meanings. For example, a cooling lab connects the parameters in Newton's law of cooling with the measured room temperature, initial temperature of the system and amount of insulation.
4) Ability to integrate multiple representations. Thus, the student can use graphs of potential energy, as well as equations and charts to represent the energy balance in chemical reactions.
5) Understand the implications of scaling and functional dependence.
6) Estimation. Students must be able to quantify their experience and establish a sense of scale.
What the authors conclude is timely and apropos: teaching physics to biology students requires far more than watering down a calculus-based course for engineers and adding a few superficial biology applications. What we really need to see is physicists working closely with biologists in order to develop a physics course that satisfies both instructors and students in both disciplines.