The Concepts of Calculus are Essential

Charley Knight
Oct 28, 2018 · 4 min read

Calculus is on the chopping block as degree programs seek to streamline and increase graduation rates. This is true even within college STEM majors. This is misguided and will do a great disservice to our students.

Like philosophy, calculus teaches us how to think. Most STEM educators have had the benefit of taking calculus. Those that support removing Calculus as a requirement should critically reflect on how they would, or could, understand the world without the knowledge of Calculus. For me, it is so foreign that it is hard to fathom.

As a proponent of quantitative training in our biology degree, I was recently asked if I require calculations on my exams, and if students were required to use calculus. The assumption was that if even I do not require students to use the ‘math’ of calculus, then we should not require calculus for our degree.

I think this is a misguided notion for several reasons. Not the least of which is that calculus teaches us how to think. Its more than just the detailed rules of derrivation and integration. For me, calculus is about rates, changes in rates, and how these rates can be summed to predict quantities. These intuitions have profound and far reaching effects on how I conceptualize the biological world — which is full of rates.

One far reaching example comes from climate change science and politics. There is an oft cited phrase that we must “reduce the rate of CO2 emission”. A rate is a change through time. Clearly reducing the rate of CO2 emission is essential to ward off the negative impacts of elevating CO2 in our atmosphere.

Often, however, when the details of climate policy and projections are studied, it is often to “limit the rate of increase in the rate” of CO2 emmission. To keep the rate of increase flat. In fact that is the “business as usual scenerio”. The contrast is the more dire increasing rate of CO2 increase, which has typified human history since the industrial revolution.

Likewise, some mandates are to reduce CO2 emission levels to 1992 levels on a per capita basis. Because the population has grown, this CO2 emmision amount would be considerably more today than what was emitted in 1992. Business as usuall 1992 will not decrease the amount of CO2 in our atmosphere.

The area under the curve of CO2 emmission rate is the amount of CO2 that escapes to our atmosphere across any time period. For many of us, this may seem intuitive. If it is not, you should take calculus.

Here is another example of the importance of calculus from another one of my classes, Ecosystem Ecology. Net Ecosystem Productivity (NEP) is the amount of biomass retiained by a system across a year. NEP has two components. Gross Primary Productivity (GPP) and Ecosystem Respiration (ER). GPP creates biomass, ER returns biomass to the atmosphere as CO2. Forgive me this brief equation: NEP=GPP-ER.

The follwoing graph shows the daily and seasonal progression of NEP, GPP, and ER in a temperate forest (Chapin, Matson and Vitousek 2011).

My ecosystem ecology students have to look at these graphs and tell me whether the system has stored carbon across a day, or the season. A positive sum of NEP across a period of time represents carbon storage. It should be clear that the system stored carbon across the day, but less clear that there was a net gain across the year. If this is intuitive for you, it might be because you took calculus.

In addition, there are many other calculus concepts that illustrate biological phenomenon in this figure. For example, there is a linear rise in GPP with time of day and season, until a point. There is an inflection point in other words. Why?

In the case of time of day, it represents an amount of light when all leaves begin to have enough light to saturate the rate of photosynthesis. More light does not lead to incrimentally more photosynthessis.

In the case of the time of year when GPP falls off its linear rise, it represents a time when the leaf area of the system has saturated. Incrementally more leaf area does not add more GPP.

I can spend a whole one hour lecture talking about the biological inferences that can be deduced from just these curves. And they all relate to concepts presented in calculus. It is a mistake to think that the detailed ‘math’ of calculus is always required. But the concepts of calculus are essential.

Data Driven Investor

from confusion to clarity, not insanity

Charley Knight

Written by

Professor of Evolution & Ecology, Cal Poly, San Luis Obispo, CA, USA

Data Driven Investor

from confusion to clarity, not insanity

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