# Calculus in Chemistry

## Main Question or Discussion Point

I was wondering as to just how deeply chemistry relies on calculus. I'm great at all my chemistry homework and studies, but calculus is a real struggle for me. Not that it's impossible, just with the resources I have it's incredibly difficult. I worry that in the future, as in when I get to grad school, I may not be able to perform as well as I do now. Could someone tell me what I should focus on in calculus to keep strong in chemistry? I'm thinking about going for a degree in Biochemistry or Genetics, have also thought about carreers concerning quantum chemistry.

There is a great deal of calculus (and more) in physical chemistry.

Let me just say this: calculus, relative to all other sorts of math, is not that conceptually hard. You will have to do group theory eventually, and that's HARD math.

In Biochemistry, integration and differential equations are heavily utilized to derive kinetic rate laws. Biochemistry is heavily evolving with physical chemistry and chemical physics, and now you're beginning to see many disciplines of biochemistry taught from a more physical based orientation (x-ray crystallography, statistical mechanics, molecular physics, quantum chemistry, density functional theory, and so forth).

Population biology and genetics is heavily endowed with ordinary an partial differential equations (for example: predator-prey populations and so forth).

However, from my personal experience, this is not the norm but sub specialties within these various fields.

In physical chemistry and chemical physics, the range of mathematics is vast. These particular fields overlap heavily with atomic and molecular physics. Therefore the language of mathematics is ever increasing and includes differential geometry, topology, group theory, graph theory, and much more.

However, sub-fields in chemistry like organic, medicinal, inorganic, and so forth rarely (again from personal experience) utilize math beyond calculus and simple group theory(point groups) unless they're further sub specialized with a more theoretical approach.

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There's alot of overlap between condensed matter physics and physical chemistry or even analytical chemistry as well, so the thermodynamics, solid state physics and statistical mechanics will be important too. These require at least vector calculus and linear algebra.

Statistics and signal processing is used in analytical chemistry. Analytical chemistry is part of every other chemistry, since you have to characterize your products.

Group theory is used in both crystallography (physical chemistry) and molecular spectroscopy (analytical chemistry). There's also complex analysis.

Some highly applied things in physical and analytical chemistry, such as biosensors and high efficiency photovoltaics, make use of solid state physical phenomena like surface plasmon resonance.

I won't mention biochemistry too much since I don't know much about it, but in my intro class, there was stuff about statistical mechanics of protein denaturation and yes, the derivation of rate laws in enzyme kinetics.

But in organic synthesis, inorganic synthesis and medicinal chemistry, you don't need math beyond calculus.

Borek
Mentor
Short version: there are branches of chemistry where heavy weight math is a must, there are branches where calculus is an overkill.

Have a look in your local library at

The Chemistry Maths Book by Erich Steiner.

It suitable to accompany Chemical sciences up to degree level, but he makes it very easy and clear and starts from a high school base.
The book can be understood by any competent upper level high school student, who would be able to see where things are heading.