Mathematics in Physics and Chemistry

‘Mathematics is the queen of all sciences’ – those are the words of Carl Friedrich Gauss the greatest mathematician of all time.

Mathematics is an important tool for science. Math is most widely used in other sciences. Physics, Chemistry, astronomy, engineering rely most heavily upon mathematical ideas.

Students who consider studying Physics or Chemistry will need a relatively strong Math background.

Mathematics in Physics

Physics is the natural science which explores concepts like mass, energy, matter and its motions. Strong foundation in Algebra, Trigonometry, Geometry, and calculus is essential for physics. Mathematical methods are absolutely necessary to deal with important concepts in physics.

The following are some examples.

(1) Electromagnetic theory is the branch of physics that studies the group of forces associated with electric charges. Vector Analysis is very important for the understanding and developing of Electromagnetic theory.

(2) Group theory is useful in Spectroscopy, Quantum mechanics, Solid state physics, and Nuclear physics.

(3) Fourier techniques are important for the analysis of all linear systems in physics.

(4) Matrix Analysis is necessary for understanding Quantum Mechanics.

(5) Complex numbers are used extensively in physics to describe Electromagnetic Waves and Quantum Mechanics.

Mathematics in Chemistry

Chemistry is the natural science which explores the composition and properties of substances. Math is essential for chemistry. The necessary mathematical background for the study of chemistry includes basic algebra, some trigonometry, and calculus.

The following are some examples.

(1) Being able to balance chemical equations is a very important skill for chemistry students. It’s a simple mathematical exercise. Balancing a chemical equation refers to establishing the mathematical relationship between the amounts of reactants and products involved in the chemical reaction.

Let’s go more in detail.

A chemical equation is a statement that describes what happens in a chemical reaction.

In a chemical equation, we place the reactants (substances undergoing chemical reaction) on the left side of the equation and the products (substances produced in a chemical reaction) on the right side of the equation. We have reactants and products separated by an arrow and the arrow always points in the direction of the products.

Consider the reaction of carbon with oxygen gas to produce carbon-dioxide.

C + O2 ---> CO2                    (2 is subscript)

The above equation is already balanced, because, it has an equal number of atoms of each element in the reactants and the product. One carbon atom (C) and two oxygen atoms (O) on the left side of the equation and it’s the same on the right side too.

Let’s look at one more example.

Sodium chloride is the common salt. Sodium and chlorine form sodium chloride.

Na + Cl2 ---> NaCl                 (2 is subscript)

The above equation is NOT balanced. It has two chlorine atoms on the left side, but, only one on the right side of the equation.

Let’s balance this chemical equation.

2Na + Cl2 ---> 2NaCl             (2 is subscript only in Cl2)

It works! Notice that now there are equal number of atoms of each element in the reactants and the product.

Chemical equations can be balanced conveniently using matrices or simultaneous equations.

A number of fields of chemistry use a significant amount of Math.

(2) Electrochemistry is a branch of chemistry that studies the chemical action of electricity and the production of electricity by chemical reactions. Diffusion in electrochemistry is completely based on differential equations.

(3) Biochemistry is the study of the chemical processes in living organisms. Even biochemistry has important topics which depend heavily on binding theory and kinetics.