Mathematics in Physics and Chemistry

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

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 orChemistry will need a relatively strong Math background.

Mathematicsin Physics

Physicsis the natural science which explores concepts like mass, energy, matter andits motions. Strong foundation in Algebra, Trigonometry, Geometry, and calculusis essential for physics. Mathematical methods are absolutely necessary to dealwith important concepts in physics.

Thefollowing are some examples.

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

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

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

(4)Matrix Analysis is necessary forunderstanding Quantum Mechanics.

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

Mathematicsin Chemistry

Chemistry is the natural science whichexplores the composition and properties of substances. Math is essential for chemistry. The necessarymathematical background for the study of chemistry includes basic algebra, sometrigonometry, and calculus.

Thefollowing are some examples.

(1) Being able to balance chemical equations is avery importantskill for chemistry students. It’s a simple mathematical exercise. Balancing a chemicalequation refers to establishing the mathematical relationship between theamounts of reactants and products involved in the chemical reaction.

Let’s go more in detail.

A chemical equation is a statement thatdescribes what happens in a chemical reaction.

In a chemical equation, we place thereactants (substances undergoing chemical reaction) on the left side of theequation and the products (substances produced in a chemical reaction) on theright side of the equation. We have reactants and products separatedby an arrow andthe arrow always points in the direction of the products.

Considerthe reaction of carbon with oxygen gas to produce carbon-dioxide.

C+ O2 ---> CO2                    (2 issubscript)

The above equation is already balanced,because, it has an equal number of atoms of each element in the reactants andthe product. One carbon atom (C) and two oxygen atoms (O) on the left side ofthe 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 andchlorine form sodium chloride.

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

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

Let’s balance this chemical equation.

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

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

Chemicalequations can be balanced conveniently using matrices or simultaneousequations.

Anumber of fields of chemistry use a significant amount of Math.

(2) Electrochemistry is a branch of chemistrythat studies the chemical action of electricity and the production ofelectricity by chemical reactions. Diffusion in electrochemistry is completelybased on differential equations.

(3) Biochemistry is the study of the chemicalprocesses in living organisms. Even biochemistry has important topics whichdepend heavily on binding theory andkinetics.