## Archive for August 31st, 2022

### Are these all the math you need to do physics? Why Not then graduate in Math first and consider physics as higher graduate level?

Posted on: August 31, 2022

Base Matter Man

Aug 12, 2022

All the math you need for a Física Degree

When you study physics you use a lot of math. This puts people off from studying it, but it can be far less frightening when you know what you’re up against.

I’ve just completed my degree, and I want to talk about it. So, here’s a brief overview of all the math classes I took.

Precalculus

Precalculus should not exist. It is a testament to how poorly we teach math in American high schools. All it is, is a hodgepodge of concepts from Algebra, Geometry, and Trigonometry, which happen to come up often in Calculus.

I say it shouldn’t exist, because we should learn these concepts in our ordinary algebra/geometry classes, but we don’t. That being said, there is nothing to fear here.

There’s no real prerequisites to learning it. You do need to learn it though. You don’t need to be a pro at calculus to get a physics degree, but you do need to be able to do trigonometry in your sleep.

Math is a language, and algebra is its grammar.

You have to learn the basics first.

Once that’s out of the way, you learn Calculus. You do this in 3 stages, whose naming convention is terrible. Cálculo I is differential Calculus. Calculus II is Integral Calculus. Calculus III is three-dimensional calculus.

Calculus I (Derivatives)

In calculus I you learn about Limits, that is, approaching something forever without ever actually touching it. This is a far more profound idea than you will ever realize and many people have dedicated their entire lives to understanding it. It is this base idea, from which the rest of calculus arise.

After you get a basic handle on limits, you learn derivatives. A derivative is a measure of how something changes. The derivative of position is velocity, and the derivative of velocity is acceleration. this is why calculus is sometimes called the “study of change”. (And what could be the derivative of acceleration? any third derivative in physics?)

Nature is in a constant state of flux, physics is partially the study of this flux, so understanding change is imperative.

Calculus II (Integrals)

In arithmetic, there are basic operations: addition, subtraction, multiplication, and division. In calculus the two fundamental operations are Derivatives and Integrals.

You get derivatives in Cal I and you get Integrals in Cal II.

Loosely speaking an integral is the area under a curve, which might seem unimportant but you can then manipulate integrals to find the area of any shape.

In classical geometry we can find the area of circles, triangles, and rectangles. In calculus, you can find the exact area of any shape imaginable. It’s hard to explain how significant that is, but all of physics moving forward depends on it.

Integrals are considerably harder to solve than Derivatives, so this course will be taught like a tool bag of techniques for solving different integrals.

You’ll also discuss infinite sequences and series, that is infinite lists of numbers following some pattern and infinite summations of those lists of numbers.

Sequences and Series have interesting philosophical implication and aren’t too hard to understand, but i would rank this as the hardest math course I had to take while in college.

It gets easier after this.

Calculus III (3D Calculus)

Once you master Derivatives and Integrals, you are taught to generalize those ideas to three dimensions. This involves lots of new “analytic Geometry” and the most beautiful theorems.