Ordinary differential equations (ODEs) have solutions that depend on only one variable. **Partial **differential equations (PDEs) have solutions that depend on **multiple variables**.

Linear algebra is a

languagefirst,methodologysecond.Keith Thompson

By **order**, we mean the highest order derivative that appear in the differential equation.

A **solution** to the above ODE is a function

For some appropriate domain points. You can also call this a solution, too:

A differential equation is called **autonomous** if the independent variable does not appear on both sides.

If you want to find that **initial value problem**. In order to determine that value for some ODE, we need to specify a condition called the initial value. Sometimes, it’s not always possible to solve a differential equation explicitly, so occasionally we view them as “direction fields” or sometimes called “slope fields.” Then there are also isoclines, which are super cool looking.

It would not be a linear algebra post without mention of one of the most used tools from that scientific field today: the **matrix**. No, not the one that Neo has to navigate. The one mathematicians use! It’s definition is super simple. It’s just a rectangular array of entries, arranged in rows and columns.

If you want an even more abstracted and more powerful version though, I suggest you read about tensors!

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