Entering a Differential Equations

[dpsciarrino]

I'm entering a differential equations course this coming semester. Is there anything I should review in the coming weeks?

 

[lurflurf]

Courses vary. You could review partial fractions, complex numbers, integrals, linear algebra, and differential equations. Is this a first course? A second course?

 

[dpsciarrino]

Courses vary. You could review partial fractions, complex numbers, integrals, linear algebra, and differential equations. Is this a first course? A second course?

This is a first course. That list is a bit intimidating since I haven't had a lick of linear algebra. haha

 

[lurflurf]

Well then you should be safe from "As you recall from linear algebra.."
A little bit of linear algebra is helpful in differential equations, but it can be introduced as needed. You might want to know what an eigenvalue is, how to solve linear equations, what a matrix is, and what a linear operator is. The derivative is a linear operator so
D(a u+b v)=a Du+b Dv
which is helpful at times.
We write a linear equation such as
$${\begin{array}{cc}
a x+b y=u \\
c x+d y=v \\
\end{array} } \\
\text{in matrix form as} \\
\left( {\begin{array}{cc}
a & b \\
c & d \\
\end{array} } \right) \left( {\begin{array}{cc}
x \\
y \\
\end{array} }\right)
\left( \begin{array}{cc} u \\ v \end{array} \right)$$
D cos(x)=-sin(x)
D sin(x)=cos(x)
which we might like to write in matrix form as
$$\mathrm{D} \left( \begin{array}{cc} \cos(x) \\ \sin(x) \end{array} \right) = \left( {\begin{array}{cc}
0 & -1 \\
1 & 0 \\
\end{array} } \right) \left( {\begin{array}{cc}
\cos(x) \\
\sin(x) \\
\end{array} }\right)$$

You might believe at first that such notions and notations make things harder but they make them easier.

 

[the_wolfman]

This is a first course. That list is a bit intimidating since I haven't had a lick of linear algebra. haha

For an introductory course in differential equations I wouldn't worry about reviewing linear algebra. If you get to systems of ODES (where linear algebra is used) they'll review/introduce the necessary ideas. However this often doesn't come up until a 2nd course in differential equations.