I'm a self study in math, computer vision and machine learning. I just finished partial derivative and has no background in Ordinary differential equation(ODE). Do I need to study ODE in order to understand Fourier series and Fourier Transform? The Fourier series and Fourier Transform appears in my computer vision class and I feel unfamiliar with some notations.
maybe ODE will also benefit when I study deep learning too?
As far as I know, the reason why differential equations are studied to some extent before you get into Fourier series is that Fourier series are used in understanding the heat equation $$ \frac{\partial u}{\partial t} = \text{constant} \cdot \sum_k \frac{\partial^2 u}{\partial x_k^2} $$ and the wave equation $$ \frac{\partial^2 u}{\partial t^2} = \text{constant} \cdot \sum_k \frac{\partial^2 u}{\partial x_k^2} $$ and some more exotic equations than those.
You can understand a lot about Fourier series without that, but understanding what they're good for requires that.
The book on Fourier series and Fourier integrals by Dym and McKean has lots of examples of what they're used for. (But it's not the best place to learn theory of integration, the topic of one of the chapters, and the omission of everything involving the use of generalized functions (such as Dirac's delta and its derivatives) might reasonably be objected to by some.)