What's coming in the second part of this course?

• Fourier transform. Given $f(x)$, we want to express $f(x) = \int e^{ikx} g(k) dk$, since $e^{ikx}$ is easy to deal with.
• Laplace transform. Given $f(t)$, on $t \in [0, \infty)$, we want to write $f(t) = \int_{p>0} e^{-pt} g(p) dp$.

Why do we care? We want to use $e^{ikx}$ to model oscillation, and we want to use $e^{-pt}$ to model decay.