I'm pursuing my PhD in Theoretical Physics. I love tutoring, and I love the idea of imparting education to curious students. In my opinion, teaching math and physics the correct way, is really important, because it either makes or breaks their faith in those subjects. I tend to have really interactive and fun sessions, so I've heard from other students. Interactive classes/lectures are what I missed in my undergraduate days, and I want to make it up to the world by tutoring.
Verify the statement of Example 2 . Also verify that $y=\cosh x$ and $y=\sinh x$ are solutions of $y^{\prime \prime}=y$
Solve Example 4 using the general solution $y=a \sinh x+b \cosh x$.
Verify that $y=\sin x, y=\cos x, y=e^{i x}$, and $y=e^{-i x}$ are all solutions of $y^{\prime \prime}=-y$.
Find the distance which an object moves in time $t$ if it starts from rest and has an acceleration $d^{2} x / d t^{2}=g e^{-k t}$. Show that for small $t$ the result is approximately (1.10), and for very large $t$, the velocity $d x / d t$ is approximately constant. (This problem corresponds roughly to the motion of a parachutist.)
Find the position $x$ of a particle as a function of time $t$ if its acceleration is $d^{2} x / d t^{2}=A \sin \omega t$
