Partial differential equations (PDE), involves two or more variables and at least one of their derivatives. It has extensive applications in physics and engineering as well as many other branches of mathematics.

MathWit currently focus on bridge in undergraduate level PDE courses and graduate level PDE courses and help prepare you for your graduate study. We have many examples from a database of past homework problems, exam questions, qualify exam questions for some PH.D programs. After a few classes at MathWit, you will be more confident on this subject and your future study or research.

The following is part of a sample from the problem solving tutorial:

\[T(r,\theta)=\frac{1}{2}g_0+\sum\limits_{n=1}^{\infty}\frac{1}{\pi}\left(\frac{r}{R}\right)^n\int_{0}^{2\pi} \left[\cos n\theta \cos nx f(x) +\sin n\theta \sin nx f(x)\right]dx\]

\[=\frac{1}{2\pi}\int_{0}^{2\pi} f(x)dx +\sum\limits_{n=1}^{\infty}\frac{1}{\pi}\left(\frac{r}{R}\right)^n\int_{0}^{2\pi} f(x)\cos n(\theta -x)dx\]

\[=\frac{1}{2\pi}\int_{0}^{2\pi} f(x)dx+\frac{1}{\pi}\int_{0}^{2\pi} f(x)\sum\limits_{n=1}^{\infty}\left(\frac{r}{R}\right)^n\cos n(\theta -x)dx \]

For the sum inside the last integral of the above, we can use the following technique:

\[\sum\limits_{n=1}^{\infty}a^n\cos nx =Re \sum\limits_{n=1}^{\infty} \left(ae^{ix}\right)^n =Re\frac{ae^{ix}}{1-ae^{ix}} \]

After some routine calculations, we ......