Nt1310 Unit 1 Linear Study

There are several things that I appreciate from this class:

\begin{enumerate}

\item[1]

\[ u_t=Ku_{xx}+Q\]

To solve the above equation most of the time (For the sake of simplicity) we set $K=1$. This is how I solved similar type of equations in my undergraduate study. But you explained the importance of K. You said, for a small rod, K is not that important as in airplane (K is a material property). I will never forget this. I'm really interested studying PDE and to see the world through mathematics and then work for a new invention.\\

\item[2] You have introduced short and sweet ways of simplifying. It save my time in different ways.

I. Integration by parts: Story of the big brother and the little brother.\\

II. A simple way of getting inverse of a special type of matrix.\\

It helps me to understand the idea behind the linear algebra. The fundamental problem of linear algebra: Solve the system of linear equation.\\ \item[4] All most all the time you intended to explain the problems in both physical and mathematical way. It helps me to understand the things that we are capable to do as mathematicians.\\

\item[5] I really like the motivation that you gave before explain the Green's function. You have divided the black board in to two parts and explained the concept of Green's function by comparing with the system $Ax=b$. Then I saw the connection of linear algebra and functional space. I clearly understood the different between a linear operator and a differential