Differential and Difference

2 tests

• 7th/8th week
• 14th/15th week
  FInal Exam

2x 18pts for tests, 8pts for activity
60pts for exam, 30pts required for pass

Probable short-pass
Cheat-sheet on the tests/exam

$f(x)=e^x$ and $(e^x{)}^{\prime }=e^x$
Assume that $f^{\prime }(x)=f(x)$. Unknown: function $f(x)$
$g^{\prime }(x)=(\frac{f(x)}{e^x}{)}^{\prime }=\frac{f^{\prime }(x)e^x-f(x)(e^x{)}^{\prime }}{(e^x{)}^2}=\frac{0}{(e^x{)}^2}=0$, so
$g(x)=0\to g(x)=C$
$f(x)=g(x)\cdot e^x=C{e}^x$

Sometimes we can use an initial condition
$f^{\prime }(x)=f(x)$
$f(0)=3\leftarrow$ initial condition

Lectures

Tutorials

1. Tut 1
2. Tut 2
3. Tut 3