I am emailing a link of this to everyone on the class list every Friday afternoon. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jpmccarthymaths@gmail.ie and I will add you to the mailing list.

Pending…

## Next Week

We will continue our work on the Inverse Laplace Transform and finally solve some differential equations. This is the metaphor that explains the use of Laplace Methods in the solution of same:

Suppose that you come across a poem written in English of whose meaning you don’t understand. However suppose that you know a French-speaking gentleman who is a master of interpreting poems. So you translate the poem into French and send it to the French gentleman. The French gentleman writes a perfectly good interpretation of the poem in French and sends this back to you where you translate it back into English and you have the meaning of the poem.

1. Poem in English = Differential Equation
2. Interpretation in English = Solution of Differential Equation
3. Translate into French = Take Laplace Transform
4. Poem in French (better interpreter) = Algebraic Equation (easier to solve)
5. Interpretation in French = Laplace Transform of Solution of Differential Equation
6. Translate back into English = Inverse Laplace Transform

## More Explanations

Somebody told me the beauty of learning about maths off a video is that you can pause the lecturer. I found these online and I have to say I like these lectures a lot… not many examples but we do them in class even if you seem to think that I don’t!

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/

We would have covered lectures 11 to 14 last year.

Lectures 19 & 20 are relevant for us. Lecture 22 and 23 are where this stuff ends up being really useful (not in MATH7021 unfortunately).