This is just a quick reminder. If you find any of this confusing, there is a very important trick for making it easier – practice, practice, practice! It doesn’t take years to master this, it takes a few hours every week for a few weeks. You will become more and more familiar with the techniques and learn intuitively to know which technique to use in which situation.
Let’s start with the very basics.

If , what is its derivative? ie. how do we find a function such that:

The answer of course is . We use our normal differentiation rules which you should now be very familiar with. How about if I told you that there was some function whose derivative was – ie. we reversed the question:

What is a function whose gradient at a point is ?

How do you find what is? We are trying to solve the equation

for .…

I will attempt to post notes for the coming sixty lectures on a daily basis. You can either ask questions about the topics which you don’t understand here, or email me directly, or of course come and chat in my office when I’m around.

• These notes are for the second semester of MAM1000. They are neither complete nor exact and no responsibility is held for the accuracy within. Mistakes are undoubtedly included. That being said, I hope that they can be a useful resource in addition to the course textbook (Stewart) and additional online materials.
• I am always very grateful when people find mistakes in these notes. These may be in the form of spelling, grammar, calculational errors, typos in formulae, typesetting errors and anything else which doesn’t seem to make sense. If an explanation is not clear, please contact me and I will do my best to explain it in another way.