The first rule of bootcamp is: You DO talk about bootcamp!

I know that the start of the semester is busy, but now is the time to consolidate what you learnt last semester if you feel that you are struggling. It will take a good number of hours each week for a couple of weeks, but with effort you can do it. It’s really useful to go through these with other people, but it’s also important to spend some time going through exercises on your own. I suggest finding a balance between the two.

I’m going to list some links below, some of which have explanations, some of which have videos and many of which have exercises. Here’s your task if you choose to accept it:

  1. Put aside Whatsapp, Facebook, news feeds, anything distracting and make sure that you are in a quiet place – if possible take the material offline so you don’t have to have any internet connection when you are going through these.
  2. Make sure you have pen and paper ready. Actively writing is infinitely more useful than just thinking about whether you know how to solve a problem
  3. Choose which topic you are going to focus on and set your timer for an hour
  4. Read through the topic and take notes for yourself
  5. Go through as many exercises as you can in the time you’ve given yourself
  6. After the hour is up, go for a stretch, a walk, a breather for 15 minutes
  7. Come back and go through any of the questions which you got stuck on and go through another hour’s worth
  8. Stop
  9. Come back the next day and look at the questions you struggled with the day before
  10. Repeat

After you have been through as much of the material as is in the links, send an email to me and tell me how it’s going. Let me know:

  1. Do you now understand the topic?
  2. Do you need more questions?
  3. Do you need more explanation?
  4. What has been the biggest stumbling block?
  5. What has been the greatest insight so far?

Note that there will be some questions in here which we haven’t covered and so you will have to figure out if there is something that you are not expected to know. If you are not sure, send me a message and I’ll tell you whether you should be able to do it.

Here are some useful links which I’ve found for the topics which you have asked about:

Related rates:

Optimization: – check out the section on optimization.

Graph sketching:

Integration by substitution

Integration by parts


Inverse functions

Applications of derivatives

Newton’s method

If there are any other topics which I’ve not listed here which you would like to have more questions on, let me know and I’ll find some suitable ones for you.

Trig integrals


Integration by trig substitution


Integration by partial fractions


Improper integrals


The comparison theorem


Proof by Induction


Proof by Contradiction – these are somewhat harder to find good examples of


The Binomial Theorem


I’ve been told that this is a rather useful video to help understand the binomial theorem if you’ve struggled with the class material. With thanks to Sasha T!


Complex Numbers

Differential equations



First order linear:


Second order linear homogeneous with constant coefficients:


Vectors and Matrices


More video links from Vula announcements

Partitions and Ramanujan’s amazing role in understanding them.

Here’s a Khan Academy video on Related Rates.

the limit of x->0 of sin(x)/x is in isiXhosa

Here’s a Khan academy video about the Mean Value theorem. I couldn’t find the same video in Xhosa, but I did find a proof by induction video in Xhosa.

Graham’s Number – an unimaginably large number which is talked about in the Numberphile video here.

Taylor series

this video

How clear is this post?