## Sticky Post – Read this first. Categories and Links in Mathemafrica

The navigability of Mathemafrica isn't ideal, so I have created this post which might guide you to what you are looking for. Here are a number of different categories of post which you might like to take a look at: First year mathematics notes and resources (particularly for the University [...]

By | January 17th, 2018|0 Comments

## Why did we choose that range for theta when doing trig substitutions?

Remember when we are doing a trig substitution, for instance for an integral with:   $latex \sqrt{a^2-x^2}$   We said that we should choose $latex x=a\sin\theta$, which seemed reasonable, but we also said that $latex -\frac{\pi}{2}\le\theta\le\frac{\pi}{2}$. Where did this last bit come from? Well, we want a couple of things to [...]

By | August 2nd, 2018|2 Comments

## Integrals with sec and tan when the power of tan is odd

We went through an example in class today which was   $latex \int tan^6\theta \sec^4\theta d\theta$   In this case we took out two powers of sec and then converted all the other $latex \sec$ into $latex\ tan$, which left a function of tan times $latex sec^2\theta d\theta$. We wanted [...]

## Fundamental theorem of calculus example

We did an example today in class which I wanted to go through again here. The question was to calculate   $latex \frac{d}{dx}\int_a^{x^4}\sec t dt$   We spot the pattern immediately that it's an FTC part 1 type question, but it's not quite there yet. In the FTC part 1, [...]

## Is MAM1000W Making You Anxious?

Hello, my name is Jeremy :-) I am new to the MAM1000W team of tutors - if you want to read more about my background you can take a look at my bio in the MAM1000W document on Vula. In short, I returned to UCT last year to do my [...]

## Calculus for the ambitious, by Tom Korner, a review, by Henri Lauri

Amazon link This is a lovely book: strong emphasis on ideas; a lively sense of humour; a sure logical touch; historical detail that is accurate, relevant, yet quirky (takes some doing!). What's not to like? Well, there's this: it is not easy to decide whether to recommend the book to [...]

## The Recamán sequence

In case you have watched the following video about the Recamán sequence. and want to play around with it in Mathematica. Here is my code for doing so: nums = {0}; For[i = 1, i < 66, i++, If[nums[[-1]] - i > 0 && Position[nums, nums[[-1]] - i] [...]

## Music by the Numbers, From Pythagoras to Schoenberg – By Eli Maor, a review

NB. I was sent this book as a review copy. From Princeton University Press Music by the numbers leads us on a journey, as stated in the title, from Pythagoras to Schoenberg. In many ways the endpoint is stated early on, giving us clues that a revolution in [...]

## What can be computed? A practical guide to the theory of computation – by John MacCormick, a review

NB. I was sent this book as a review copy. From Princeton University Press. It's not often that a textbook comes along that is compelling enough that you want to read it from cover to cover. It's also not often that the seed of inspiration of a textbook [...]

## On Gravity, a brief tour of a weighty subject – By Tony Zee, a review

NB. I was sent this book as a review copy. From Princeton University Press In the era when our eyes are being opened to the Universe in the gravitational spectrum via the recent gravitational wave observations, this book is exactly what is needed to communicate to the general [...]