Math Exploration Ideas On Calculus

[Karthik]

I am facing problems in my math exploration. I have chosen a topic i want to do on calculus but not getting any idea. So i hope someone could help me

[IB Math Helper]

Hi Karthik,

Here are some ideas you might find useful for calculus.

Primarily calculus is useful for optimization problems or using data to find the derivatives (or integrals) for some meaningful unit.

Here are some ideas for IAs off the top of my head:

1) Finding the optimal volume of a cylindrical can given constraints such as material costs and what not. This is a classic problem that all teachers know about so you can add your own spin to this by researching material costs yourself or looking up available data online and also factoring in that the can is not entirely cylindrical (there a depression in the bottom of most cans) and explaining why. This is just one idea for personal engagement but perhaps you can think of more.

2) Tracking the speed of Olympic athletes in the 100m dash. If you can plot data, you can use the derivative function to find the speed at different points along the race. You'll be surprised to find out that runners do not run at a constant speed and can investigate why.

3) The usefulness of the inflexion point (second derivative) in certain populations. For example, if you plot the data of Japan's population over time, you will see that over the past few years the population has been declining. However, by studying the rate of the rate of change of the population (i.e. the second derivative) can provide an earlier signal of declining growth.

These are 3 different ideas in different domains to get you started. Think of some other domains where calculus might be useful and I'm sure you'll find something that suits you.

Hope this helps.

[Karthik]

Hi

thank you so much for the ideas

 wanted to know if any calculus topics could be implemented in car because i love cars i thought why use calculus to do something in it. so i went through some websites but couldn't find anything related with it. if you don't mind can u please help me out.

[IB Math Helper]

I can only help to a certain extent. At the end of the day, this needs to be your project.

There are so many things you can deal with when it comes to cars and calculus: speed, rate of consumption of oil, brakes. Helps to know some physics behind these concepts.

I don't know anything about cars and I thought of those 3 ideas. Get a pen to paper and just start brainstorming ideas. Consider ideas where you can collect data (and if you can't collect data, try to find secondary data). 

[Nureshka]

Hi IB Math Helper. I'm interested with the 100m dash topic. Can you guide me more about the topic? I did so many search and read lots of research paper about this 100m dash. But I still couldn't get how deep the application of calculus going to be use. Do I have to come out with equations after plotting the graphs? 

I really appreciate and so looking forward to your reply. Thanks so much.