Question

What mathematical ideas are you curious to know more about as a result of studying the topics this week? Give one example of a question about the material that you'd like to explore further and describe why this is an interesting question to you.

Topics:

• Newton’s Method
• The Integral

Answer 1

Newton's method quickly finds a good approximation for roots of a function. So you can ask why does it converge faster than other alternatives. You can question mathematically approaching its rate of convergence as compared with other methods.

Also since, it needs an initial guess near the root, but sometimes function has extrema or point of inflection close the root, thereby diverging the solution. So you can ask how to select a good initial guess for such functions.

Integral is among the most important topics of calculus. You can ask about its applications in real life. One more interesting question would be its relation to limits. Since differentials can be evaluated by limits and vice versa, is there a similar way with integral and limits. Integrals are called antiderivatives, so it would be interesting to explore their relationship with limits.