How can we relate calculus, trigonometry etc in real life

Question

I have always wondered what does trigonometry, calculus, logarithms solve real world problems? Where do they apply in real life? Is there any simple book where I can understand it?

Answer 1

I am gonna go with two examples I commonly give to my students.

Trigonometry: This one is historical. Indians in 6th century were able to work out the distance ratio between moon-earth and sun-earth by realizing that when they see a half moon, the angle between earth-moon-sun has to be a right angle and they can use their trigonometric functions (which they knew already) to work out what the distance to the sun is, relative to the distance to the moon.

Source of the picture, more info on this

Calculus: A much more vague example, but one that has had success with non-mathematical people has been a simple idea of how derivatives might be used in the real world. If one knows that derivatives relate to the slope, then I begin by drawing a plane with air flowing around it, such as this:

Planes that cannot fly are not a good idea and so is trial-and-error method of building twenty planes and see which one does the best. That's where the maths come in, calculating the airflow (Which is demonstrated here by the slope given by the derivative, although in reality it's of course not quite that easy - mathematically speaking).

add: Logarithms Watch this numberphile video for a nice example.

Hope this gives some illustration of the endless ways mathematics can be used in the "real world"

Answer 2

Maths(calculus or anything) Says the logic and develops a model of thinking that is problem solving oriented. so it is base on top of which we reason and build. eg: Computer science and technology and complex smartphones!!! if you take courses on physics or computer science and any other engineering courses you may connect the dots.You don't find the direct implementation but you see bits and pieces of concepts implemented in real life or things around us. Good Luck