Question

What is the application of calculus?

Answer 1

It costs nothing to be kind.

Answer 2

Let's role-play: If you were an epidemiologist, and you had reliable information of a global pandemic, you could use calculus to find when the rate of people falling ill (and reporting it) begins to decrease [second derivative test].

If you were a factory manufacturer, and you wanted to produce the dolls for the minimum amount of cost, maximizing on profit, you could use calculus to find exactly what the optimal amount is.

It helps if your calc textbook talks about applications in some depth. On the more light-hearted side, if you're a chef you can use calculus to calculate the velocity of a falling pizza as a function of time ("Calculus and Pizza," Clifford Pickover)

Answer 3

If something changes and causes something else to change, calculus (called analysis in higher mathematics) is a convenient way to calculate and describe the changes.

There are a multitude of applications, falling bodies, minimum and maximum values.

Answer 4

calculus deals with various problems in maths - eg ,variable rates of change, areas under curves. it has applications in physics, chemistry, economics, astronomy, mechanics and many other disciplines.

Answer 5

i invented calculus, ask me

Answer 6

If something changes and causes something else to change, calculus (called analysis in higher mathematics) is a convenient way to calculate and describe the changes.

this is only true when small changes in the independent variable leads to small changes in the dependent variable ( ie, continuous)

Answer 7

not for discrete x

Answer 8

Swapping back and forth between the discrete and the continuous is often only a matter of degree (or scale) eg probability is essentially discrete but with a continuous theory.

Answer 9

calculus is made for continuous change , not discrete

Answer 10

What is made for discrete changes?

Answer 11

there is a discrete differential equations, discrete probability, discrete difference equations

Answer 12

its different,

Answer 13

fortunately many variables in the world (height, temperature, width, age, population, mass, weight) are continuous, so calculus can be used with them. but i see what cantor is saying.

Answer 14

james, youre function earlier blows up when t goes to zero, so you cant bound the initial principal

Answer 15

did i just say population was continuous? that's not true. population is discrete. whoops.

Answer 16

You can use finite difference methods,

I don't disagree that the difference between discrete and continuous is an important one but usually its just a question of interpretation.

Answer 17

of course at a fundamental quantum level, reality appears to behave discretely (but is described with probability )

Answer 18

it is often the case we treat population as continuous variable

Answer 19

for instance when you have populations in millions , and the changes are relatively small compared to the population

Answer 20

i take that back, when the x axis is zoomed out, basically, that has the effect of smoothing out all the kinks. if you force continuity

Answer 21

I disagree with the population part

Answer 22

errr, the y axis or population i mean

Answer 23

we use continuous models to discuss population,

Answer 24

Population

Answer 25

This thread got really busy really quick...

Thanks for all the interesting replies, everyone!

Answer 26

we use continuous models to model population...but the key word is "model." a model is a simplification of reality. the reality is that population is discrete. you can't have 2.43 people, unless you're in Hiroshima.

Answer 27

well a stepwise function over time, if time is zoomed out, you get a continous curve

Answer 28

kind of like how a discrete probability distribution becomes continous

Answer 29

@jamesm I definitely don't approve of people who confuse the model with reality, that's why interpretation is key.

Answer 30

james, thats why population is in millions

Answer 31

if pop is in millions you dont get 2.43 people, but 2.43 million people , which is fine

Answer 32

of course if your model gives you 2.4343323485 people, then youre right :)

Answer 33

in millions

Answer 34

so i guess the problem is not solved by using bigger units

Answer 35

Cantorset2 ur a guru

Answer 36

so we're using the continuous model , because it is accurate "up to" the important features of the actual population

Answer 37

ajeemo, im a neophyte. :)

Answer 38

'cantorset' is a group guru, but his account has been temporarily suspended

Answer 39

making the units larger won't do much to discretize a coontinuous model...there are a number of functions invented for that purpose...like the rounding function and the floor function

Answer 40

wait what?
can you give me an example

Answer 41

Quantization

Answer 42

yes...and quantization

Answer 43

oh right, you can floor or ceiling youre infinite decimal continous population to a convenient realistic population

Answer 44

realistic units,
whats quantisation

Answer 45

but the point is, the continous shape and the equation concisely summarise the population. briefly

Answer 46

http://en.wikipedia.org/wiki/Quantization

"Quantization is the procedure of constraining something from a relatively large or continuous set of values (such as the real numbers) to a relatively small discrete set (such as the integers)."