Practical Applications of Calculus: Finding Motivation for Learning Maths

[BogMonkey]

I usually have no shortage of motivation because I like to think about all the practical applications that I could use this theory for in my future endeavours and also how the theory I'm learning expands on and fills in the gaps of what I already know. In maths I can't automatically think of many applications for the principles though. I read an explanation of differentiation and integration which explained how differentiation of the equation for a displacement/time graph yields the equation for a velocity/time graph and the second derivative yields the equation for an acceleration time graph, and how integration does the opposite. That gave me new motivation for learning calculus because I finally saw something I might actually use it for. Basic calculus that is I can't imagine any practical applications of knowing how to differentiate or integrate more complex equations though. Can anyone list a few examples like that which give you a good reason to learn the kinda stuff they teach in a first year maths course?

 

[chiro]

Calculus is all about analysis and change. Typically when we want to model the behaviour of some phenomenon we know information about how changes occur.

In single variable calculus you have a single input and one output. In several variable calculus you can have a vector output and several inputs. By using the tools that mathematicians have developed throughout the last 400 years you can analyze how things change, solve for analytic versions of functions or simulate models where changes are known but do not have an analytic solution.

Typically in applied maths we know the changes. Sometimes we can turn that into an analytic function but more often than not we can't. So we turn to numeric analysis for tools in analyzing and making sense of output.

Now i have just mentioned mainly applied mathematics. We can take functions that represent continuous probability distributions and we take our analysis and apply it to statistics.

After a bit of experience you are able to as a scientist get data whether it be a natural or man made process and model any phenomena. With calculus and its family of tools, you can make an analysis of the behaviour, and depending on what needs to be answered come up with suggestions or solutions to describe it. Like with acceleration being velocities derivative and displacement being velocities integral, you end up being able to come up with methods to link the variables in an unknown problem together.

It could be related to fluid flow, electricity and magnetism, classical mechanics, basically anything and in analyzing you use the same methods and mindset to analyze these problems.

Also if you end up learning math in depth (ie diff equations, linear algebra, analysis, etc) then you will have a big toolkit of transforming one thing mathematically into another. You might for example have a cyclic function and by the use of Fourier series you transform it into its Fourier representation. In applied math your interested in the methods that the pure mathematicians of centuries passed have given you but in pure math you would probably extend theoretical results.

Also I should point out an important thing that all areas of math are interconnected. You can for example use the framework of linear algebra with differential equations to solve various forms and when used in this context provide a more appealing framework than doing it without it.

In applied math I learned about difference equations in my first year. A lot of the application was things like financial math, annuities, fish engineering and others. Then with differential equations there are tonnes of examples (like cooling for example). In second year it was classical mechanics and heat modeling.

Before I came to uni I had various experience as a computer programmer. One application of differential calculus is standard texture mapping which is the heart of rendering in video games and animation.

There are a lot of fields that use a lot of varied type of math. Entertainment is one, Actuarial Sciences are another. You can find a lot of different areas that use applied math but find what interests you and there are a lot of options generally to choose from.

If you get a good lecturer they will probably teach you the "why" and not just the "how" of mathematics. As everything sinks in it will hopefully click with you about why things work and why they are done the way they are done.

I wish you all the best with your decisions and your future.

 

[BogMonkey]

Thanks a lot! What you said "being able to come up with methods to link the variables in an unknown problem together" got me thinking. The only 3 variables I've thought about are acceleration, velocity and displacement but there are probably plenty of these variables within variables that I'll come across.

I'm not a programmer myself but I know PHP fairly well but I've yet to come across anything which incorporates any knowledge of maths. Then again PHP uses variables, functions and loops (sets).