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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?

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