Difference between revisions of "Calculus"
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| − | Other than a mental exercise and to show how smart someone is, I never saw much use in spending the time and effort to | + | Other than a mental exercise and to show how smart someone is, I never saw much use in spending the time and effort to learn calculus in depth. Numerical methods are used to do calculations, not calculus, so what is it really used for? |
The ''ideas'' underlying calculus though, they are what's valuable. Particularly the concept of infinitesimal, which blew my mind when I first heard of it. | The ''ideas'' underlying calculus though, they are what's valuable. Particularly the concept of infinitesimal, which blew my mind when I first heard of it. | ||
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| − | Calculus can be used to create equations for model systems, which are then calculated on computers and compared to the real result. | + | Calculus can be used to create equations for model systems, which are then calculated on computers and compared to the real result. In these cases integrals within limits can be useful, but even here the integrations of various equations are listed in tables so there is no need to memorize them. In addition, as with all math, calculus only approximates reality. |
Calculus also allowed for the creation of useful tools, such as the Fourier Transform. Understanding the concept of Fourier transformation is useful, but going through the math of it also seems a waste of brain space. | Calculus also allowed for the creation of useful tools, such as the Fourier Transform. Understanding the concept of Fourier transformation is useful, but going through the math of it also seems a waste of brain space. | ||
Revision as of 16:20, 24 March 2020
Other than a mental exercise and to show how smart someone is, I never saw much use in spending the time and effort to learn calculus in depth. Numerical methods are used to do calculations, not calculus, so what is it really used for? The ideas underlying calculus though, they are what's valuable. Particularly the concept of infinitesimal, which blew my mind when I first heard of it.
An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. A change in this quantity is called a differential, usually notated as dx, if x is the variable.
Calculus can be used to create equations for model systems, which are then calculated on computers and compared to the real result. In these cases integrals within limits can be useful, but even here the integrations of various equations are listed in tables so there is no need to memorize them. In addition, as with all math, calculus only approximates reality.
Calculus also allowed for the creation of useful tools, such as the Fourier Transform. Understanding the concept of Fourier transformation is useful, but going through the math of it also seems a waste of brain space.
The ideas behind each of the tools of calculus will be described, but detailed math behind is left for others.
