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Is there a part of physics that there is no calculus in it?

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    $\begingroup$ One could do all of physics without calculus, but it would be incredibly tedious. A look at old physics books, especially Newton's "Principia" can easily convince you of that. A somewhat easier read that demonstrates the same problem would be Copernicus' "De revolutionibus orbium coelestium" and Kepler's works. In essence, you would "re-invent the calculus wheel" all the time. $\endgroup$
    – CuriousOne
    Jul 6, 2016 at 5:26
  • $\begingroup$ What do you think? Why do you think physics might not have existed before then? $\endgroup$
    – sammy gerbil
    Jul 6, 2016 at 5:32
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    $\begingroup$ @sammygerbil Because I think physics science has been created by observation of phenomenons (variations) and without calculus how can we talk about variations? $\endgroup$
    – lucas
    Jul 6, 2016 at 5:35
  • $\begingroup$ The Greeks had some real breakthroughs in physics and they also made some doozies... all without calculus. $\endgroup$
    – CuriousOne
    Jul 6, 2016 at 6:01
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    $\begingroup$ Is this on topic for us? I thought recently we have considered pure history questions to be off topic and sent them to History of Science and Mathematics. $\endgroup$
    – David Z
    Jul 6, 2016 at 7:55

4 Answers 4

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Infinitesimal calculus was first formulated by Isaac Newton and Gottfried Leibniz in the mid-17th century. By that time, a number of qualitative and quantitative physical laws had been formulated. Here are some examples of the quantitative laws:

Dynamics

  • Laws of planetary motion (Kepler)
  • Motion of falling bodies, pendula, projectiles (Galileo, Torricelli)

Optics

  • Inverse-square law for light intensity (Kepler)
  • Law governing the angle of refraction (Snell, Descartes)

Hydrostatics and Hydrodynamics

  • Law of hydrostatic pressure (Torricelli)
  • Rate of flow through a small hole (Torricelli)

Material Science

  • Square-cube law governing strength of structures under proportional scaling (Galileo)
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  • $\begingroup$ Thank you for your attention! Please read my comments to CuriousOne. $\endgroup$
    – lucas
    Jul 6, 2016 at 6:53
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    $\begingroup$ You might include Torricelli's work on pressure, optics, fluids and projectile motion. $\endgroup$
    – dmckee --- ex-moderator kitten
    Jul 7, 2016 at 4:22
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Note: Following answer is just my humble opinion

Galileo is the forefather of the modern physics. He has discovered law of inertia and law of acceleration. It may be worth noting that He was unaware of even very basic mathematics (like fractions). He had shown law of acceleration with the help the water clock and integer numbers.

Moreover, Newton has verified his law of gravity (and motion) from the moon trajectory. These laws are in the form of equations, derived by Kepler for which data is taken by his predecessors. If Kepler and his predecessors have not done the Herculean task of mapping the planetary orbits it would be difficult for Newton to establish the validity of laws of motion.

Mathematics is definitely required for easier understanding of the laws of nature and that's why we are using more and more advanced mathematics in the physics. However, saying that there is no physics before the existence of one branch of mathematics, in my opinion it is outright disrespect for the hard work of our forefathers.

I would also like to add that although mathematics comes before humans start to understand the physics but even today people use term "Physical Arguments" that essentially means that one is trying to explain the phenomena without mathematics or with minimal mathematics and mostly from logical arguments.

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  • $\begingroup$ brilliant answer $\endgroup$
    – Obama2020
    Nov 14 at 19:34
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There are several examples of fields in physics which don't require calculus and were born far before its invention. For example:

  • Geometric Optics: some of the laws governing light propagation were formulated by ancient Greeks. Catoptrics (from the Greek κατοπτρικός, "specular") has been studied by Euclid (350 BC) and Hero of Alexandria (10-70 AD).
  • Statics: the study of the equilibrium of rigid bodies does not require calculus, but only geometry. Statics has been for obvious reasons (architecture) studied since forever: Archimedes wrote an essay on statics entitled On the Equilibrium of Planes, in which he establishes the law of the lever and calculates the center of gravity of various geometrical figures using only geometry. While it is true that some proofs contain a primitive form of calculus (for example the part regarding parabolic segments), many results are obtained using only Euclidean geometry.
  • Astronomy: Ancient Greeks used geometry to obtain remarkable results in the field of astronomy. Aristarchus of Samos wrote an essay entitled On the Sizes and Distances of the Sun and Moon and Erathostenes was able to calculate the circumference of the Earth.

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Other examples include hydrostatics and the study of projectile motion (ballistic).

Also, keep in mind that many ancient physical theories didn't make use of mathematics at all. Take for example Aristotelian physics. We may laugh at such a theory today, but we would be silly to do so: such a theory basically dominated the scientific world for two thousand years. For example, the aristotelian theory of projectile motion (the Theory of Impetus) came under slight criticism only during the Middle Ages (!) and we have to wait first Galilei and then Newton (Philosophiæ Naturalis Principia Mathematica was first published in 1687) for a satisfactory theory of projectile motion.

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  • $\begingroup$ Thank you for your attention and time! I don't know what other people do, but I personally never laugh at them. I always respect to the past efforts. BTW, thank you because of useful historical information! I like that. $\endgroup$
    – lucas
    Jul 12, 2016 at 10:58
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There's a lot of physics which is miles away from calculus but the problem is it's not accurate I think 80-90% of that is totally piece of junk and remaining is way more hard to understand without calculus but if you want you can do it like proof of kinamatical equation can be given simply by calculating area under those graphs but that's lot more hard than simply by using calculus

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