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How to evaluate a proof that seems to be using induction informally?

Evaluating "Correctness" There are many things that I dislike about the argument given, but these things are (perhaps) largely related to (1) the amount of time a student might have been ...
Xander Henderson's user avatar
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1 vote

How to evaluate a proof that seems to be using induction informally?

The proof is hard to follow because there is no equality sign or words between the second and the third line. That said, the idea of the proof is correct. If the goal is to teach rigorous mathematics, ...
Tommi's user avatar
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2 votes

Earliest real-world uses of Calculus and Linear Algebra

It's easier to say what is not touched by calculus or linear algebra. All physics after Newton involved Calculus. Your touchscreen, for example requires an understanding of capacitance, and simple ...
Steph's user avatar
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1 vote

Earliest real-world uses of Calculus and Linear Algebra

Back in Greece long ago around 400 to 200 BC by Eudoxus and Archimedes according to Wikipedia calculating the area under a parabola for instance.
stackoverblown's user avatar
3 votes

Earliest real-world uses of Calculus and Linear Algebra

I'd like to offer you another idea, to look at the question from the Methodology POV. IMHO most of the mathematical/science solution have had some application before they were understood, and then ...
Pirin's user avatar
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1 vote

Earliest real-world uses of Calculus and Linear Algebra

I nominate search engines. Algorithms like page rank are excellent applications of linear algebra. I also nominate neural networks. Deep learning and neural networks are underneath generative AI, like ...
user52817's user avatar
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12 votes

Earliest real-world uses of Calculus and Linear Algebra

I want to find what the earliest real-world applications of Calculus were. By real-world application, I mean a device, instrument or technology which made lives better. Let's assume that: Earliest = ...
Pedro's user avatar
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8 votes

Earliest real-world uses of Calculus and Linear Algebra

In the late 18th century, ships leaving Europe for other continents routinely brought with them books such as trigonometrical tables and astronomical almanacs. Those almanacs included ephemerides, a.k....
jpmarinier's user avatar
3 votes

Earliest real-world uses of Calculus and Linear Algebra

I tried researching it (online, not exhaustively). The earliest I could find for a real technological (economic) benefit of calculus was structural (civil) engineering as early as the 1700s with beam ...
user23961's user avatar
8 votes

Earliest real-world uses of Calculus and Linear Algebra

Maxwell's equations (1861) are a set of coupled partial differential equations. They led to Heinrich Hertz demonstrating radio waves in 1887. Marconi sent messages to British battleships in 1899. I ...
Peter Balch's user avatar
8 votes

Earliest real-world uses of Calculus and Linear Algebra

By real-world application, I mean a device, instrument or technology which made lives better and would have been simply impossible without Calculus or Linear Algebra. In the case of calculus, I don't ...
kjdfhlkdfjh's user avatar
3 votes

Earliest real-world uses of Calculus and Linear Algebra

Maybe Archimedes' figuring out that the volume of a sphere is 2/3 the volume of the smallest cylinder surrounding that sphere? This work was performed some time in the third century BCE.
SoronelHaetir's user avatar
8 votes

Earliest real-world uses of Calculus and Linear Algebra

The Mercator projection (1569). This map projection revolutionized naval navigation. The vertical coordinate $y$ depends on the latitude $\varphi$. In modern language, it is the integral of the ...
Gerald Edgar's user avatar
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