mathematics

Hiroshi Okamura

Hiroshi Okamura is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hiroshi Okamura rather than just read about it. In short: Hiroshi Okamura (岡村博, Okamura Hiroshi; November 10, 1905 – September 3, 1948) was a Japanese mathematician who made contributions to analysis and the theory of differential equations. He was a professor at Kyoto University.

Key takeaways

Hiroshi Okamura belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hiroshi Okamura to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hiroshi Okamura from memory before moving on to harder problems.

Reference excerpt

Hiroshi Okamura (岡村博, Okamura Hiroshi; November 10, 1905 – September 3, 1948) was a Japanese mathematician who made contributions to analysis and the theory of differential equations. He was a professor at Kyoto University. He discovered the necessary and sufficient conditions on initial value problems of ordinary differential equations for the solution to be unique. He also refined the second mean value theorem of integration.

Works Hiroshi Okamura (1941), "Sur l'unicité des solutions d'un système d'équations différentielles ordinaires", Mem. Coll. Sci., Kyoto Imperial Univ. (in French), 23: 225–231 Hiroshi Okamura (1942), "Condition nécessaire et suffisante remplie par les équations différentielles ordinaires sans points de Peano", Mem. Coll. Sci., Kyoto Imperial Univ. (in French), 24: 21–28 Hiroshi Okamura (1943), "Sur une sorte de distance relative à un système différentiel", Nippon Sugaku-Buturigakkwai Kizi Dai 3 Ki (in French), 25: 514–523 Hiroshi Okamura (1950), "On the surface integral and Gauss-Green's theorem", Memoirs of the College of Science, University of Kyoto, A: Mathematics, 26 (9): 5–14, doi:10.1215/kjm/1250778050 (posthumous)

References

Worked examples

Example 1 — a first encounter with Hiroshi Okamura

Start with the simplest possible case. Write down what Hiroshi Okamura claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hiroshi Okamura before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hiroshi Okamura ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hiroshi Okamura

In research: Hiroshi Okamura appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hiroshi Okamura in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hiroshi Okamura is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1905 births, 1948 deaths, 20th-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Hiroshi Okamura outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hiroshi Okamura in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hiroshi Okamura means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hiroshi Okamura out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hiroshi Okamura in simple terms?

Why does Hiroshi Okamura matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hiroshi Okamura?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hiroshi Okamura.