mathematics

James Thomas Beale

James Thomas Beale 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 James Thomas Beale rather than just read about it. In short: James Thomas (J. Thomas "Tom") Beale (born 1947) is an American mathematician, specializing in fluid dynamics, partial differential equations, and numerical analysis.

Key takeaways

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

Reference excerpt

James Thomas (J. Thomas "Tom") Beale (born 1947) is an American mathematician, specializing in fluid dynamics, partial differential equations, and numerical analysis. J. Thomas Beale grew up in Savannah, Georgia. In 1967 he graduated from California Institute of Technology (Caltech) with a B.S. in mathematics. In 1973 he received his PhD in mathematics from Stanford University. His PhD thesis Purely imaginary scattering frequencies for exterior domains. was written under the supervision of Ralph S. Phillips. Soon after receiving his PhD Beale became a faculty member at Tulane University. In 1983 he resigned from Tulane University and became a professor at Duke University, where he retired as professor emeritus in 2016. In 1994 Beale was an invited speaker with talk Analytical and numerical aspects of fluid interfaces at the International Congress of Mathematicians in Zurich. From June 28 to 30, 2010, the mathematics department of Duke University held a conference in his honor.

References

Worked examples

Example 1 — a first encounter with James Thomas Beale

Start with the simplest possible case. Write down what James Thomas Beale 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 James Thomas Beale 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 James Thomas Beale 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 James Thomas Beale

In research: James Thomas Beale 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 James Thomas Beale 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: James Thomas Beale is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1947 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for James Thomas Beale 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 James Thomas Beale in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what James Thomas Beale 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 James Thomas Beale out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is James Thomas Beale in simple terms?

James Thomas (J. Thomas "Tom") Beale (born 1947) is an American mathematician, specializing in fluid dynamics, partial differential equations, and numerical analysis.

Why does James Thomas Beale 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 James Thomas Beale?

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 James Thomas Beale.