mathematics

Richard Beals (mathematician)

Richard Beals (mathematician) 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 Richard Beals (mathematician) rather than just read about it. In short: Richard William Beals (28 May 1938, Erie, Pennsylvania) is an American mathematician who works on partial differential equations and functional analysis. He is known as the author or co-author of several mathematical textbooks.

Key takeaways

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

Reference excerpt

Richard William Beals (28 May 1938, Erie, Pennsylvania) is an American mathematician who works on partial differential equations and functional analysis. He is known as the author or co-author of several mathematical textbooks. Beals studied at Yale University earning a B.A. in 1960, an M.A. in 1962, and a Ph.D. in 1964 under Felix Browder with thesis Non-Local Boundary Value Problems for Elliptic Partial Differential Operators. In the academic year 1965/1966 he was a visiting assistant professor at the University of Chicago, where he became in 1966 an assistant professor and later a professor. In 1977 he became a professor at Yale University. Beals received the Quantrell Award. Beals works on inverse problems in scattering theory, integrable systems, pseudodifferential operators, complex analysis, global analysis and transport theory. He has been married since 1962 and has three children. He should not be confused with the mathematics professor at Rutgers University named R. Michael Beals (born in 1954), who is Richard Beals's brother.

Works Beals, Richard (2004). Analysis: an introduction. Cambridge, UK: Cambridge University Press. ISBN 978-0-511-64842-7. OCLC 667041380. Beals, Richard; Greiner, Peter (1988). Calculus on Heisenberg manifolds. Annals of Mathematics Studies. Vol. 119. Princeton, N.J.: Princeton University Press. doi:10.1515/9781400882397. ISBN 0-691-08500-5. MR 0953082. OCLC 17765652. Advanced mathematical analysis; periodic functions and distributions, complex analysis, Laplace transform and applications, Springer Verlag 1973; 2013 pbk edition with M. Salah Baouendi and Linda Preiss Rothschild (eds.) Microlocal Analysis, American Mathematical Society 1984 with Roderick Wong: Special functions: a graduate text, Cambridge University Press 2010 Beals, Richard; Wong, Roderick (2016). Special Functions and Orthogonal Polynomials. Cambridge: Cambridge University Press. doi:10.1017/cbo9781316227381. ISBN 978-1-316-22738-1. MR 3524801. (Revised with 4 new chapters.) Topics in Operator Theory, University of Chicago Press 1971 Beals, Richard; Deift, Percy; Tomei, Carlos (1988). Direct and inverse scattering on the line. Providence, R.I.: American Mathematical Society. doi:10.1090/surv/028. ISBN 0-8218-1530-X. MR 0954382. OCLC 17875951. 2015 pbk edition

References

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Worked examples

Example 1 — a first encounter with Richard Beals (mathematician)

Start with the simplest possible case. Write down what Richard Beals (mathematician) 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 Richard Beals (mathematician) 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 Richard Beals (mathematician) 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 Richard Beals (mathematician)

In research: Richard Beals (mathematician) 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 Richard Beals (mathematician) 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: Richard Beals (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1938 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard Beals (mathematician) 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 Richard Beals (mathematician) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Richard Beals (mathematician) 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 Richard Beals (mathematician) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Richard Beals (mathematician) in simple terms?

Why does Richard Beals (mathematician) 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 Richard Beals (mathematician)?

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 Richard Beals (mathematician).