mathematics

Leopoldo Penna Franca

Leopoldo Penna Franca 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 Leopoldo Penna Franca rather than just read about it. In short: Leopoldo Penna Franca (April 7, 1959 – September 19, 2012, in Rio de Janeiro, Brazil) was a Brazilian-American mathematician. He received his PhD in 1987 from Stanford University in engineering under Thomas J.

Key takeaways

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

Reference excerpt

Leopoldo Penna Franca (April 7, 1959 – September 19, 2012, in Rio de Janeiro, Brazil) was a Brazilian-American mathematician. He received his PhD in 1987 from Stanford University in engineering under Thomas J. R. Hughes. After graduation, he worked at the pt:Laboratório Nacional de Computação Científica - LNCC in Brazil. From 1993 to 2011, he was a full professor and researcher of mathematics at the University of Colorado Denver. From 2008 to 2010, he was a visiting professor and researcher of mathematics at the Federal University of Rio de Janeiro - UFRJ / Coppe at the Civil Engineering Department in collaboration to Alvaro Coutinho. From 2011 until 2012, he worked for IBM Research Brazil. He was known for his work on stabilized finite element methods. He was a recipient of the United States Association for Computational Mechanics - USACM. Received in 1999 the Gallagher Young Investigator Award for "outstanding accomplishments in computational mechanics, particularly in the published literature, by a researcher 40 years old or younger". He was listed as an ISI Highly Cited Author in Engineering by the ISI Web of Knowledge, Thomson Scientific Company.

References

External links Leopoldo Penna Franca at the Mathematics Genealogy Project Leopoldo Penna Franca publications indexed by Google Scholar

Worked examples

Example 1 — a first encounter with Leopoldo Penna Franca

Start with the simplest possible case. Write down what Leopoldo Penna Franca 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 Leopoldo Penna Franca 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 Leopoldo Penna Franca 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 Leopoldo Penna Franca

In research: Leopoldo Penna Franca 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 Leopoldo Penna Franca 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: Leopoldo Penna Franca is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1959 births, 2012 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Leopoldo Penna Franca 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 Leopoldo Penna Franca in 20 minutes

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

Frequently asked questions

What is Leopoldo Penna Franca in simple terms?

Why does Leopoldo Penna Franca 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 Leopoldo Penna Franca?

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 Leopoldo Penna Franca.