mathematics

Philip Hartman

Philip Hartman 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 Philip Hartman rather than just read about it. In short: Philip Hartman (May 16, 1915 – August 28, 2015) was an American mathematician at Johns Hopkins University working on differential equations who introduced the Hartman–Grobman theorem. He served as Chairman of the Mathematics Department at Johns Hopkins for several years.

Key takeaways

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

Reference excerpt

Philip Hartman (May 16, 1915 – August 28, 2015) was an American mathematician at Johns Hopkins University working on differential equations who introduced the Hartman–Grobman theorem. He served as Chairman of the Mathematics Department at Johns Hopkins for several years. He has an Erdös number of 2. His book gives a necessary and sufficient condition for solutions of ordinary initial value problems to be unique and to depend on a class C1 manner on the initial conditions for solutions. He died in August 2015 at the age of 100. The Hartman–Watson distribution is named after him and Geoffrey S. Watson.

Publications Hartman, Philip (2002) [1964], Ordinary differential equations, Classics in Applied Mathematics, vol. 38, Philadelphia: Society for Industrial and Applied Mathematics, ISBN 978-0-89871-510-1, MR 1929104

References

External links Philip Hartman at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Philip Hartman

Start with the simplest possible case. Write down what Philip Hartman 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 Philip Hartman 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 Philip Hartman 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 Philip Hartman

In research: Philip Hartman 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 Philip Hartman 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: Philip Hartman is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1915 births, 2015 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Philip Hartman 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 Philip Hartman in 20 minutes

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

Frequently asked questions

What is Philip Hartman in simple terms?

Why does Philip Hartman 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 Philip Hartman?

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 Philip Hartman.