mathematics

James Keener

James Keener 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 Keener rather than just read about it. In short: James "Jim" Paul Keener is an American mathematician, currently Distinguished Professor at University of Utah. He is recognized as a pioneer in the field of mathematical physiology and cardiology.

Key takeaways

James Keener 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 Keener to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of James Keener from memory before moving on to harder problems.

Reference excerpt

James "Jim" Paul Keener is an American mathematician, currently Distinguished Professor at University of Utah. He is recognized as a pioneer in the field of mathematical physiology and cardiology.

Biography Jim Keener received his PhD from the California Institute of Technology in 1972. Initially intending to work on bifurcation theory, he came across a paper by Otto Rossler that implied that heartbeat can be modeled using chaos theory. Looking to investigate this claim, he picked up the Textbook of Medical Physiology by Arthur Guyton to build some foundational knowledge in cardiology and discovered examples of dynamical systems that had previously been untouched by the applied mathematics community. He was invited to join the faculty at the University of Utah in 1978 by Frank Hoppensteadt to start a new group in mathematical biology. He served as editor-in-chief of the SIAM Journal on Applied Mathematics and was named a SIAM Fellow in 2012.

Publications Keener, J.P. (1999). Principles of Applied Mathematics: Transformation and Approximation (2nd ed.). Perseus Books. ISBN 0-7382-0129-4. Keener, J.P.; Sneyd, J. (2008). Mathematical Physiology (2nd ed.). Springer.

References

Worked examples

Example 1 — a first encounter with James Keener

Start with the simplest possible case. Write down what James Keener 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 Keener 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 Keener 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 Keener

In research: James Keener 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 Keener 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 Keener is common in secondary-school and first-year university syllabi. It links to neighbouring topics 21st-century American mathematicians, American applied mathematicians, American mathematician stubs, so understanding it makes those chapters shorter.
In everyday life: Look for James Keener 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “James Keener” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study James Keener in 20 minutes

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

Frequently asked questions

What is James Keener in simple terms?

James "Jim" Paul Keener is an American mathematician, currently Distinguished Professor at University of Utah. He is recognized as a pioneer in the field of mathematical physiology and cardiology.

Why does James Keener 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 Keener?

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 Keener.