mathematics

Michael E. Taylor

Michael E. Taylor 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 Michael E. Taylor rather than just read about it. In short: Michael Eugene Taylor (born 1946) is an American mathematician working in partial differential equations. Biography Taylor obtained his bachelor's degree from Princeton University in 1967, and completed his Ph.D. under the supervision of Heinz Otto Cordes at the University of California, Berkeley (Hypoelliptic Differential Equations).

Key takeaways

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

Reference excerpt

Michael Eugene Taylor (born 1946) is an American mathematician working in partial differential equations.

Biography Taylor obtained his bachelor's degree from Princeton University in 1967, and completed his Ph.D. under the supervision of Heinz Otto Cordes at the University of California, Berkeley (Hypoelliptic Differential Equations). He held a professorship at the State University of New York at Stony Brook and is now the William R. Kenan Professor of Mathematics at the University of North Carolina at Chapel Hill. In 1986 he was awarded the Lester Randolph Ford Award. For 2026 he was awarded the Leroy P. Steele Prize for Mathematical Exposition. He is a member of the American Academy of Arts and Sciences. In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto (Microlocal analysis in spectral and scattering theory and index theory). He is a fellow of the American Mathematical Society. He is married to mathematician Jane M. Hawkins.

Notable publications Books.

Michael E. Taylor. Pseudodifferential operators. Princeton Mathematical Series, 34. Princeton University Press, Princeton, N.J., 1981. xi+452 pp. ISBN 0-691-08282-0 Michael E. Taylor. Noncommutative harmonic analysis. Mathematical Surveys and Monographs, 22. American Mathematical Society, Providence, RI, 1986. xvi+328 pp. ISBN 0-8218-1523-7 Michael E. Taylor. Pseudodifferential operators and nonlinear PDE. Progress in Mathematics, 100. Birkhäuser Boston, Inc., Boston, MA, 1991. 213 pp. ISBN 0-8176-3595-5 Michael E. Taylor. Tools for PDE. Pseudodifferential operators, paradifferential operators, and layer potentials. Mathematical Surveys and Monographs, 81. American Mathematical Society, Providence, RI, 2000. x+257 pp. ISBN 0-8218-2633-6 Michael E. Taylor. Measure theory and integration. Graduate Studies in Mathematics, 76. American Mathematical Society, Providence, RI, 2006. xiv+319 pp. ISBN 978-0-8218-4180-8, 0-8218-4180-7 Michael E. Taylor. Introduction to differential equations. Pure and Applied Undergraduate Texts, 14. American Mathematical Society, Providence, RI, 2011. 409 pp. ISBN 978-0-8218-5271-2 2nd edition. ISBN 978-1-4704-6762-3. Michael E. Taylor. Partial differential equations I. Basic theory. Second edition. Applied Mathematical Sciences, 115. Springer, New York, 2011. xxii+654 pp. ISBN 978-1-4419-7054-1 Michael E. Taylor. Partial differential equations II. Qualitative studies of linear equations. Second edition. Applied Mathematical Sciences, 116. Springer, New York, 2011. xxii+614 pp. ISBN 978-1-4419-7051-0 Michael E. Taylor. Partial differential equations III. Nonlinear equations. Second edition. Applied Mathematical Sciences, 117. Springer, New York, 2011. xxii+715 pp. ISBN 978-1-4419-7048-0 Dorina Mitrea, Irina Mitrea, Marius Mitrea, and Michael Taylor. The Hodge-Laplacian. Boundary value problems on Riemannian manifolds. De Gruyter Studies in Mathematics, 64. De Gruyter, Berlin, 2016. ix+516 pp. ISBN 978-3-11-048266-9, 978-3-11-048438-0, 978-3-11-048339-0 Michael E. Taylor. Introduction to complex analysis. Graduate Studies in Mathematics, 202. American Mathematical Society, Providence, RI, 2019. xiv+480 pp. ISBN 978-1-4704-5286-5 Articles.

Jeffrey Rauch and Michael Taylor. Exponential decay of solutions to hyperbolic equations in bounded domains. Indiana Univ. Math. J. 24 (1974), 79–86. doi:10.1512/iumj.1975.24.24004 Jeff Cheeger, Mikhail Gromov, and Michael Taylor. Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differential Geom. 17 (1982), no. 1, 15–53. doi:10.4310/jdg/1214436699 Dorina Mitrea, Marius Mitrea, and Michael Taylor. Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds. Mem. Amer. Math. Soc. 150 (2001), no. 713, x+120 pp. doi:10.1090/memo/0713

References

External links Homepage

Worked examples

Example 1 — a first encounter with Michael E. Taylor

Start with the simplest possible case. Write down what Michael E. Taylor 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 Michael E. Taylor 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 Michael E. Taylor 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 Michael E. Taylor

In research: Michael E. Taylor 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 Michael E. Taylor 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: Michael E. Taylor is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1946 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Michael E. Taylor 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 “Michael E. Taylor” →

Affiliate

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

How to study Michael E. Taylor in 20 minutes

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

Frequently asked questions

What is Michael E. Taylor in simple terms?

Michael Eugene Taylor (born 1946) is an American mathematician working in partial differential equations. Biography Taylor obtained his bachelor's degree from Princeton University in 1967, and completed his Ph.D. under the supervision of Heinz Otto Cordes at the University of California, Berkeley (…

Why does Michael E. Taylor 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 Michael E. Taylor?

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 Michael E. Taylor.