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| + | ====== Exponential asymptotics for the physical sciences ====== | ||
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| + | This will be a course page for the Autumn 2024 [[https:// | ||
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| + | ==== Outline ==== | ||
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| + | There are many interesting situations where exponentially-small phenomena, beyond-all-orders of regular perturbative expansions, dictate crucially important features of a physical problem. For example, such exponential asymptotics may govern the appearance of surface ripples in water. Or they may dictate the non-existence of solutions to a differential equation. This course will introduce you to a fascinating array of such problems arising in the physical sciences. It will be accessible to a wide range of students from different mathematical backgrounds; | ||
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| + | ==== Key details ==== | ||
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| + | All meetings are online and commence 7 October and run for 8 weeks. | ||
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| + | Meeting times: | ||
| + | * Mondays 3-4pm | ||
| + | * Wednesdays 3-4pm | ||
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| + | Please feel free to email me at [[mailto: | ||
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| + | ==== Tentative list of topics ==== | ||
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| + | - An introduction to the history of exponential asymptotics; | ||
| + | - Review of essential techniques in asymptotic analysis | ||
| + | - The exponential integral and complementary error function | ||
| + | - The Airy equation: from steepest descents to the Borel plane | ||
| + | - The Pearcey equation and the higher-order Stokes phenomenon I | ||
| + | - The Pearcey equation and the higher-order Stokes phenomenon II | ||
| + | - On the universality of exponential asymptotics; | ||
| + | - Linear eigenvalue problems and the quantum harmonic oscillator | ||
| + | - Water waves at low speeds I | ||
| + | - Water waves at low speeds II | ||
| + | - Viscous fingering I | ||
| + | - Viscous fingering II | ||
| + | - PDEs I | ||
| + | - PDEs II | ||