Mathematical Sciences: Uniform Asymptotic Approximations

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The principal investigator proposes to work on error analysis problems in the area of asymptotic approximations. These include exponential asymptotics, coalescing saddle-points in the method of steepest descent and for solutions of linear ordinary differential equations, and Airy function expansions. Asymptotic analysis is used in many branches of mathematics and hence in science. The questions being investigated may reveal details of scientific phenomena not apparent to the casual glance.