MATH648M-HANDOUTS

Handout 1 Syllabus

Handout 2 Bibliography

Handout 3 Airys-Integral

Handout 4 Introduction

Handout 5 Asymptotics

Handout 6 Asymptotics-cont.

Handout 7 Asymptotics of integrals

Handout 8 Laplace method

Handout 9 Method of steepest descents

Handout 10 Stationary phase method

Handout 11 Matching asymptotic expansions

Handout 12 Boundary layer theory for ODEs

Handout 13 Boundary layer theory for ODEs

Handout 15 Boundary layer theory for ODEs

Handout 16 Boundary layer theory for ODES

Handout 17 Boundary layer theory for elliptic PDEs

Handout 18 Boundary layer theory for PDEs

Handout 19 Interior boundary layers

Handout 20(a) Two scale methods (part 1)

Handout 20(b) Two scale methods (part 2)

Handout 21 Renormalized two scale methods

Handout 22 Distributions

Handout 23 Introduction to Probability

Handout 24 Probability

Handout 25 Brownian Motion

Handout 26 Brownian Motion

Handout 27 Wiener Measure

Handout 28 Monte Carlo Method

Handout 29 Langevin Equation

Handout 29b Fokker Planck Equation

Handout 30 Summary-1

Handout 31 Summary-2

Handout 32 Asset Prices Model

Handout 33 Modeling

Handout 34 Black-Scholes Equation