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18.305

Advanced Analytic Methods in Science and Engineering

3-0-9 units · Graduate

Covers expansion around singular points: the WKB method on ordinary and partial differential equations; the method of stationary phase and the saddle point method; the two-scale method and the method of renormalized perturbation; singular perturbation and boundary-layer techniques; WKB method on partial differential equations.

Fall 2004

Topics

  • The Differential Operator
  • Complex Analysis
  • First Order Partial Differential Equations
  • Second Order Partial Differential Equations
  • Separation of Variables
  • Singular Points of Ordinary Differential Equations
  • Regular Singular Points of Ordinary Differential Equations
  • Irregular Singular Points of Ordinary Differential Equations
  • The WKB Approximation
  • Turning Point
  • The Laplace Method
  • Method of Stationary Phase
  • Asymptotic Expansions of Integrals
  • Boundary Layers and Singular Perturbation
  • Interior Turning Points

Readings

  • Cheng, Hung. Advanced Analytic Methods in Continuum Mathematics: Fundamentals for Science and Engineering. Boston, MA: Luban Press, 2004. ISBN: 0975862502.
    Listed reading
  • Bender, C., and S. Orszag. Advanced Mathematical Methods for Scientists and Engineers . New York, NY: McGraw-Hill, 1978. Reprinted by Springer-Verlag, New York, 1998. ISBN: 0387989315.
    Listed reading
  • Mei, C. C. Mathematical Analysis in Engineering . Cambridge, England: Cambridge University Press, 1995. ISBN: 0521460530.
    Listed reading

Prerequisites & course information

Prereq: 18.04 , 18.075 , or 18.112 G (Fall) 3-0-9 units

Sources