AM9511b: Asymptotics and Special Functions

Voting for course meeting times

Notes

• 1.4.2010 Painleve Transcendents
• 8.3.2010 Asymptotic Expansion of integrals
• 1.3.2010 Hypergeometric functions
• 25.02.2010 the Gamma Function
• 22.02.2010 Jacobian Elliptic Functions
• 8.02.2010 The Method of Dominant Balance
• 28.01.2010 Asymptotics and asymres.mw
• 25.01.2010 Computability of ln z
• 21.01.2010 More on the logarithm and The Paradox of Bernoulli & Leibniz. Maple worksheet tiny.mw
• 13.01.2010 Introduction. Also, Complex numbers from my Calculus class.
• 13.01.2010 My algebraic proof ln(z) is not an algebraic function

Maple worksheets

• 1.4.2010 Painleve
• 8.3.2010 Airy
• 4.3.2010 chebyshev
• 1.3.2010 hypergeom
• Newton341
• Frobenius and Taylor series (3.2 and 3.3)
• seriesflavours.mw (Right click and save)
• Riemann.mw (Right click and save)
• ghost.mw

References

• E-BOOKS at UWO:
  1. Symbolic Integration I [electronic resource] : Transcendental Functions / by Manuel Bronstein.
  2. Differential equations: linear, nonlinear, ordinary, partial/A.C. King, J. Billingham, and S.R. Otto (search under e-books with keyword "asymptotic"). Chapter 11 and Chapter 12 are relevant to our needs. try this link from on-campus
• D.J. Jeffrey, Branching out with inverse functions
• R.M. Corless, J.H. Davenport, D.J. Jeffrey, S.M. Watt: According to Abramowitz and Stegun, SIGSAM Bulletin, Vol 34 (2), pp 58--65. PDF version.
• R.M. Corless, D.J. Jeffrey: Graphing elementary Riemann surfaces. SIGSAM Bulletin, Vol 32(1), issue 123, pp11-17 (1998). PDF version.
• Introduction to the Table-Maker's Dilemma and their computation of the worst-case bounds.