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Professor

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(205) 934-2154
University Hall 4024

Research and Teaching Interests: Differential equations, inverse problems, number theory

Office Hours: By appointment

Education:

  • Ph.D., Flinders University, Mathematics.

I was born in Sydney, Australia, and for my Ph.D. studied differential equations with my advisor and mentor Douglas Sears. My advisor in turn studied at Oxford University in England under the great analyst E.C. Titchmarsh, who was known for his work in differential equations and on the Riemann zeta function in number theory. I have taught at Universities in South Africa, the UK, and Canada, in addition to my current position at UAB.

Research Interests

As a mathematical tool the differential equation is one of the most powerful devices that we mathematicians possess. It can be used to resolve difficult theoretical issues. Perhaps more importantly, from my perspective, when used in mathematical models the differential equation uniquely allows us to reliably predict future behaviour in systems, and more generally to probe the world around us. Examples that come to mind here include weather forecasting, ultrasound imaging, reflection seismology in oil exploration, and potentially (from our current work) reliable economic forecasting.

Recent Courses

  • MA 126, MA 227: Calculus
  • MA 252: Introduction to Differential Equations
  • MA 461: Partial Differential Equation Modeling
  • MA 755: Advanced Partial Differential Equations

Select Publications

  • Knowles, Ian; LaRussa, Mary A. Lavrentiev's theorem and error estimation in elliptic inverse problems. In B. M. Brown, J. Lang, I. G. Wood (Eds.) Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends, 91-104, Operator Theory: Advances and Applications, volume 219, Springer Birkhauser, 2012.
  • Knowles, Ian; LaRussa, Mary A. Conditional well-posedness for an elliptic inverse problem. SIAM J. Appl. Math. 71(2011), 952-71.
  • Knowles, Ian; Teubner, Michael; Yan, Aimin; Rasser, Paul; Lee, Jong Wook. Inverse groundwater modelling in the Willunga Basin, South Australia. Hydrogeology Journal 15 (2007), no. 6, 1107-118.
  • Knowles, Ian; Wallace, Robert. A variational method for numerical differentiation. Numer. Math. 70 (1995) no. 1, 91-110.
  • Knowles, Ian. Asymptotics of an ordinary differential equation and the Riemann hypothesis. J. Differential Equations, 83 (1990) no. 2, 207-19.

Academic Distinctions and Professional Societies

  • AMS
  • SIAM