Publications & Presentations

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v     Research papers

·        Leigh C. Becker

                    Uniformly Continuous L1 Solutions of Volterra Equations and Global Asymptotic Stability

                    CUBO, A Mathematical Journal  11, No. 3 (August 2009), pp. 1–24.

                    This paper appears in the special issue: Qualitative Properties of Functional Equations. 

                    The series of papers in this issue begins with a preface and overview by T.A. Burton (guest editor).

                    To download this entire issue (free), go to http://www.dmat.ufpe.br/CUBO/pg/download.html.

·        Leigh C. Becker

                    Function bounds for solutions of Volterra equations and exponential asymptotic stability

                    Nonlinear Analysis: Theory, Methods & Applications 67, No. 2 (July 2007), pp. 382–397.

                          Digital Object Identifier Information:  doi:10.1016/j.na.2006.05.016

                    Abstract  (PDF format)     Abstract (DVI format)     Abstract (Science Direct [www.sciencedirect.com])

·        Leigh C. Becker

                    Principal matrix solutions and variation of parameters for a Volterra integro-differential equation and its adjoint

                    Electronic Journal of Qualitative Theory of Differential Equations, No. 14 (2006), pp. 1–22.

                    To download the paper in PDF format, click here. 

                    To download the paper in DVI or PostScript format, click here.

                    Note: A version of the paper can also be found on pp. 34–51 in the monograph Liapunov Functionals for Integral Equations

                    by T. A. Burton, Trafford Publishing (2008).  To view this version on the web, click here.

·        Leigh C. Becker and T. A. Burton

                    Stability, fixed points and inverses of delays

                    Proceedings of the Royal Society of Edinburgh, 136A, No. 2 (May 2006), pp. 245–275.

                    Abstract  (PDF format)     Abstract (DVI format)     Abstract (IngentaConnect [www.ingentaconnect.com])

·        Leigh C. Becker and T. A. Burton

                    Jensen’s Inequality and Liapunov’s Direct Method  

                    CUBO, A Mathematical Journal  6, No. 3 (October 2004), pp. 67–90.

                    Abstract  (PDF format)     Abstract (DVI format)     Abstract  (PostScript format)     Abstract (MS Word)

                    Download preprint (PDF format)

                    Photos of authors:

                    L. C. Becker & T. A. Burton at the AMS Meeting in Portland, Oregon June 20-22, 2002

                    Becker at the Oregon coast June 23, 2002

·        L. C. Becker, T. A. Burton, and S. Zhang

                    Functional differential equations and Jensen's inequality

                    Journal of Math­emat­ical Anal­ysis and Applications 138, No. 1 (1989), Academic Press, Orlando, pp. 137–156.

                    Download preprint (pdf format)      Download preprint (dvi format)   

·        L. C. Becker and T. A. Burton

                     Asymptotic stability criteria for delay-differential equations

                     Proceedings of the Royal Society of Edinburgh  110A (1988), pp. 31–44.

·        L. C. Becker, T. A. Burton, and T. Krisztin

                     Floquet Theory for a Volterra equation

                     Journal of the London Mathematical Society (2) 37 (1988), pp. 141–147.

·        L. C. Becker, T. A. Burton, and S. Zhang

                     Functional differential equations and Jensen's Inequality

                     Dynamics of Infinite Dimensional Systems (Hale, J. K. and Chow, S. N., eds.)

                     NATO ASI Series, Vol. F37 (1987), Springer-Verlag, New York, pp. 31–38.

 

v     Other publications

·        Leigh C. Becker

                     Constant Delay Differential Equations and the Method of Steps

                     Maple Application Center  (June 8, 2009).

                     (To view the HTML version or to download the Maple worksheet, click on the above hyperlink.)

·        Leigh C. Becker

                     Scalar Volterra Integro-Differential Equations

                     Maple Application Center  (August 2007).

                     (To view the HTML version or to download the Maple worksheet, click on the above hyperlink.)

·        Leigh C. Becker and Micah Wheeler

                     Numerical and Graphical Solutions of Volterra Integral Equations of the Second Kind

                     Maple Application Center  (June 2005).

                     (To view the HTML version or to download the Maple worksheet, click on the above hyperlink.)

·        L. C. Becker

                     Review of Functional differential equations and Jensen's Inequality in Zentralblatt für Mathematik (1988).

·        Leigh C. Becker

                     Setting the Stage with APR Problems

                     Mathematics and Computer Education  (1984, Fall), 18(3), pp. 189–195.

                     Included in the University of South Florida Center for Teaching Enhancement’s Critical & Creative Thinking Skills Mathematics Bibliography. 

 

v     Dissertation

·        Leigh C. Becker

                     Stability Considerations for Volterra Integrodifferential Equations 

                     Ph.D. dissertation, Southern Illinois University at Carbondale, Dissertation Research Award 1979, Advisor: T. A. Burton.

                     Download  dissertation (pdf format)

                     Note: Revised and more concise versions of the part of the dissertation dealing with the principal matrix solution (aka the resolvent)
can also be found in

                     (1)  the paper “Principal matrix solutions and variation of parameters for a Volterra integro-differential equation and its adjoint”,

                           Electronic Journal of Qualitative Theory of Differential Equations, No. 14 (2006), pp. 1–22

                     and

                     (2)  the monograph Liapunov Functionals for Integral Equations by T. A. Burton, Trafford Publishing (2008), pp. 34–51.

                           To view it on the web, click here.

 

v     Acknowledgements of solutions of problems 

·        Problem 82-19:  A binomial coefficient summation, SIAM Review  25 (1983), p. 576.

·        Problem 184:  TYCMJ (now the College Mathematics Journal) 13, No. 3 (1982), p. 211.

·        Problem 194:  TYCMJ (now the College Mathematics Journal) 13, No. 5 (1982), p. 341.

 

v     Unpublished

o       Textbook with ancillaries

·        Leigh C. Becker

                     Ordinary Differential Equations: Concepts, Methods, and Models

                     CBU Press, 2009–2010 edition, 487 pages (work in progress)

·        Leigh C. Becker

                     Complete Solutions of Selected Problems for Ordinary Differential Equations: Concepts, Methods, and Models

                     Web site: www.cbu.edu/~lbecker/231Ans.htm

·        Leigh C. Becker

                     Maple worksheets for Ordinary Differential Equations: Concepts, Methods, and Models

                     Web site:  www.cbu.edu/~lbecker/Maple/M231/231maple.htm

 

o       Miscellanea

·        L. C. Becker

                     ODE Experiments Using Maple, CBU Press, 1998.

·        L. C. Becker

                     The function y = (1 + 1/x)x and the number e,  (Lab 4 in Laboratory Manual for Calculus II)

                     Christian Brothers University (1991), 29-39.

 

v     Presentations

·        November 7, 2009 – Differential Equations Weekend Conference hosted by the University of Memphis.  Gave a talk entitled Uniformly continuous and asymptotically stable solutions of Volterra integro-differential equations.

·        July 4, 2008 – WCNA 2008 in Orlando, Florida (Fifth World Congress of Nonlinear Analysts, July 2–July 9).  Presented a 45-minute invited lecture entitled “Uniformly continuous L1 solutions of Volterra equations and global asymptotic stability” in the session “Qualitative Properties and Application of Functional Equations” and chaired part of this session. 

                    Photos:

                    Speakers at the “Qualitative Properties & Application of Functional Equations” session (July 4 & 5, 2008):

                    Muhammad Islam, Min He, Alphonso Casal, Colleen Kirk, T. A. Burton, Tetsuo Furumochi, Leigh C. Becker, Bo Zhang, Youssef Raffoul, Liancheng Wang, & Henri Schurz (not shown).

                    Lynne Marie Becker at the Hyatt Grand Cypress Resort Pool in Orlando (July 7, 2008).

·        March 16, 2007 – “Asymptotic Stability for Scalar Linear Volterra Integro-Differential Equations,” Mathematical Association of America Southeastern Section 86th Annual Meeting, Georgia Southern University, Statesboro, GA.

·        January 5-8, 2005 – Joint Mathematics Meetings in Atlanta, Georgia.  Co-chaired the American Mathematical Society Session on Ordinary Differential Equations (Jan. 7).  Presented a paper (coauthor T.A. Burton, Northwest Research Institute) entitled "Fixed Points and Stability of a Volterra Equation with Variable Delay."

·        July 1, 2004 – WCNA 2004 in Orlando, Florida (Fourth World Congress of Nonlinear Analysts, June 30–July 7).  Presented a 45-minute invited lecture entitled “Stability, Fixed Points, and Inverses of Delays” in the session “Application of Fixed Point Theory to Functional Equations” and chaired part of this session. 

·        March 26, 2004 – “Fixed Points and Stability of an Equation with Variable Delay” (with T. A. Burton), Mathematical Association of America Southeastern Section meeting, Austin Peay State University, Clarksville, TN.

·        June 21, 2002 – “Jensen’s Inequality and Liapunov’s Direct Method,” Special Session on Qualitative Properties and Applications of Functional Equations, American Mathematical Society Meeting in Portland, Oregon.

·        November 6, 2001 – “Mathematical Scientists & What They Do,” Mu Alpha Theta Induction Ceremony 2001 at Ridgeway High School.

·        October 21, 2000 – At the request of Institutional Advancement, talked at Sacred Heart Catholic Church in Memphis about CBU.

·        September 25, 1997 – “Maple in CBU Mathematics Courses,” CBU President’s Circle.

·        August 22, 1996 – presented a demonstration of a Maple lesson entitled “Integral Curves and Contours of Exact Equations”, CBU President’s Workshop.

·        February 9, 1996 – talk to the CBU student chapter of the MAA entitled “She loves me, she loves me not” (linear system of ordinary differential equations).

·        August 30, 1990 ─ "Simulating and Stimulating with Baseball Cards," Mathematics & Computer In-Service, Ridgeway High School, Memphis.

·        November 10-11, 1989 ─ “Asymptotic Stability Criteria for Delay-Differential Equations,” 18th Midwest Differential Equations Conference, Southern Illinois University at Carbondale.

·        August 1988 ─ conducted two days of a four-day workshop for Memphis high school mathematics teachers on elementary differential equations in the BC calculus curriculum.  Participants were shown how to use the HP-28S calculator when solving and graphing ordinary differential equations.

·        December 2, 1987 ─ “Floquet Theory for Volterra Equations II”, Differential Equations Seminar, Memphis State University.

·        November 25, 1987 ─ “Floquet Theory for Volterra Equations I”, Differential Equations Seminar, Memphis State University.

·        October 23-24, 1987 ─ co-author of “Floquet Theory for Volterra Equations”, Midwest-Southeast Differential Equations Conference, Vanderbilt University, Nashville, TN.

·        1983 – consulting work on a mathematical model of a shutter for a certain type of camera for DeZign Corporation.

·        May 13, 1982 – “A Variation of Parameters Formula for Volterra Integral Equations”, Mathematical Sciences Colloquium, Memphis State University.

·        April, 1982 – “Setting the Stage with APR Problems”, regional Mathematical Association of America meeting at Emory University in Atlanta, Georgia.

·        January 25, 1979 – “Some Results for Volterra Integrodifferential Equations”, American Mathematical Society Session on Ordinary Differential Equations, Biloxi, Mississippi.

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