Professor Theodore A . Burton

T. A. Burton (denoted by T. A. throughout this paper) was born on September 7, 1935 on a farm in Kansas, the fifth child of seven in the family. It was a peak of the Great Depression and when the dust storms wrecked havoc on the Mid-Western United States. Entire buildings were buried in the dust. The economy was so poor that farmers turned their livestock loose and left the area. At the age of five, T. A. and his family moved to Idaho, then to California, and finally to the Cascade Mountains of the state of Washington where he completed an elementary and high school. On the day he graduated from high school he was drafted into the army for two years, emerging with veteran’s rights to a college education. In 1959 he graduated from the Washington State College with a Bachelor of Science with Honors. His record earned him a full fellowship for three years of study toward a Ph.D. in mathematics. On August 5, 1961 he married the love of his life, Fredda Jean Anderson. His graduate work began in 1959 under the direction of the late Donald W. Bushaw. Bushaw was a student of Solomon Lefschetz and his dissertation concerned the first paper on optimal control. But Lefschetz was also deeply interested in differential equations of various Liénard types and Bushaw inherited that interest, assigning to T. A. a problem on global stability of a nonlinear oscillator. There was much literature on the problem and its generalizations. Lefschetz gathered a number of outstanding foreign and American researchers to study the problem, whose most important aspects were well-defined. The problem was old, going back to Lagrange, and it is taught to every student in a basic course on differential equations. We consider a number of physical problems, such as a spring-mass-dashpot system, and use Newton’s second law of motion under numerous assumptions to obtain the equation of motion x′′ + ax′ + bx = 0