James O. C. Ezeilo

James Okoye Chukuka Ezeilo (17 January 1930 – January 2013^[1]) was the first professor of mathematics in Nigeria. He was often regarded as the father of modern mathematics in the country^[2] and was the fifth vice chancellor of the University of Nigeria, Nsukka. He was Vice Chancellor of Bayero University Kano from 1977 to 1978. He was an alumnus of Cambridge University and died in 2013.^[3]

James O. C. Ezeilo
Born	(1930-01-17) January 17, 1930 (age 94) Nanka, Anambra State, Nigeria
Died	2013 Lagos, Nigeria
Academic background
Alma mater	University of Cambridge
Academic work
Discipline	Mathematics
Sub-discipline	Ordinary differential equations
Institutions	University College Ibadan University of Nigeria, Nsukka Bayero University, Kano

Ezeilo had been born in Nanka, a town in Anambra State.^[4]

Research

Ezeilo pioneered the use of Leray-Schauder degree type arguments to obtain existence results for periodic solutions of ordinary differential equations.^[5]

Third-order ODEs

In 1959, Ezeilo studied the stability of the third-order ODE ${\displaystyle {\overset {...}{x}}+f(x,{\dot {x}}){\ddot {x}}+g(x){\dot {x}}+h(x)=0}$ near the trivial solution ${\displaystyle x=0}$.^[6] Stability holds if ${\displaystyle f(x,y)\geq \delta _{0}}$ for some positive constant ${\displaystyle \delta _{0}}$, ${\displaystyle g(y)/y\geq \delta _{1}}$for some positive constant ${\displaystyle \delta _{1}}$, ${\displaystyle h(x)/x\geq \delta _{2}}$ for some positive constant ${\displaystyle \delta _{2}}$, and ${\displaystyle h'(x)\leq c}$ for some constant c where ${\displaystyle \delta _{0}\delta _{1}-c\geq 0}$, and ${\displaystyle y{\frac {\partial f}{\partial y}}}$ is always nonpositive.^[6] He also studied the existence of periodic solutions to the third-order ODE ${\displaystyle {\overset {...}{x}}+a{\ddot {x}}+b{\dot {x}}+h(x)=p(t)}$.^[7] In 1966, he, together with H. O. Tejumola, generalized this work even further to study vector equations of the form ${\displaystyle {\overset {...}{X}}+A{\ddot {X}}+B{\dot {X}}+H(X)=P(t,X,{\dot {X}},{\ddot {X}})}$.^[8]

Fourth and fifth order ODEs

In 1962, Ezeilo studied the stability of the fourth-order equation ${\displaystyle x^{(4)}+f({\ddot {x}}){\overset {...}{x}}+\alpha _{2}{\ddot {x}}+g({\dot {x}})+h(x)+\alpha _{4}x=p(t)}$.^[9] In 1978 he studied the fifth-order equations ${\displaystyle x^{(5)}+a_{1}x^{(4)}+a_{2}{\overset {...}{x}}+a_{3}{\ddot {x}}+a_{4}{\dot {x}}+f(x)=0}$ and the two generalizations ${\displaystyle x^{(5)}+a_{1}x^{(4)}+a_{2}{\overset {...}{x}}+h({\dot {x}}){\ddot {x}}+g(x){\dot {x}}+f(x)=0}$ and ${\displaystyle x^{(5)}+\psi ({\ddot {x}}){\overset {...}{x}}+\phi ({\ddot {x}})+\theta ({\dot {x}})+f(x)=0}$.^[10]

Honour

J.O.C. EZEILO TWIN THEATRE BAYERO UNIVERSITY KANO STATE OLD CAMPUS

One of the past vice chancellors of Bayero University Kano state, a Twin lecture theatre was named in his honour, J. O. C. Ezeilo Twin theatre which is located at Bayero University old campus opposite the department of Human physiology.^{[citation needed]}

Death

Ezeilo died in January 2013^[4][1] after a brief illness in Lagos.^[11]

References

1. "EBASI". ebasi.org. Retrieved 2024-09-23.
2. "James O. C. Ezeilo". Mathematicians of the African Diaspora. The Mathematics Department of The State University of New York at Buffalo. Retrieved 20 December 2017.
3. "Professor James O. C. Ezeilo". Edward Bouchet Abdus Salam Institute. Retrieved 20 December 2017.
   - "J.O.C. Ezeilo (1930–2013)". The Sun News (Nigeria). EBASI. Retrieved 20 December 2017.
4. "J.O.C. Ezeilo (1930-2013)". The Sun News. Retrieved 2023-08-15.
5. "James O. C. Ezeilo". Mathematicians of the African Diaspora. The Mathematics Department of The State University of New York at Buffalo. Retrieved 21 January 2018.
6. Ezeilo, J. O. C. (1960). "On the stability of solutions of certain differential equations of the third order" (PDF). The Quarterly Journal of Mathematics. 11 (1): 64–69.
7. Ezeilo, J. O. C. (November 1959). "On the existence of periodic solutions of a certain third-order differential equation". Mathematical Proceedings of the Cambridge Philosophical Society. 56 (4): 381–389. doi:10.1017/S0305004100034678. ISSN 1469-8064.
8. Ezeilo, J. O. C.; Tejumola, H. O. (December 1966). "Boundedness and periodicity of solutions of a certain system of third-order non-linear differential equations". Annali di Matematica Pura ed Applicata. 74 (1): 283–316. doi:10.1007/BF02416460. ISSN 0373-3114.
9. Ezeilo, James O. C. (1962). "On the boundedness and the stability of solutions of some differential equations of the fourth order". Journal of Mathematical Analysis and Applications. 5: 134–146.
10. Ezeilo, J. O. C. (September 1978). "Instability theorems for certain fifth-order differential equations". Mathematical Proceedings of the Cambridge Philosophical Society. 84 (2): 343–350. doi:10.1017/S030500410005516X. ISSN 0305-0041.
11. "Tribute to Professor J O C Ezeilo, CON". Maths History. Retrieved 2024-09-23.