James O. C. Ezeilo Explained

Birth Date:17 January 1930
Birth Place:Nanka, Anambra State, Nigeria
Death Date:2013
Death Place:Lagos, Nigeria
Discipline:Mathematics
Sub Discipline:Ordinary differential equations
Alma Mater:University of Cambridge
Workplaces:University College Ibadan
University of Nigeria, Nsukka
Bayero University, Kano

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]

Ezeilo had been born in Nanka, a town in Anambra State.

Research

Ezeilo pioneered the use of Leray-Schauder degree type arguments to obtain existence results for periodic solutions of ordinary differential equations.[4]

Third-order ODEs

In 1959, Ezeilo studied the stability of the third-order ODE

\overset{...}{x}+f(x,

x

)\ddot{x}+g(x)

x

+h(x)=0

near the trivial solution

x=0

.[5] Stability holds if

f(x,y)\geq\delta0

for some positive constant

\delta0

,

g(y)/y\geq\delta1

for some positive constant

\delta1

,

h(x)/x\geq\delta2

for some positive constant

\delta2

, and

h'(x)\leqc

for some constant c where

\delta0\delta1-c\geq0

, and
y\partialf
\partialy
is always nonpositive. He also studied the existence of periodic solutions to the third-order ODE

\overset{...}{x}+a\ddot{x}+b

x

+h(x)=p(t)

.[6] In 1966, he, together with H. O. Tejumola, generalized this work even further to study vector equations of the form

\overset{...}{X}+A\ddot{X}+B

X

+H(X)=P(t,X,

X

,\ddot{X})

.[7]

Fourth and fifth order ODEs

In 1962, Ezeilo studied the stability of the fourth-order equation

x(4)+f(\ddot{x})\overset{...}{x}+\alpha2\ddot{x}+g(

x

)+h(x)+\alpha4x=p(t)

.[8] In 1978 he studied the fifth-order equations

x(5)+a1x(4)+a2\overset{...}{x}+a3\ddot{x}+

a
4x

+f(x)=0

and the two generalizations

x(5)+

(4)
a
1x

+a2\overset{...}{x}+h(

x

)\ddot{x}+g(x)

x

+f(x)=0

and

x(5)+\psi(\ddot{x})\overset{...}{x}+\phi(\ddot{x})+\theta(

x

)+f(x)=0

.[9]

Honour

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.

Death

Ezeilo died in January 2013[10] after a brief illness in Lagos.[11]

References

  1. Web site: EBASI . 2024-09-23 . ebasi.org.
  2. Web site: James O. C. Ezeilo . The Mathematics Department of The State University of New York at Buffalo. Mathematicians of the African Diaspora. 20 December 2017.
  3. Web site: Professor James O. C. Ezeilo . . 20 December 2017.
    - Web site: J.O.C. Ezeilo (1930–2013). EBASI. The Sun News (Nigeria). 20 December 2017.
  4. Web site: James O. C. Ezeilo . The Mathematics Department of The State University of New York at Buffalo. Mathematicians of the African Diaspora. 21 January 2018.
  5. Ezeilo . J. O. C. . 1960 . On the stability of solutions of certain differential equations of the third order . The Quarterly Journal of Mathematics . 11 . 1 . 64–69.
  6. 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 . en . 56 . 4 . 381–389 . 10.1017/S0305004100034678 . 1469-8064.
  7. 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 . en . 74 . 1 . 283–316 . 10.1007/BF02416460 . 0373-3114.
  8. Ezeilo . James O. C. . 1962 . On the boundedness and the stability of solutions of some differential equations of the fourth order . . 5 . 134-146.
  9. Ezeilo . J. O. C. . September 1978 . Instability theorems for certain fifth-order differential equations . Mathematical Proceedings of the Cambridge Philosophical Society . en . 84 . 2 . 343–350 . 10.1017/S030500410005516X . 0305-0041.
  10. Web site: J.O.C. Ezeilo (1930-2013) . 2023-08-15 . The Sun News . en-US.
  11. Web site: Tribute to Professor J O C Ezeilo, CON . 2024-09-23 . Maths History . en.