View source for James O. C. Ezeilo

{{short description|Nigerian mathematician}}{{Infobox academic
| birth_date = {{birth date|1930|1|17}}
| birth_place = [[Nanka]], Anambra State, Nigeria
| death_date = {{death date and age|2013|||1934|1|17}}
| death_place = [[Lagos]], Nigeria
| discipline = Mathematics
| sub_discipline = [[Ordinary differential equations]]
| alma_mater = [[University of Cambridge]]
| workplaces = [[University College Ibadan]]<br>
[[University of Nigeria, Nsukka]]<br>
[[Bayero University, Kano]]
}}

'''James Okoye Chukuka Ezeilo''' (17 January 1930 – January 2013<ref name=":1">{{Cite web |title=EBASI |url=https://ebasi.org/JEzeilo.html |access-date=2024-09-23 |website=ebasi.org}}</ref>) was the first professor of mathematics in Nigeria. He was often regarded as the father of modern mathematics in the country<ref>{{Cite web|url=http://www.math.buffalo.edu/mad/PEEPS/ezeilo_james.html|title=James O. C. Ezeilo |publisher=The Mathematics Department of [[The State University of New York at Buffalo]]|website=Mathematicians of the African Diaspora|access-date=20 December 2017}}</ref> 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.<ref>{{Cite web|url=http://ebasi.org/JEzeilo.html|title=Professor James O. C. Ezeilo |website=[[Edward Bouchet Abdus Salam Institute]] |access-date=20 December 2017}}<br>- {{Cite web|url=http://ebasi.org/Ezeilo_20130507190036/index.html|title=J.O.C. Ezeilo (1930–2013)|publisher=EBASI|work=[[The Sun News (Nigeria)]]|access-date=20 December 2017}}</ref>

Ezeilo was born in [[Nanka]], a town in [[Anambra State]].<ref name=":2" />

== Research ==
Ezeilo pioneered the use of Leray-Schauder degree type arguments to obtain existence results for periodic solutions of [[ordinary differential equations]].<ref>{{Cite web|url=http://www.math.buffalo.edu/mad/PEEPS/ezeilo_james.html|title=James O. C. Ezeilo |publisher=The Mathematics Department of [[The State University of New York at Buffalo]]|website=Mathematicians of the African Diaspora|access-date=21 January 2018}}</ref>

=== Third-order ODEs ===
In 1959, Ezeilo studied the stability of the third-order ODE <math>\overset{...}{x} + f(x, \dot{x})\ddot{x} + g(x)\dot{x} + h(x) = 0</math> near the trivial solution <math>x = 0</math>.<ref name=":0">{{Cite journal |last=Ezeilo |first=J. O. C. |date=1960 |title=On the stability of solutions of certain differential equations of the third order |journal=The Quarterly Journal of Mathematics |volume=11 |issue=1 |pages=64–69|doi=10.1093/qmath/11.1.64 }}</ref> Stability holds if <math>f(x, y)\geq\delta_0</math> for some positive constant <math>\delta_0</math>, <math>g(y)/y\geq\delta_1</math>for some positive constant <math>\delta_1</math>, <math>h(x)/x\geq\delta_2</math> for some positive constant <math>\delta_2</math>, and <math>h'(x)\leq c</math> for some constant ''c'' where <math>\delta_0\delta_1 - c\geq 0</math>, and <math>y\frac{\partial f}{\partial y}</math> is always nonpositive.<ref name=":0" /> He also studied the existence of periodic solutions to the third-order ODE <math>\overset{...}{x} + a\ddot{x} + b\dot{x} + h(x) = p(t)</math>.<ref>{{Cite journal |last=Ezeilo |first=J. O. C. |date=November 1959 |title=On the existence of periodic solutions of a certain third-order differential equation |url=https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/abs/on-the-existence-of-periodic-solutions-of-a-certain-thirdorder-differential-equation/4F2A6F0A0C2A6C20C48BDC3324C6218F |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |language=en |volume=56 |issue=4 |pages=381–389 |doi=10.1017/S0305004100034678 |issn=1469-8064}}</ref> In 1966, he, together with [[H. O. Tejumola]], generalized this work even further to study vector equations of the form <math>\overset{...}{X} + A\ddot{X} + B\dot{X} + H(X) = P(t, X, \dot{X}, \ddot{X})</math>.<ref>{{Cite journal |last1=Ezeilo |first1=J. O. C. |last2=Tejumola |first2=H. O. |date=December 1966 |title=Boundedness and periodicity of solutions of a certain system of third-order non-linear differential equations |url=http://link.springer.com/10.1007/BF02416460 |journal=Annali di Matematica Pura ed Applicata |language=en |volume=74 |issue=1 |pages=283–316 |doi=10.1007/BF02416460 |issn=0373-3114}}</ref>

=== Fourth and fifth order ODEs ===
In 1962, Ezeilo studied the stability of the fourth-order equation <math>x^{(4)} + f(\ddot{x})\overset{...}{x} + \alpha_2\ddot{x} + g(\dot{x}) + h(x) + \alpha_4 x = p(t)</math>.<ref>{{Cite journal |last=Ezeilo |first=James O. C. |date=1962 |title=On the boundedness and the stability of solutions of some differential equations of the fourth order |journal=[[Journal of Mathematical Analysis and Applications]] |volume=5 |pages=134–146|doi=10.1016/0022-247X(62)90009-4 }}</ref> In 1978 he studied the fifth-order equations <math>x^{(5)} + a_1 x^{(4)} + a_2\overset{...}{x} + a_3\ddot{x} + a_4\dot{x} + f(x) = 0</math> and the two generalizations <math>x^{(5)} + a_1x^{(4)} + a_2\overset{...}{x} + h(\dot{x})\ddot{x} + g(x)\dot{x} + f(x) = 0 </math> and <math>x^{(5)} + \psi(\ddot{x})\overset{...}{x} + \phi(\ddot{x}) + \theta(\dot{x}) + f(x) = 0 </math>.<ref>{{Cite journal |last=Ezeilo |first=J. O. C. |date=September 1978 |title=Instability theorems for certain fifth-order differential equations |url=https://www.cambridge.org/core/product/identifier/S030500410005516X/type/journal_article |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |language=en |volume=84 |issue=2 |pages=343–350 |doi=10.1017/S030500410005516X |bibcode=1978MPCPS..84..343E |issn=0305-0041}}</ref>

== Honour ==
[[File:JOC EZEILO TWIN THEATRE BAYERO UNIVERSITY OLD CAMPUS KANO STATE.jpg|thumb|J. O. C. Ezeilo twin theatre on the old campus at [[Bayero University Kano]] ]]
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.{{cn|date=August 2023}}

== Death ==
Ezeilo died in January 2013<ref name=":2">{{Cite web |title=J.O.C. Ezeilo (1930-2013) |url=https://ebasi.org/Ezeilo_20130507190036/index.html |access-date=2023-08-15 |website=The Sun News |language=en-US}}</ref><ref name=":1" /> after a brief illness in [[Lagos]].<ref>{{Cite web |title=Tribute to Professor J O C Ezeilo, CON |url=https://mathshistory.st-andrews.ac.uk/Extras/Ezeilo_tribute/ |access-date=2024-09-23 |website=Maths History |language=en}}</ref>

== References ==
<references />

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{{DEFAULTSORT:Ezeilo, James O C}}
[[Category:1930 births]]
[[Category:2013 deaths]]
[[Category:Academic staff of the University of Nigeria]]
[[Category:Alumni of the University of Cambridge]]
[[Category:20th-century Nigerian mathematicians]]
[[Category:Vice-chancellors of the University of Nigeria]]
[[Category:Fellows of the African Academy of Sciences]]

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