I am a Professor of Mathematics in the Department of Mechatronics Engineering at Istanbul Commerce University.

This semester, Fall  2021, I am teaching:

Although all classes are remote, I continue to teach my classes in my own classroom to make learning easier and to be closer to my students. Here are some recent pictures from my class:

Mathematical Analysis-2  and Matematik Analiz 4

The homework component of your grade in  courses  MAT 121and  ENG 126  are  determined by online WeBWorK assignments. Enter the url http://webwork.ticaret.edu.tr/webwork2/  in your web browser. You should see a list of available courses.  To find your course, you will need to know your course code (i.e , MAT 122, ENG126, ENG227,..) ,  year and semester.

My office is  B205 (Küçükyalı), and my office hours are

  • Monday &Thursday: 1 pm-3 pm.
  •  also by appointment.

Please stop by to say hi!

 

 


 

Message to Students

Dear students:
As the rest of humanity, we are going through difficult times that require proactive measures from every individual. Please understand the importance of social distancing and hygiene to fight this virus. This is no joke, please do not get out of your houses unless necessary. Wear a mask and gloves when you have to go outside. Remember to wash your hands often for 20 seconds and try to keep your houses clean. Make sure to clean whatever you buy from outside.

 
I understand that it can be very frustrating, and many of you may be experiencing loneliness, boredom, or even anxiety. I hope we can get over this soon. But in order to do so, we must work together as we follow the rules.
 
All the best.
 
Prof. Dr. Ismail Kömbe

Prof. Dr. İsmail Kömbe

Department of Mechatronics

Istanbul Commerce University

Küçükyalı E5 Kavşağı İnönü Cad. No: 4,
Küçükyalı 34840 / İstanbul

Phone: TBA

Office: B205

E-mail: ikombe [at] ticaret (dot) edu (dot) tr,  ikombe40 [at] gmail (dot) com

Education:

Ph.D.  Mathematics, The University of Memphis,  Memphis, TN, USA, 2003

M.A. Mathematics, The University of Pittsburgh, Pittsburgh, PA, USA, 1995

B.S. Mathematics,  Ankara  University,  Ankara, TÜRKİYE, 1990

High School, Ankara Atatürk Lisesi, Ankara, TÜRKİYE, 1986


Biography:

Dr. Kömbe  received his Ph.D. in 2003 from  the University of Memphis  under the direction of J. A. Goldstein. He spent one year as a post doctoral fellow at  the University of Missouri. In 2004, he was appointed as an Assistant Professor at Oklahoma City University and then  was promoted to Associate Professor in 2007, tenured in 2009  respectively  at Oklahoma City University.

Dr. Kömbe’s research interests are in the Partial Differential Equations and Geometric Analysis. In April 2009, Dr. Kömbe received the Distinguished Achievement in the Scholarship of Discovery Award in recognition of excellence in disciplinary research at Oklahoma City University.

At the Oklahoma City University, Dr. Kömbe taught a wide range of mathematics courses, including College Algebra, Single Variable and Multivariable Calculus, Advanced Calculus, Differential Equations, Linear Algebra, Mathematical Statistics, Complex Variables, Discrete Mathematics, Real Variables, and Abstract Algebra.

Dr. Kömbe joined the faculty in the mathematics department at İstanbul Commerce University during the fall of 2011. He teaches a wide range of courses including Single Variable and Multivariable Calculus, Advanced Calculus, Differential Geometry, Real Analysis, Partial Differential Equations, Linear Algebra, Engineering Mathematics, Differential Equations. Besides undergraduate courses he also  teaches graduate courses including Fourier Analysis and  Boundary Value Problems, Measure Theory, Partial Differential Equations,  Calculus on Manifolds, and  Sobolev Spaces and Geometric Inequalities.

Dr. Kömbe’s current research interests include Hardy, Rellich and Heisenberg Uncertainty Principle type inequalities and their sharp versions on complete manifolds.


MathSciNet Links:


Publications:

→Years : 2011 — İstanbul Commerce Univesity:

32) Kombe, Ismail ” Fourth Order  Partial Differential Equations with Singular Lower Order Term on Riemannian Manifolds  ” (submitted)

31) Gisele Goldstein, Jerome Goldstein, Ismail Kombe, Reyhan Tellioğlu ” Nonexistence of positive solutions for nonlinear
parabolic Robin problems and Hardy-Leray Inequalities” To appear in  Annali di Matematica Pura ed Applicata, 2021.

30) Sümeyye Bakım, Gisele Goldstein, Jerome Goldstein, Ismail Kombe ” Nonexistence Results for Parabolic Equations
Involving the p-Laplacian and Hardy-Leray Type Inequalities on Riemannian Manifolds ” Journal of Evolution Equations, (21) 2, 2021.

29)  Gisele Goldstein, Jerome Goldstein, Ismail Kombe, Reyhan Tellioğlu ” Nonlinear Parabolic Equations with Robin Boundary Conditions and Hardy-Leray Type Inequalities”, Stochastic Processes and Functional Analysis: New Perspectives,  To appear in  Contemporary Mathematics  774,  Amer. Math. Soc., Providence, RI, 2021.

28) Sümeyye Bakım, Gisele Goldstein, Jerome Goldstein, Ismail Kombe ” Fast Diffusion Equations on Riemannian Manifolds  “, Differential and Integral Equations, 33(9-10),  (2020), 507-526.

27)  Kombe, Ismail;  Yener, Abdullah “A General Approach to weighted L^p-Rellich type inequalities related to Greiner operator”, Communications on Pure and Applied Analysis, 18(2), (2018), 869-886.

26)  Kombe, Ismail;  Yener, Abdullah  “General weighted Hardy type inequalities related to Baouendi-Grushin operators”,  Complex Variables and Elliptic Equations, 63(3), (2018),  420-436.

25) Goldstein, Jerome; Kombe, Ismail; Yener, Abdullah   “A General Approach to Weighted Rellich Type inequalities on Carnot Groups”, Monatshefte für Mathematik, 186(1),  (2018), 1-24.

24) Kombe, Ismail; Ahmetolan, Semra “Improved  Hardy and Rellich type inequalities with two weight functions”, Mathematical Inequalities & Applications, Volume 21, Number 3 (2018), 885–896.

23)  Kombe, Ismail;  Yener, Abdullah  “Weighted Rellich type inequalities related to Baouendi-Grushin operators”, Proceedings of the American Mathematical Society, 145(11), 2017,  4845-4857.

22) Goldstein, Jerome; Kombe, Ismail; Yener, Abdullah   ” A Unified Approach to Weighted Hardy Type inequalities on Carnot groups”   Discrete and Continuous Dynamical Systems-Series A, 37(4),  (2017), 2009-2021.

21) Kombe, Ismail; Ahmetolan, Semra “Sharp Hardy and Rellich type inequalities with two weight”, Mathematical Inequalities & Applications, Volume 19, Number 3 (2016), 937–948.

20) Kombe, Ismail; Yener, Abdullah “Weighted Hardy and Rellich type inequalities on Riemannian manifolds”, Mathematische Nachrichten, 289 (2016),  issue 8-9, 994-1004.

19) Kombe, Ismail,  “Hardy and Rellich-type inequalities with remainders for Baouendi-Grushin vector fields’’, Houston Journal of Mathematics, Volume 41, No.3 (2015), 849-873.

 18)  Kombe, Ismail,     “ On the nonexistence of positive solutions to Doubly Nonlinear equations for Baouendi-Grushin operators”, Discrete and Continuous Dynamical Systems-Series A (DCDS-A),  Volume 33, Number 11&12, (2013), 5167-5176.

17) Kombe, Ismail;   Özaydın, Murad,  “Hardy-Poincare, Rellich and uncertainty principle inequalities on Riemannian manifolds”, Transactions of the American Mathematical Society, 365 (2013), 5035-5050.

16)  Kombe, Ismail;  Ahmetolan, Semra, “Sharp uncertainty principle and Hardy-Poincaré inequalities on sub-Riemannian manifolds”, Mathematical Inequalities & Applications, Volume 15, Number 2 (2012), 457–467.


→Years: 2004 — 2011 (Oklahoma City University):

15) Kombe, Ismail, “Sharp weighted Rellich and uncertainty principle inequalities on Carnot groups”, Commun. Appl. Anal. 14 (2010), no. 2, 251–271.

14) Kombe, Ismail; Özaydin, Murad, “Improved Hardy and Rellich inequalities on Riemannian manifolds”,  Trans. Amer. Math. Soc. 361 (2009), no. 12, 6191–6203.

13) Goldstein, Jerome A.; Kombe, Ismail, “The Hardy inequality and nonlinear parabolic equations on Carnot groups”,  Nonlinear Anal. 69 (2008), no. 12, 4643–4653.

12) Goldstein, Jerome A.; Kombe, Ismail, “Gaussian estimates and instantaneous blowup”,  Positivity 12 (2008), no. 1, 75–82.

11) Ruiz Goldstein, Gisèle; Goldstein, Jerome A.; Kombe, Ismail, “The power potential and nonexistence of positive solutions”,  Differential equations: inverse and direct problems, 183–195, Lect. Notes Pure Appl. Math., 251, Chapman & Hall/CRC, Boca Raton, FL, 2006,

10) Kombe, Ismail, “Nonlinear degenerate parabolic equations for Baouendi-Grushin operators”,  Math. Nachr. 279 (2006), no. 7, 756–773.

9) Kombe, Ismail, “On the nonexistence of positive solutions to nonlinear degenerate parabolic equations with singular coefficients”,  Appl. Anal. 85 (2006), no. 5, 467–478.

8) Kombe, Ismail, “Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations”,  Abstr. Appl. Anal. 2005, no. 6, 607–617.

7) Goldstein, Gisele Ruiz; Goldstein, Jerome A.; Kombe, Ismail, “Nonlinear parabolic equations with singular coefficient and critical exponent”,  Appl. Anal. 84 (2005), no. 6, 571–583.

6) Goldstein, Jerome A.; Kombe, Ismail, “Nonlinear degenerate parabolic equations on the Heisenberg group”,  Int. J. Evol. Equ. 1 (2005), no. 1, 1–22.


→Years: 2004  —  University of Missouri:

5) Kombe, Ismail, “The linear heat equation with highly oscillating potential”, Proc. Amer. Math. Soc. 132 (2004), no. 9, 2683–2691.

4) Kombe, Ismail “Doubly nonlinear parabolic equations with singular lower order term”,  Nonlinear Anal. 56 (2004), no. 2, 185–199.


→Years: 1999 — 2003  (The University of Memphis):

3) Kombe, Ismail; “Linear and nonlinear parabolic partial differential equations with singular lower order term”, Thesis (Ph.D.)–The University of Memphis. 2003. 131 pp. ISBN: 978-0496-43293-6, ProQuest LLC, Thesis.

2) Goldstein, Jerome A.; Kombe, Ismail, “Nonlinear degenerate parabolic equations with the singular lower-order term”,  Adv. Differential Equations 8 (2003), no. 10, 1153–1192.

1) Goldstein, Jerome A.; Kombe, Ismail, “Instantaneous blow up”,  Advances in differential equations and mathematical physics (Birmingham, AL, 2002), 141–150, Contemp. Math., 327, Amer. Math. Soc., Providence, RI, 2003.


Ph. D Students:

  • Abdullah Yener graduated in July 2017. He is currently an Assistant Professor at Istanbul Commerce University, Istanbul, Turkey.
  • Sümeyye Bakım  graduated in July 2021. She is currently an Assistant Professor at KTO Karatay University, Konya, Turkey.
  • Reyhan Tellioğlu is a graduate student at Istanbul Commerce University.

Master of Science  Students: 

  • Abdullah Yener graduated in July 2013.
  • Erkan  Gürsu graduated in July 2017.

Teaching:

I love teaching and that is one of the main reasons I am at Istanbul Commerce University. You can reach my course web pages via the above links. The following is a list of classes that I have taught at Oklahoma City University (OCU) and İstanbul Commerce University.

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2004-2005 (Oklahoma City University) Fall College Algebra
College Algebra
Calculus and Analytic Geometry I
Calculus III
Spring College Algebra
College Algebra
Calculus and Analytic Geometry II
Real Variables
2005-2006 (OCU) Fall College Algebra
Abstract Algebra
Calculus and Analytic Geometry I
Calculus III
Spring College Algebra
College Algebra
Calculus and Analytic Geometry II
Differential Equations
2006-2007 (OCU) Fall College Algebra
Advanced Calculus
Calculus and Analytic Geometry I
Calculus III
Spring College Algebra
College Algebra
Calculus and Analytic Geometry II
Differential Equations
2006-2007 (OCU) Fall College Algebra
Abstract Algebra
Calculus and Analytic Geometry I
Calculus III
Spring Complex Variables
College Algebra
Calculus and Analytic Geometry II
Differential Equations
2007-2008 (OCU) Fall College Algebra
Abstract Algebra
Calculus and Analytic Geometry I
Calculus III
Spring College Algebra
Discrete Mathematics
Calculus and Analytic Geometry II
Differential Equations
2008-2009 (OCU) Fall College Algebra
Linear Algebra
Calculus and Analytic Geometry I
Calculus III
Spring College Algebra
College Algebra
Calculus and Analytic Geometry II
Differential Equations
2009-2010 (OCU) Fall College Algebra
Abstract Algebra
Calculus and Analytic Geometry I
Probability and Statistics I
Spring College Algebra
College Algebra
Calculus and Analytic Geometry I
Differential Equations
2010-2011 (Oklahoma City University) Fall College Algebra
College Algebra
Calculus and Analytic Geometry II
Calculus III
Introduction to Differential Geometry (Independent study)
Spring College Algebra
Complex Variables
Calculus and Analytic Geometry I
Linear Algebra
Introduction to Measure and Integral (Capstone course)

Istanbul Commerce University


Spring

2011-2012 (Istanbul Commerce University) Fall Kısmi Türevli Denklemler
Diferansiyel Geometri
Matematiksel İstatistik
Ayrık Matematik
Business Statistics( 2 section)
Mesleki İngilizce I
Uygulamalı Matematik I(Graduate)
Spring Reel Analiz
Mesleki İngilizce II
Mühendislik Matematiği ( 2 section)
Uygulamalı Matematik II(Graduate)
2012-2013 (Istanbul Commerce University) Fall Kısmi Türevli Denklemler
Mesleki İngilizce I
Business Statistics
Matematik Analiz III
Ölçüm Teorisi (Graduate)
Spring Matematik Analiz IV
Reel Analiz I
Diferansiyel Geometri
Linear Algebra
İleri Kısmi Diferansiyel Denklemler(Graduate)
2013-2014 (Istanbul Commerce University) Fall Kısmi Türevli Denklemler I
Mathematical Analysis I
Matematik I
Matematik Analiz III
2013-2014 (Istanbul Commerce University) Spring Diferansiyel Geometri
Mathematical Analysis II
Mesleki İngilizce
Matematik Analiz IV
Sobolev uzayları ve Geometrik Eşitsizlikler(Graduate)
2014-2015 (Istanbul Commerce University) Fall Kısmi Türevli Denklemler I
Mathematical Analysis I
Mathematics I
Mesleki İngilizce I
Ölçüm Teorisi (Graduate)
Spring Diferansiyel Geometri
Mathematical Analysis II
Mathematics II
Mesleki İngilizce II
Matematik Analiz IV
2015-2016 (Istanbul Commerce University) Fall Kısmi Türevli Denklemler I
Mathematical Analysis I
Mathematics I
Mesleki İngilizce I
Ölçüm Teorisi (Graduate)
Spring Diferansiyel Geometri
Mathematical Analysis II
Mathematics II
Advanced Engineering Mathematics(Graduate)
Matematik Analiz IV
2016-2017 (Istanbul Commerce University) Fall Kısmi Türevli Denklemler I
Mathematical Analysis I
Mathematics I
Mesleki İngilizce I
Ölçüm Teorisi (Graduate)
Spring Engineering Mathematics II
Mathematical Analysis II
Engineering Mathematics I
2017-2018 (Istanbul Commerce University) Fall Engineering Mathematics I
Mathematical Analysis I
Engineering Mathematics II
Geometrik Analiz(Graduate)
Spring Engineering Mathematics I
Mathematical Analysis II
Engineering Mathematics II
2019-2020 (Istanbul Commerce University) Fall Engineering Mathematics I
Mathematical Analysis I (2 section)
Matematik Analiz IV
Spring