Arizona State University Mathematics Differential Equations Pdf

Dr. Mahbubur Rahman
Associate Professor & Graduate Programs Director
Department of Mathematics and Statistics
University of North Florida
1 UNF Drive, Building 14/2727
Jacksonville, FL-32224

I have developed a course on Mathematical Modeling for senior undergraduate students. Interested students are encouraged to contact me to know more about the future offerings of the course!!

Office Phone : (904) 620-3748
E-mail: mrahman@unf.edu
URL:http://www.unf.edu/~mrahman

Professional Experience :

May 2018- Graduate Programs Director,Department of Mathematics and Statistics, University of North Florida, Jacksonville, Florida-32224.

August 2010- Associate Professor, Department of Mathematics and Statistics, University of North Florida, Jacksonville, Florida-32224. August 2005- July 2010, Assistant Professor, Department of Mathematics and Statistics, University of North Florida, Jacksonville, Florida-32224. Research Interests: Mathematical Modelling in Biology, Stochastic Differential Equation, Computational Mathematics, Numerical Analysis, Dynamical Systems Educational Background : Post-doctoral Research Fellow: Advisors: Dr. Timothy Ginn and Dr. Frank Loge, University of California, Davis, 2005.
Ph.d. thesis Advisors: Prof. Z. Jackiewicz and Prof. Bruno D. Welfert, Arizona State University, Arizona, 2004.
M.Sc. thesis Advisor: Prof. Powel Gora, Concordia University, Montreal, 1997.

Awards :

STEM Fellow, 2012-13,UNF
Summer research Grant 2007-08, UNF
Summer research Grant 2006-07, UNF
Summer Teaching Grant 2006-07, UNF
Graduate Research Award- 2004, Mathematics and Statistics Department, Arizona State University, Tempe.

Publications: [ 1]. Numerical Solution of Fredholm integro-differential equation modelling neural network, Z. Jackiewicz, M. Rahman, B. D. Welfert, Appl. Numer. Math. 56(2006), 423-432. FIDE.pdf [2]. Markov versus Gaussian white noise arises and in propagation of wave arising in mathematical neurosciences, M. Rahman, Proceedings of Neural, Parrallel, Scientific Computations 3(2006)203-206. MarkovvsGauss.pdf [3]. Stochastic Approximation of Perturbed Fredholm Volterra integro-differential equation arising in Mathematical Neurosciences, M. Rahman, Z. Jackiewicz, B. D. Welfert, Applied Mathematics and Computation 186(2007),1173-1182. SDE.pdf

[4]. Numerical Solution of Fredholm integro-differential equation Modeling theta dot neural network, Applied Mathematics and Computation 195(2008)523-536, Z. Jackiewicz, M. Rahman, B. D. Welfert. thetadot.pdf

[5]. Asymptotic properties of M.L.E's for distributions generated from s 2-parameter weibul distribution by a generalized log-logistic transformation, Journal of Probability and Statistical Science (JPSS), Vol8, No2(2010), pp 199-214, J. Gleaton and M. Rahman. AGLLW.pdf

[6].

Functional central limit theorem for Markov processes and chain s,Journal of Probability and Statistical Science (JPSS), 11(2) 111-127, August 2013, M. Rahman and B. D. Welfert. CLT.pdf [7]. Modeling the Effect of the Cytokine Interleukine-2 on Tumor-immune Dynamics with Michaelis-
Menten Kinetics as Functional Responses , Proceedings of the 18th International Mathematics Conference 2013 25-27, Bangladesh, M. M. Rahman
[8].
Asymptotic properties of M.L.E's for distributions generated from s 2-parameter inverse Gaussian distribution by a generalized log-logistic transformation, Gleaton and M. Rahman, 12(1), 85-99, 2014.

[9]. Asymtotic estimate of variance with applications to stochastic differential equations arises in mathematical neuroscience, Communications in Statistics-Theory and Methods, 47:2(2018), 289-306.

[10] Mathematical modeling analysis to simulate the dynamics of Immune cells, HIV, and Tuberculosis, AJUR , Volume 14(1)35-48, Rumana Ahmed & Mahbubur Rahman, 2017.
[11]
Stability and Accuracy Analysis of [1] theta Scheme for a Convolutional Integro-Differential Equation, Differential Equations and Dynamical Systems
https://doi.org/10.1007/s12591-019-00476-w, Springer, 2019, S. Bhowmik & M. Rahman.

[12]. Wave propagation in noisy systems near saddle node bifurcation in limit cycles, M. Rahman, in preparation. [13]. Stochastic differential equation arising in mathematical neurosciences, in preparation.

[14]. Stability analysis of horizontal gene transfer of kinetic network, in preparation.

Conference/Seminar presentation:

Stochastic Approximations of Fredholm Volterra Integro Differential Equations arising in Mathematical Neurosciences , 20th International Mathematics Conference 2017, Dec. 8-10, University of Dhaka , Bangladesh, M. M. Rahman (Keynote speaker ).

Development of a Dynamical system for the simulation of Immune cells and atigens, SIAM Conference on Computational Science and Engineering, Atlanta, Feb. 27-March 3, 2017, Rumana Ahamed & M. Rahman

Wave propagation in a noisy system near a saddle node on a limit cycle bifurcation, The 36th Southeastern Atlantic Regional Conference on Differential Equations, Florida Gulf Coast University, Fort Myers, November 5-6, 2016, M. Rahman

Simulation of Stochastic Differential Equations arises in mathematical neurosciences, American Mathematical Society (AMS) Joint Meetings, San Antonio, Texas, January 10-13, 2015, M. Rahman .

Modeling the Effect of the Cytokine Interleukine-2 on Tumor-immune Dynamics with Michaelis-
Menten Kinetics as Functional Responses , 18th International Mathematics Conference 2013 20-22 March 2014 at Independent University, Bangladesh, M. M. Rahman (Invited speaker ). Introduction to Mathematical modeling in Biology, Siam UNF chapter talk, UNF, April 2013, M. RahmanAsymptotic Properties of MLE's for Distributions Generated from an Exponential-Class Distribution by a generalized Log-Logistic Transformation, ASA, Miami, Florida, 2011, J. Gleaton & M. Rahman.Computer Simulation of Stochastic Differential Equations arises in Mathematical Neurosciences, First Coast Meeting Florida Section MAA, UNF, Florida, Jan 29th 2010, M. Rahman.Modeling Gene Transfer of Kinetic Network in Aquifer Media, Joint Mathematics Meeting, Washington DC, Jan. 7-9, 2009, M. Rahman.Stochastic approximations of differential equations equations arises in mathematical neurosciences, Fifth International Conference on Dynamic System and Applications, Atlanta, May 30- June2, 2007.Markov versus Gaussian white noise arises and in propagation of wave arising in mathematical neurosciences, Third International Conference in Neural, Parrallel, Scientific Computation, Atlanta, Georgia, 9-12th August, 2006 (Invited speaker). Stochastic Differential Equation and its Application , Department of Civil and Environmental, University of California at Davis, 23rd May, 2005.
Central Limit Theorems for Markov Processe s, Graduate Math. Seminar, Arizona State University, 23rd March, 2004.

Numerical Approximations to Stochastic Differential Equations and their Applications in Mathematical Neurosciences( Computational Math. Pro. Seminar, Arizona State University, 25th Sept'03).

Student Supervision:

Randy Lee, Topics in Dynamical Systems, 2018

Lipi Roy A Study of the Dynamics of Raves, Clubs, and Ecstasy arising in mathematical epidemiology , Graduate Presentation, April 2015.

Rumana Ahmed, A Study of nonlinear Dynamics of Immune Cells, HIV, and Tuberculosis, Dec. 2014

Joseph Ferrara, A Study of nonlinear Dynamics in Mathematical Biology, Master of Science Thesis, July 2013.

Mike Hamilton, A Review of Mathematical Modeling of Pathways to Diabetics, Graduate presentation, May 2012.

Vignesh Vudatha, Worked on Modeling of Immune System Interaction between Tumor, Effector, and Cytokine Cells for Mammals, 2010

SPRING 2019

Trigonometry MAC1114	CALCULUS III(MAC 2313)	CALCULUS I(MAC 2311)
Syllabus	Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz	Announcements

FALL 2018

Ordinary Differential Equations (MAP 2302)	Ordinary Differential Equations (MAP 6336)
Syllabus	Syllabus
Announcements/Homework/Quiz
DFIELD8 PPLANE8

SUMMER 2018: Calculus II (MAC2312):

SPRING 2018

Mathematical Biology (MAP 6489)	CALCULUS III(MAC 2313)
Syllabus	Syllabus
	Announcement/Homework/Quiz
DFIELD8 PPLANE8
lotka-Voltera
Burst_FS.ode

FALL 2017

Calculus III (MAC 2313)	Ordinary Differential Equations(MAP 2302)	Numerical Analysis (MAD 4401)
Syllabus	Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz	Announcements
Selected_solutions_sec 11.3&11.4 Multiple_Integ_Handout (11/24/17)		BisectRahman NewtonRahman SecantRahman
Power_point_sec 13.8 Power_point_sec 14.1 Power_point_sec 14.2

SUMMER 2017: Calculus II (MAC2312):

Spring 2017

Ordinary Differential Equations (MAP2302)	Clculus III (MAC2313)
Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz
DFIELD8 PPLANE8
Answer_key_Homework_5
Practice Problems for Final

FALL 2016

Calculus III (MAC2313)	CALCULUS I(MAC 2311)	Trigonometry (MAC 1114)
Syllabus	Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz	Announcements/Homework/Quiz
Answer key quiz 3	Answer_key_Quiz4	Answer_key_Quiz4

SUMMER 2016

SPRING 2016

SCIENTIFIC COMPUTING (MAP 6385)	CALCULUS I(MAC 2311)
Syllabus	Syllabus
	Announcement/Homework/Quiz
DFIELD8 PPLANE8
lotka-Voltera
Burst_FS.ode

FALL 2015

Numerical Analysis (MAD 4401)	PRE-CALCULUS (MAC 1147)	ODEs( MAP 2302)
Syllabus	Syllabus	Syllabus
	Announcements/Homework/Quiz	Announcement/Homework/Quiz
DFIELD8 PPLANE8		DFIELD8 PPLANE8 VOLTERRA.m
Notes_on_Matlab BisectRahman.m NewtonRahman.m SecantRahman.m

Tentative Review topics for final exam

Summer 2015

Spring 2015

Ordinary Differential Equations (MAP2302)	LINEAR ALGEBRA (MAS 3105)
Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz
DFIELD8 PPLANE8
Lab1 will be 02/10/2015 at Bldg. 14/Room 2743 -LAB1MAP2302.pdf

FALL 2014

Mathematical Biology (MAT 6933)	PRE-CALCULUS (MAC 1147)	CALCULUS I(MAC 2311)
Syllabus	Syllabus	Syllabus
	Announcements/Homework/Quiz	Announcement/Homework/Quiz
DFIELD8 PPLANE8
lotka-Voltera
Burst_FS.ode

SUMMER 2014: Pre-Calculus(MAC1147):

Spring 2014

Business Calculus (MAC2233)	Calculus I (MAC 2311)
Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz

FALL 2013

ODE (MAP2302)	LINEAR ALGEBRA (MAS 3105)	CALCULUS I(MAC 2311)
Syllabus	Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz	Announcements/Homework/Quiz
DFIELD8 PPLANE8
Lab1 will be 09/24/13 at Bldg. 14/Room 2743

SUMMER 2013: Ordinary Differential Equation(MAP2302):

Spring 2013

FALL 2012

CAL III (MAC2313)	Calculus I (MAC2311)	Trigonometry (MAC1114)
Syllabus	Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz	Announcements/Homework/Quiz
SOLUTION_EX28_SEC13.8	TRIG. FORMULAS
	Rule for Logarithms
	Graphing Calculator Help	Graphing Calculator Help
	VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH) CALCULUS.ORG

SUMMER 2012:

Calculus I (MAC2311):

SPRING 2012 TEACHING

Mathematical Biology ( MAT 6933)	Calculus I (MAC 2311)
Syllabus.doc	Syllabus.doc
Homework/Announcements	Homework/Quiz/Announcements
	TRIG. FORMULAS
DFIELD8 PPLANE8	Graphing Calculator Help
lotkavolterra.m schander.m schanderRLG.m fourierAV1.m	Rule for Logarithms
LAB1 (04/03/12)- SIMULATING ANALYZING USING Matlab/PPLANE8 LAB2(04/05/2012)-SIMULATING ANALYZING USING XPPAUT LAB3 (04/10/2012-SIMULATING ANALYZING USING XPPAUT	links: VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH) CALCULUS.ORG TUTORIALS

FALL 2011 ( Taught)

Linear Algebra (MAS 3105)
Calculus I (MAC2311)
Business Calculus (MAC2233)

SUMMER 2011: Calculus II (MAC2312):

SPRING 2011 TEACHING

CAL III (MAC2313)	CAL I (MAC2311)
Syllabus.doc	Syllabus.doc
Announcements/Homework/Quiz Solution_exercise36_section12.4	Announcements/Homework/Quiz
LAB1: February 24th - Bldg.14/Rm.2743 mws1 mws2	TRIG. FORMULAS
LAB 2: March 10th- Bldg.14/Rm.2743 mws3	Rule for Logarithms
LAB 3: March 31st- Bldg.14/Rm.2743	Graphing Calculator Help
	VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH) CALCULUS.ORG TUTORIALS

FALL 2010 TEACHING

Numerical Analysis (MAD 4401)	Calculus for Biology (MAC 2241)
Syllabus.doc	Syllabus.doc
Announcements/Homework	Announcements/Homework/Quiz
Lab1-09/22/10 (Bldg. 14/2743) Programs root finding method: bisection.m secant.m newton.m fixedpointiter.m	TRIG. FORMULAS
Lab2-10/13/10 (Bldg. 14/2743) Progarms numerical integration: Trapezoidal.m drivertrapezoidal.m Simpson.m driversimpson.m	Rule for Logarithms
Lab3-11/03/10 (Bldg. 14/2743) DFIELD8 PPLANE8 euler.m f1.m	Graphing Calculator Help
Lab4 -11/17/10 rk2.m	VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH) CALCULUS.ORG TUTORIALS

SPRING 2010 TEACHING

ODE (MAP2302)	Calculus I (MAC2311)
Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz EXAM1-REVIEW EXAM2-REVIEW FINAL REVIEW
LAB1: February 25th - Bldg.14/Rm.2743	TRIG. FORMULAS
LAB 2: March 23rd- Bldg.14/Rm.2743	Rule for Logarithms
	Graphing Calculator Help
Sofware /Technology: MATLAB DFIELD8 PPLANE8	VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH) CALCULUS.ORG TUTORIALS

FALL 2009

ODE (MAP2302)	Calculus I (MAC2311)	Pre-calculus (MAC1147)
Syllabus	Syllabus	Syllabus
Announcements/Homework/Quiz	Announcements/Homework/Quiz EXAM1: 10/01/09	Announcements/Homework/Quiz EXAM1: 09/30/09
EXAM1: 10/01/09	TRIG. FORMULAS	TRIG. FORMULAS
LAB1:10/08/09	Rule for Logarithms	Rule for Logarithms
LAB2: 10/22/09	Graphing Calculator Help	Graphing Calculator Help
Sofware /Technology: MATLAB DFIELD7 PPLANE7	VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH) CALCULUS.ORG TUTORIALS

SUMMER 2009: Ordinary Differential Equation(MAP2302):

SPRING 2009 TEACHING

Mathematical Biology	Linear Algebra	Calculus I
Syllabus.doc	Syllabus.doc	Syllabus.doc
Homework/Announcements	Homework/Quiz/Announcements	Homework/Quiz/Announcements
		TRIG. FORMULAS
DFIELD7 PPLANE7		Graphing Calculator Help
lotkavolterra.m		Rule for Logarithms
LAB1-02/11/09-- Bldg.14/Rm.2743 LAB2-03/02/09-- Bldg.14/Rm.2743		links: VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH) CALCULUS.ORG TUTORIALS

FALL 2008 TEACHING

Ordinary Differential Equation (MAP2302)	Intensive College Algebra (MAC1990)
Syllabus.doc	Syllabus.doc
Announcements/Lists of Homworks/Quizzes	List of Homeworks/Quizzes problem
	Rule for Logarithms!!!

LAB1- Oct. 01- Bldg.14/Rm.2743 LAB 2- Oct. 22- Bldg.14/Rm.2743 LAB 3- Nov. 19- Bldg.14/Rm.2743

SUMMER 2008: Linear Algebra (MAS3105):

SPRING 2008 MATHEMATICAL MODELLNG

Syllabus.doc Homework Assignments LAB1- Feb. 06 LAB 2- Feb. 20 LAB 3- March 03 LAB 4- April 02 at Bldg.14/Rm.2743	Project Assignments:
Reading Materials: EpidemicI EpidemicII EpidemicIII StichasticModel	Sofware /Technology: XPPAUT MATLAB DFIELD7 PPLANE7 MAPLE

CALCULUS FOR BIOLOGY

FALL 2007 TEACHING

Ordinary Differential Equation	Calculus I	Intensive College Algebra
Syllabus.doc	Syllabus.doc	Syllabus.doc
Homework Assignments	Homework Assignments	Homework Assignments/Announcements
	EXAM2REVIEW	EXAM2 REVIEW
	Graphing Calculator Help	FINAL EXAM REVIEW
LAB1-10/11/07	FINAL EXAM REVIEW
LAB2-11/22/07

SUMMER 2007

SPRING 2007

Calculus I( Special Section for Life Sciences Major, MAC 2311, CRN 10616)	Calculus for Business(MAC 2233, CRN 12647)
Syllabus.doc	Syllabus.doc
Announcements/Homework	Announcements/Homework
VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH)	Graphing Calculator Help
Practice Problems /Review for Exam1	Practice Problems /Review for Exam1
LAB1- March 14 Bldg 14/2743	Guide for Optimization problems(Section 4.4-4.5)
LAB2- March 28 Bldg 14/2743	Rule for Logarithms!!!(Review for section 5.1-5.2)
Guide for Optimization Problems(Section 6.2)	Practice Problems/ Review for Exam 2
Practice problems/Review for Exam 2	EXAM 2 SOLUTION KEY
PROJECT 1(APPLICATIONS TO LIFE SCIENCES)	PRACTICE PROBLEMS FOR FINAL
PRACTICE PROBLEMS FOR FINAL	SOLUTION FOR EX 42(SECTION 6.4)

COURSES TEAUGHT(FALL 2006):

Differential Equation	Calculus -I	PreCalculus	College Algebra
Syllabus.html Syllabus.doc	Syllabus.html Syllabus.doc	Syllabus.html Syllabus.doc	Syllabus.html Syllabus.doc
Homework	Homework	Homework	Homework
DFIELD7 PPLANE7	Graphing Calculator Help
LAB1- Sept. 20 LAB 2- Oct . 11 LAB 3- Nov. 01 LAB 4- Nov. 15 at Bldg.14/Rm.2743	links: VISUAL CALCULUS(BY DR. LAWRENCE S. HUSCH) CALCULUS.ORG TUTORIALS	TRIG. FORMULAS

SUMMER-2006: COLLEGE ALGEBRA-MAC 1105(CRN 50328): SYLLABUS TEST2 REVIEW/SAMPLE PROBLEMS

FINAL REVIEW/SAMPLE QUESTIONS

Past Teaching:

Spring 2006

Mathematical Biology(MAC 6933 Syllabus)

Pre-Calculus(MAC 1147 Syllabus)

Fall 2005

Calculus with analytic Geometry-III MAC 2313

ANNOUNCEMENTS FOR MAC 2313 CLASS
MAC 2313 Syllabus

Review Chap 9
Review Chap 10

Calculus of Business Mac 2233

ANNOUNCEMENTS FOR MAC 2233 CLASS
MAC 2233 Syllabus

Graphing Calculator Help

Classes Taught :

Summer 2007( Mac 2313)-Cal-III	Spring 2007(Mac 2311(Calculus for Life Sciences), , Mac 2233)	Fall 2006(Map 2302, Mac 2311, Mac 1147, Mac 1105)
Summer 2006( Mac 1105)	Spring 2006(Mac 6933, Mac 1147)	Fall 2005(Mac 2322, Mac 2313)
Calculus with analytic Geometry-III Mat 272 ,Mat 271 Calculus with Analytic Geometry-II(ASU)	Mat 270 Calculus with Analytic Geometry-I(ASU)	Mat 170 Pre-Calculus(ASU)
Mat117 Introduction to Algebra(ASU)	Math 106 Fundamentals of Algebra(ASU)	Math 001 Fundamentals of Algebra(Purdue School of Science)
Math 203 Diff. & Integral Calculus (Univ. of Concordia)	Math 200 Fundamental concepts of Algebra (University of Concordia)	Topology,Fortran 77,Diff. & Integral Calculus,Advanced Algebra(Univ. of Chittagong)

Fall 2003

Calculus with analytic Geometry-II Mat 271
Announcements
Mat 271 Syllabus

Mat271 Hw Assignment

WebWork
Test1 Review

Maple Lab Session

LAB1
LAB2
SnowmanLab

Some Links:

American Mathematical Society
SIAM
MAA

Math Competitions Archive

Math Olympiad

Mathematical Modeling Contest

http://www.duvalschools.org/static/aboutdcps/departments/acadprog/mathematics/index.asp