Roy Goodman
Professor, Mathematical Sciences
- roy.goodman@njit.edu
- 973-642-4261
- 504a Cullimore Hall (CULM)
About Me
Roy completed his Ph.D. in 1999 at New York University's Courant Institute. He spent two years as a postdoc, splitting his time between Lucent Bell Laboratories and Princeton University. He joined the NJIT Department of Mathematical Sciences in 2001. He is currently Associate Chair for Graduate Studies.
Education
Ph.D.; New York University; Mathematics; 1999
B.S.; University of Michigan-Ann Arbor; Mathematics; 1994
Website
2026 Fall Courses
MATH 792B - PRE DOCTORAL RESEARCH
MATH 790A - DOCT DISSERTATION & RES
MATH 676 - ADV ORDINARY DIFFE EQ
MATH 791 - GRADUATE SEMINAR
Teaching Interests
Applied and applicable mathematics: calculus, linear algebra, numerical methods, analysis, differential equations, dynamical systems, asymptotics, mathematical modeling
Past Courses
MATH 111: CALCULUS I
MATH 112: CALCULUS II
MATH 211: CALCULUS IIIA
MATH 222: DIFFERENTIAL EQUATIONS
MATH 227: MATHEMATICAL MODELING
MATH 331: INTRO PARTIAL DIFF EQ
MATH 332: INTRO COMPLEX VARIABLES
MATH 337: LINEAR ALGEBRA
MATH 337: LINEAR ALGEBRA HONORS
MATH 340: APPLIED NUMERICAL METHODS
MATH 440: ADV APPL NUMERICAL METH
MATH 440: ADVANCED APPLIED NUMERICAL METHODS
MATH 450: METHODS OF APPLIED MATH
MATH 451: HONORS- METHODS APPL MATH II
MATH 451: METHODS APPL MATH II
MATH 473: INTERMED DIFFEREN EQUATN
MATH 573: INTERMED DIFF EQUATIONS
MATH 611: NUMER METH FOR COMPUTATN
MATH 614: NUMERICAL METHODS I
MATH 671: ASYMPTOTIC METHODS I
MATH 676: ADV ORDINARY DIFFE EQ
MATH 707: ST: DYNAMICAL SYSTEMS
MATH 722: WAVE PROPAGATION
MATH 791: GRADUATE SEMINAR
Research Interests
Wave equations, dynamical systems, invariant manifolds, numerical computation
Journal Article
Roy H. Goodman, Grace Conte, Jeremy L. Marzuola. 2025. "QGLAB: A MATLAB Package for Computations on Quantum Graphs." SIAM Journal on Scientific Computing, vol. 47, no. 2, pp. B428-B453.
Atul Anurag, Roy H. Goodman, Ellison K. O'Grady. 2024. "A new canonical reduction of three-vortex motion and its application to vortex-dipole scattering." Physics of Fluids, vol. 36, pp. 067110.
Jimmie Adriazola, Roy H. Goodman. 2023. "Apodizer Design to Efficiently Couple Light into a Fiber Bragg Grating." SIAM Journal on Applied Mathematics, vol. 83, no. 3, pp. 1126-1145.
Jimmie Adriazola, Roy H. Goodman, Panayotis G. Kevrekidis. 2023. "Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential1." Communications in Nonlinear Science and Numerical Simulation, vol. 122, pp. 107219 (14 pp.).
Roy H. Goodman, Brandon M. Behring. 2023. "Transition to instability of the leapfrogging vortex quartet." Mechanics Research Communications, vol. 128, pp. 104068.
Jimmie Adriazola, Roy H. Goodman. 2022. "An Optimal Control Approach to Gradient-Index Design for Beam Reshaping." Journal of the Optical Society of America A, vol. 39, no. 5, pp. 907--915.
Jimmie Adriazola, Roy H. Goodman. "A Reduction-Based Strategy for Optimal Control of Bose-Einstein Condensates." Physical Review E, vol. 105, pp. 025311(1-16).
Timothy E Favor, Roy H. Goodman, J. Douglas Wright. 2020. "Solitary Waves in Mass-in-Mass Lattices." Zeitschrift für Angewandte Mathematik und Physik, vol. 71, no. 6, pp. 1-20.
Amir Sagiv , Adi Ditkowski, Roy H. Goodman, Gadi Fibich. 2020. "Loss of physical reversibility in reversible systems." Physica D: Nonlinear Phenomena, vol. 410, pp. 132515.
Amir Sagiv, Adi Ditkowski, Roy H. Goodman, Gadi Fibich. 2020. "Loss of Physical Reversibility in Reversible Systems." Physica D: Nonlinear Phenomena, vol. 410, pp. 132515.
Brandon M. Behring, Roy H. Goodman. 2019. "Stability of leapfrogging vortex pairs: A semi-analytic approach." Physical Review Fluids, vol. 4, no. 12, pp. 124703.
Roy H. Goodman, Maurizio Porfiri. 2019. "Topological features determining the error in the inference of networks using transfer entropy." Mathematics in Engineering, vol. 2, no. 1, pp. 34-54.
Adilbek Kairzhan, Dmitry E. Pelinovsky, Roy H. Goodman. 2019. "Drift of Spectrally Stable Shifted States on Star Graphs." SIAM Journal on Applied Dynamical Systems, vol. 18, no. 4, pp. 1723-1755.
Roy H. Goodman. 2019. "NLS Bifurcations on the bowtie combinatorial graph and the dumbbell metric graph." Discrete and Continuous Dynamical Systems, vol. 39, no. 4, pp. 2203--2232.
Roy H. Goodman. 2017. "Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential." Physica D: Nonlinear Phenomena, vol. 359, pp. 39--59.
Roy H. Goodman, Aminur Rahman, Michael J Bellanich, Catherine Morrison. 2015. "A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment." Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 25, no. 4, pp. 043109.
Roy H. Goodman, Panayotis G. Kevrekidis, Ricardo Carretero-González. 2015. "Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates." SIAM Journal on Applied Dynamical Systems, vol. 14, no. 2, pp. 699-729.
Roy H. Goodman, Jeremy L. Marzuola, Michael I. Weinsten. 2015. "Self-trapping and Josephson tunneling solutions to the nonlinear Schrodinger / Gross-Pitaevskii Equation." Discrete and Continuous Dynamical Systems--Series A / American Institute of Mathematical Sciences , vol. 35, no. 1, pp. 225-246.
Jacek K. Wróbel, Roy H. Goodman. 2013. "High-order adaptive method for computing two-dimensional invariant manifolds of three-dimensional maps." Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 7, pp. 1734-1745.
Roy H. Goodman. 2011. "Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes." J. Phys. A Math. Theor., vol. 44, no. 42, pp. 425101 (28pp).
J. Blawzddiewicz, Roy H. Goodman, N. Khurana, E. Wajnryb, Yuan-Nan Young. 2010. "Nonlinear hydrodynamic phenomena in Stokes flow regime." Physica D/Elsevier, vol. 239, no. 14, pp. 1214-1224.
Roy H. Goodman, Michael I. Weinstein. 2008. "Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study." Physica D: Nonlinear Phenomena, vol. 237, no. 21, pp. 2731-2760.
Yuan-Nan Young, Jerzy Blawzdiewiecz, Vittorio Cristini, Roy H. Goodman. 2008. "Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation." Journal of Fluid Mechanics, vol. 607, pp. 209-234.
Roy H. Goodman, Richard Haberman. 2007. "Chaotic Scattering and the -Bounce Resonance in Solitary-Wave Interactions." Physical Review Letters, vol. 98, no. 10.
Roy H. Goodman, Richard Haberman. 2007. "Chaotic Scattering and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Bounce Resonance in Solitary-Wave Interactions." Physical Review Letters, vol. 98, no. 10.
Roy H. Goodman, Richard Haberman. 2005. "Vector-soliton collision dynamics in nonlinear optical fibers." Physical Review E, vol. 71, no. 5.
Roy H. Goodman, Richard Haberman. 2005. "Kink-Antikink Collisions in the phi^4 Equation: The n-Bounce Resonance and the Separatrix Map." SIAM Journal on Applied Dynamical Systems, vol. 4, no. 4, pp. 1195-1228.
Roy H. Goodman, Richard Haberman. 2004. "Interaction of sine-Gordon kinks with defects: the two-bounce resonance." Physica D: Nonlinear Phenomena, vol. 195, no. 3-4, pp. 303-323.
Roy H. Goodman, Richart E. Slusher, Michael I. Weinstein. 2002. "Stopping light on a defect: erratum." Journal of the Optical Society of America B, vol. 19, no. 11, pp. 2737.
Roy H. Goodman, Richart E. Slusher, Michael I. Weinstein. 2002. "Stopping light on a defect." Journal of the Optical Society of America B, vol. 19, no. 7, pp. 1635.
Roy H. Goodman, David S. Graff, Leonard M. Sander, Patrick Leroux-Hugon, Eric Clément. 1995. "Trigger waves in a model for catalysis." Physical Review E, vol. 52, no. 6, pp. 5904-5909.
Magazine/Trade Publication
"Four Decades of Kink Interactions in Nonlinear Klein-Gordon Models: A Crucial Typo, Recent Developments and the Challenges Ahead"
DSWeb, a website of the SIAM Activity Group in Dynamical Systems, October (4th Quarter/Autumn), 2019.
DSWeb, a website of the SIAM Activity Group in Dynamical Systems, October (4th Quarter/Autumn), 2019.
"Markdown: A Writing Tool for Every Applied Mathematician's Toolbox"
SIAM News, May, 2019.
SIAM News, May, 2019.
Book
Roy H. Goodman. "Mathematical Analysis of Fractal Kink-Antikink Collisions in the phi-4 Model." 15 pp. Springer-Verlag, 2019.
Book Review
"Review of "Methods of Mathematical Modeling" by Witelski and Bowen"
SIAM Review, May, 2017.
SIAM Review, May, 2017.