Roy Goodman

Associate Professor, Mathematical Sciences

624 Cullimore Hall

About Me

Roy has tried on various occasions to learn the banjo, but that involves sitting in a room by himself and not talking to anyone. He does that enough when he's doing math.

Education

Ph.D.; New York University; Mathematics; 1999

B.S.; University of Michigan-Ann Arbor; Mathematics; 1994

B.S.; University of Michigan-Ann Arbor; Mathematics; 1994

Website

2021 Fall Courses

MATH 790A - DOCT DISSERTATION & RES

MATH 222 - DIFFERENTIAL EQUATIONS

MATH 222 - DIFFERENTIAL EQUATIONS

Teaching Interests

applied and applicable mathematics: calculus, linear algebra, numerical methods, analysis, differential equations, 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 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 671: ASYMPTOTIC METHODS I

MATH 676: ADV ORDINARY DIFFE EQ

MATH 707: ST: DYNAMICAL SYSTEMS

MATH 722: WAVE PROPAGATION

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 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 671: ASYMPTOTIC METHODS I

MATH 676: ADV ORDINARY DIFFE EQ

MATH 707: ST: DYNAMICAL SYSTEMS

MATH 722: WAVE PROPAGATION

Research Interests

Wave equations, dynamical systems, invariant manifolds, numerical computation

Journal Article

Favor, Timothy, & Goodman, Roy, & Wright, J. (2020). Solitary Waves in Mass-in-Mass Lattices.

Sagiv, Amir, & Ditkowski, Adi, & Goodman, Roy, & Fibich, Gadi (2020). Loss of Physical Reversibility in Reversible Systems.

Behring, Brandon, & Goodman, Roy (2019). Stability of Leapfrogging Vortex Pairs: A Semi-analytic Approach.

Goodman, Roy, & Porfiri, Maurizio (2019). Topological features determining the error in the inference of networks using transfer entropy.

Kairzhan, Adilbek, & Pelinovsky, Dmitry, & Goodman, Roy (2019). Drift of spectrally stable shifted states on star graphs.

*Zeitschrift für Angewandte Mathematik und Physik*,*71*(6), 1-20.Sagiv, Amir, & Ditkowski, Adi, & Goodman, Roy, & Fibich, Gadi (2020). Loss of Physical Reversibility in Reversible Systems.

*Physica D*,*404*, 132515.Behring, Brandon, & Goodman, Roy (2019). Stability of Leapfrogging Vortex Pairs: A Semi-analytic Approach.

*Physical Review Fluids*,*4*, 124703.Goodman, Roy, & Porfiri, Maurizio (2019). Topological features determining the error in the inference of networks using transfer entropy.

*Mathematics in Engineering*,*2*(1), 34-54.Kairzhan, Adilbek, & Pelinovsky, Dmitry, & Goodman, Roy (2019). Drift of spectrally stable shifted states on star graphs.

*SIAM Journal of Applied Dynamical Systems*,*18*(4), 1723-1755. SHOW MORE

Goodman, Roy (2019). NLS Bifurcations on the bowtie combinatorial graph and the dumbbell metric graph.

Goodman, Roy (2017). Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential.

Goodman, Roy, & Rahman, Aminur, & Bellanich, Michael, & Morrison, Catherine (2015). A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment.

Goodman, Roy, & Kevrekidis, Panayotis, & Carretero-González, Ricardo (2015). Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates.

Goodman, Roy, & Marzuola, Jeremy, & Weinsten, Michael (2015). Self-trapping and Josephson tunneling solutions to the nonlinear Schrodinger / Gross-Pitaevskii Equation.

Wrobel, Jacek, & Goodman, Roy (2013). High-order Adaptive Method for Computing Two-dimensional Invariant Manifolds of Maps.

Goodman, Roy (2011). Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes.

Blawzddiewicz, J., & Goodman, Roy, & Khurana, N., & Wajnryb, E., & Young, Yuan-Nan (2010). Nonlinear hydrodynamic phenomena in Stokes flow regime.

Young, Yuan-Nan, & Blawzdiewiecz, Jerzy, & Cristini, Vittorio, & Goodman, Roy (2008). Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation.

*Discrete and Continuous Dynamical Systems*,*39*(4), 2203--2232.Goodman, Roy (2017). Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential.

*Physica D*,*359*, 39--59.Goodman, Roy, & Rahman, Aminur, & Bellanich, Michael, & Morrison, Catherine (2015). A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment.

*Chaos: An Interdisciplinary Journal of Nonlinear Science*,*25*, 8.Goodman, Roy, & Kevrekidis, Panayotis, & Carretero-González, Ricardo (2015). Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates.

*SIAM Journal of Applied Dynamical Systems / Society for Industrial and Applied Mathematics*,Goodman, Roy, & Marzuola, Jeremy, & Weinsten, Michael (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*,*35*(1), 225-246.Wrobel, Jacek, & Goodman, Roy (2013). High-order Adaptive Method for Computing Two-dimensional Invariant Manifolds of Maps.

*Communications in Nonlinear Science and Numerical Simulation*,*18*, 1734-1745.Goodman, Roy (2011). Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes.

*J. Phys. A Math. Theor.*,*44*(42), 425101 (28pp).Blawzddiewicz, J., & Goodman, Roy, & Khurana, N., & Wajnryb, E., & Young, Yuan-Nan (2010). Nonlinear hydrodynamic phenomena in Stokes flow regime.

*Physica D/Elsevier*,*239*(14), 1214-1224.Young, Yuan-Nan, & Blawzdiewiecz, Jerzy, & Cristini, Vittorio, & Goodman, Roy (2008). Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation.

*Journal of Fluid Mechanics*,*607*, 209-234.COLLAPSE

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

Markdown: A Writing Tool for Every Applied Mathematician's Toolbox

SIAM News, May 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

Book

Goodman, Roy (2019).

*Mathematical Analysis of Fractal Kink-Antikink Collisions in the phi-4 Model*. Springer-VerlagBook Review

Review of "Methods of Mathematical Modeling" by Witelski and Bowen

SIAM Review, May 2017

SIAM Review, May 2017