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

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

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.

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.

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

*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. SHOW MORE

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.

*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,

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,

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