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
2023 Spring Courses
MATH 792B - PRE DOCTORAL RESEARCH
MATH 790A - DOCT DISSERTATION & RES
MATH 790B - DOCT DISSERTATION & RES
MATH 614 - NUMERICAL METHODS I
MATH 791 - GRADUATE SEMINAR
MATH 790C - DOCT DISSERTATION & RES
MATH 790A - DOCT DISSERTATION & RES
MATH 790B - DOCT DISSERTATION & RES
MATH 614 - NUMERICAL METHODS I
MATH 791 - GRADUATE SEMINAR
MATH 790C - DOCT DISSERTATION & RES
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
Adriazola, Jimmie, & Goodman, Roy (2022). An Optimal Control Approach to Gradient-Index Design for Beam Reshaping. Journal of the Optical Society of America A, 39(5), 907--915.
Adriazola, Jimmie, & Goodman, Roy A Reduction-Based Strategy for Optimal Control of Bose-Einstein Condensates. Physical Review E, 105, 025311(1-16).
Favor, Timothy, & Goodman, Roy, & Wright, J. (2020). Solitary Waves in Mass-in-Mass Lattices. 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.
Adriazola, Jimmie, & Goodman, Roy A Reduction-Based Strategy for Optimal Control of Bose-Einstein Condensates. Physical Review E, 105, 025311(1-16).
Favor, Timothy, & Goodman, Roy, & Wright, J. (2020). Solitary Waves in Mass-in-Mass Lattices. 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.
SHOW MORE
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.
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.
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.
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-Verlag
Book Review
Review of "Methods of Mathematical Modeling" by Witelski and Bowen
SIAM Review, May 2017
SIAM Review, May 2017