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.
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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