The Department of Mathematics provides the mathematical foundation for Embry-Riddle’s degree programs, as well as a Bachelor of Science in Computational Mathematics degree and two minors, Applied Mathematics and Computational Mathematics.

Virtually every Embry-Riddle student — whether training to be a pilot, engineer, scientist, or manager — will pass through the Department of Mathematics while earning a degree. The flexibility of the Computational Mathematics degree allows well-prepared students to pursue dual majors, increasing their career options and enhancing their marketability to potential employers. Some students will gain foundational math skills, while others pursue innovative programs in pure and applied mathematics. The degree in Computational Mathematics allows students to blend mathematical theory and computational techniques to address problems that arise in a variety of scientific disciplines.

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Submissions from 2018

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Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation, Ronald Adams and Stefan C. Mancas

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Full Field Computing for Elastic Pulse Dispersion in Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, and V. Adamek

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Numerical Simulation of Energy Localization in Dynamic Materials, Arkadi Berezovski and Mihhail Berezovski

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An Asymptotic Analysis for Generation of Unsteady Surface Waves on Deep Water by Turbulence, Shahrdad Sajjadi

Submissions from 2017

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Dynamics of Discontinuities in Elastic Solids, Arkadi Berezovski and Mihhail Berezovski

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Numerical Simulation of Acoustic Emission During Crack Growth in 3-point Bending Test, Mihhail Berezovski and Arkadi Berezovski

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Traveling Wave Solutions for Wave Equations with Exponential Nonlinearities, S. C. Mancas, H. C. Rosu, and M. Perez-Maldonado

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Traveling Wave Solutions to Kawahara and Related Equations, Stefan C. Mancas

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Elliptic Solutions and Solitary Waves of a Higher Order KdV-BBM Long Wave Equation, Stefan C. Mancas and Ronald Adams

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Generalized Thomas-Fermi Equations as the Lampariello Class of Emden-Fowler Equations, Haret C. Rosu and Stefan C. Mancas

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Variational Principle for Velocity-Pressure Formulation of Navier-Stokes Equations, Shahrdad Sajjadi

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A Regression Model to Predict Stock Market Mega Movements and/or Volatility Using Both Macroeconomic Indicators & Fed Bank Variables, Timothy A. Smith and Alcuin Rajan

Submissions from 2016

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Thermoelastic Waves in Microstructured Solids, Arkadi Berezovski and Mihhail Berezovski

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Growth of Groups of Wind Generated Waves, Frederique Drullion and Shahrdad Sajjadi

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Evolution of Spherical Cavitation Bubbles: Parametric and Closed-Form Solutions, Stefan C. Mancas and Haret C. Rosu

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Existence of Periodic Orbits in Nonlinear Oscillators of Emden-Fowler Form, Stefan C. Mancas and Haret C. Rosu

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Integrable Abel Equations and Vein's Abel Equation, Stefan C. Mancas and Haret C. Rosu

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Micro Cavitation Bubbles on the Movement of an Experimental Submarine: Theory and Experiments, Stefan C. Mancas, Shahrdad G. Sajjadi, Asalie Anderson, and Derek Hoffman

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Signal Flow Graph Approach to Efficient DST I-IV Algorithms, Sirani M. Perera

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Nongauge Bright Soliton of the Nonlinear Schrodinger (NLS) Equation and a Family of Generalized NLS Equations, M. A. Reyes, D. Gutierrez-Ruiz, S. C. Mancas, and H. C. Rosu

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Ermakov Equation and Camassa-Holm Waves, Haret C. Rosu and Stefan C. Mancas

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Growth of Stokes Waves Induced by Wind on a Viscous Liquid of Infinite Depth, Shahrdad Sajjadi

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Exact Analytical Solution of Viscous Korteweg-deVries Equation for Water Waves, Shahrdad G. Sajjadi and Timothy A. Smith

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Growth of Unsteady Wave Groups by Shear Flows, Shahrdad Sajjadi, Julian Hunt, and Frederique Drullion

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Wave Motion Induced By Turbulent Shear Flows Over Growing Stokes Waves, Shahrdad Sajjadi, Serena Robertson, Rebecca Harvey, and Mary Brown

Submissions from 2015

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Two-Dimensional Structures in the Quintic Ginzburg-Landau Equation, Florent Bérard, Charles-Julien Vandamme, and Stefan C. Mancas

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Pattern Formation of Elastic Waves and Energy Localization Due to Elastic Gratings, A. Berezovski, J. Engelbrecht, and Mihhail Berezovski

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Pulses and Snakes in Ginzburg-Landau Equation, Stefan C. Mancas and Roy S. Choudhury

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Integrable Equations with Ermakov-Pinney Nonlinearities and Chiellini Damping, Stefan C. Mancas and Haret C. Rosu

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Barotropic FRW Cosmologies with Chiellini Damping, Haret C. Rosu, Stefan C. Mancas, and Pisin Chen

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Barotropic FRW Cosmologies with Chiellini Damping in Comoving Time, Haret C. Rosu, Stefan C. Mancas, and Pisin Chen

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One-Parameter Supersymmetric Hamiltonians in Momentum Space, H. C. Rosu, S. C. Mancas, and P. Chen

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Formation of Three-Dimensional Surface Waves on Deep-Water Using Elliptic Solutions of Nonlinear Schrödinger Equation, Shahrdad G. Sajjadi, Stefan C. Mancas, and Frederique Drullion

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An Economic Regression Model to Predict Market Movements, Timothy A. Smith and Andrew Hawkins

Submissions from 2014

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Computational Models for Nanosecond Laser Ablation, Harihar Khanal, David Autrique, and Vasilios Alexiades

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Ermakov-Lewis Invariants and Reid Systems, Stefan C. Mancas and Haret C. Rosu

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A Fast Algorithm for the Inversion of Quasiseparable Vandermonde-like Matrices, Sirani M. Perera, Grigory Bonik, and Vadim Olshevsky

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One-Parameter Families of Supersymmetric Isospectral Potentials From Riccati Solutions in Function Composition Form, Haret C. Rosu, Stefan C. Mancas, and Pisin Chen

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Shifted One-Parameter Supersymmetric Family of Quartic Asymmetric Double-Well Potentials, Haret C. Rosu, Stefan C. Mancas, and Pisin Chen

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A Regression Model to Investigate the Performance of Black-Scholes using Macroeconomic Predictors, Timothy A. Smith, Ersoy Subasi, and Aliraza M. Rattansi

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Not All Traces On the Circle Come From Functions of Least Gradient in the Disk, Gregory S. Spradlin and Alexandru Tamasan

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Variable Viscosity Condition in the Modeling of a Slider Bearing, Kedar Nath Uprety and Stefan C. Mancas

Submissions from 2013

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Hydrodynamic Modeling of ns-Laser Ablation, David Autrique, Vasilios Alexiades, and Harihar Khanal

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Dispersive Waves in Microstructured Solids, A. Berezovski, J. Engelbrecht, A. Salupere, K. Tamm, T. Peets, and Mihhail Berezovski

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Influence of Microstructure on Thermoelastic Wave Propagation, Arkadi Berezovski and Mihhail Berezovski

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Time-Stepping for Laser Ablation, Harihar Khanal, David Autrique, and Vasilios Alexiades

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Integrable Dissipative Nonlinear Second Order Differential Equations Via Factorizations and Abel Equations, Stefan C. Mancas and Haret C. Rosu

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Weierstrass Traveling Wave Solutions for Dissipative Benjamin, Bona, and Mahoney (BBM) Equation, Stefan C. Mancas, Greg Spradlin, and Harihar Khanal

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A Study of Energy Transfer of Wind and Ocean Waves, Shahrdad Sajjadi and Mason Bray

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Asymptotic Multi-Layer Analysis of Wind Over Unsteady Monochromatic Surface Waves, Shahrdad Sajjadi, Julian Hunt, and Frederique Drullion

Submissions from 2012

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Wave Propagation and Dispersion in Microstructured Solids, Arkadi Berezovski, Juri Engelbrecht, and Mihhail Berezovski

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On the Stability of a Microstructure Model, Mihhail Berezovski and Arkadi Berezovski

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ACE - A Model Centered REU Program Standing on the Three Legs of CSE: Analysis, Computation and Experiment, Hong P. Liu and Andrei Ludu

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Vortex Patterns Beyond Hypergeometric, Andrei Ludu

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Topology and Geometry of Mixing of Fluids, Andrei Ludu, Stefan Mancas, Ionutz Ionescu, Audrey Gbagaudi, and Matthew Schumacher

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2D Novel Structures Along an Opitcal Fiber, Charles-Julien Vandamme and Stefan C. Mancas

Submissions from 2011

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Dispersive Wave Equations for Solids with Microstructure, A. Berezovski, Juri Engelbrecht, and Mihhail Berezovski

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Two-Scale Microstructure Dynamics, Arkadi Berezovski, Mihhail Berezovski, and Juri Engelbrecht

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Waves in Microstructured Solids: A Unified Viewpoint of Modelling, Arkadi Berezovski, Juri Engelbrecht, and Mihhail Berezovski

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On the Stability of a Microstructure Model, Mihhail Berezovski and Arkadi Berezovski

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Interactions and Focusing of Nonlinear Water Waves, Harihar Khanal, Stefan C. Mancas, and Shahrdad Sajjadi

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Differential Geometry of Moving Surfaces and Its Relation to Solitons, Andrei Ludu

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Solitary Waves, Periodic and Elliptic Solutions to the Benjamin, Bona & Mahony (BBM) Equation Modified by Viscosity, Stefan C. Mancas, Harihar Khanal, and Shahrdad G. Sajjadi

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Turbulence and Wave Dynamics Across Gas–Liquid Interfaces, Shahrdad Sajjadi, Julian Hunt, Stephen Belcher, Derek Stretch, and John Clegg

Submissions from 2010

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Spatiotemporal Two-Dimensional Solitons in the Complex Ginzburg-Landau Equation, Florent Berard and Stefan C. Mancas

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Waves in Materials with Microstructure: Numerical Simulation, Mihhail Berezovski, Arkadi Berezovski, and Juri Engelbrecht

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Deformation Waves in Microstructured Materials: Theory and Numerics, Juri Engelbrecht, Arkadi Berezovski, and Mihhail Berezovski

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Book Review: Visual Motion of Curves and Surfaces, Andrei Ludu

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Elements of Study on Dynamic Materials, Marine Rousseau, Gerard A. Maugin, and Mihhail Berezovski

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Numerical Studies of Particle Laden Flow in Dispersed Phase, Shahrdad Sajjadi and Rumma Dutta

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On Osgood's Criterion for Classical Wave Equations and Nonlinear Shallow Water Wave Equations, Timothy Smith and Greg Spradlin

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Heteroclinic Solutions to an Asymptotically Autonomous Second-Order Equation, Gregory S. Spradlin

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Temporal Scales for Transport Patterns in the Gulf of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, and Mihhail Berezovski

Submissions from 2009

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Waves in Inhomogeneous Solids, Arkadi Berezovski, Mihhail Berezovski, and Juri Engelbrecht

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Periodic and Chaotic Traveling Wave Patterns in Reaction-Diffusion/Predator-Prey Models with General Nonlinearities, Stefan C. Mancas and Roy S. Choudhury

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Spatiotemporal Structure of Pulsating Solitons in the Cubic-Quintic Ginzburg-Landau Equation: A Novel Variational Formulation, Stefan C. Mancas and S. Roy Choudhury

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Numerical Simulations of Snake Dissipative Solitons in Complex Cubic-Quintic Ginzburg-Landau Equation, Stefan C. Mancas and Harihar Khanal

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Interaction of Tollmien-Schlichting Waves in the Air with the Sea Surface, Shahrdad G. Sajjadi and Harihar Khanal

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On Nonlinear Generalizations of the KdV and BBM Equations from Long Range Water Wave Theory, Timothy A. Smith

Submissions from 2008

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Models of Phototransduction in Rod Photoreceptors, Harihar Khanal and Vasilios Alexiades

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On Existence and Uniqueness Results for the BBM Equation with Arbitrary Forcing Terms, Timothy A. Smith

Submissions from 2007

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Multiphoton Response of Retinal Rod Photoreceptors, Vasilios Alexiades and Harihar Khanal

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Numerical Simulation of Waves and Fronts in Inhomogeneous Solids, A. Berezovski, M. Berezovski, J. Engelbrecht, and G. A. Maugin

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Bifurcations of Plane Wave (CW) Solutions in the Complex Cubic-Quintic Ginzburg-Landau Equation, Stefan C. Mancas and S. Roy Choudhury

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The Complex Cubi-Quintic Ginzburg-Landau Equation: Hopf Bifurcations Yielding Traveling Waves, Stefan C. Mnacas and S. Roy Choudhury

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Scattered Homoclinics to a Class of Time-Recurrent Hamiltonian Systems, Gregory S. Spradlin

Submissions from 2006

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Oscillation Criteria for First-Order Forced Nonlinear Difference Equations, Ravi P. Agarwal, Said R. Grace, and Tim Smith

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Numerical Simulation of Nonlinear Elastic Wave Propagation in Piecewise Homogeneous Media, Arkadi Berezovski, Mihhail Berezovski, and Juri Engelbrecht

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On Doubly Periodic Solutions of Quasilinear Hyperbolic Equations of the Fourth Order, T. Kiguradze and T. Smith

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Bifurcations and Competing Coherent Structures in the Cubic-Quintic Ginzburg-Landau Equation I: Plane Wave (CW) Solutions, Stefan C. Mancas and S. Roy Choudhury

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Traveling Wavetrains in the Complex Cubic-Quintic Ginzburg-Laundau Equation, Stefan C. Mancas and S. Roy Choudhury

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An Elliptic Equation with No Monotonicity Condition on the Nonlinearity, Gregory S. Spradlin

Submissions from 2004

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Response of Dark-Adapted Retinal Rod Photoreceptors, H. Khanal, V. Alexiades, and E. Dibenedetto

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Existence of Solutions to a Hamiltonian System Without Convexity Condition on the Nonlinearity, Gregory S. Spradlin

Submissions from 2003

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Computational Models for Diffusion of Second Messengers in Visual Transduction, Harihar Khanal

Submissions from 2002

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Coupling of COAMPS and WAVETECH with Improved Wave Physics, Shahrdad Sajjadi, Pat Fitzpatrick, Gueorgui Mostovoi, Yongzuo Li, and Matt Bettencourt

Submissions from 2001

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Two Photon Absorption in Chromophore Doped Solid Matrices, Stefan Mancas, Michael Canva, Yves Levy, Kathleen A. Richardson, and Giselle Roger

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Interfering Solutions of a Nonhomogeneous Hamiltonian System, Gregory S. Spradlin

Submissions from 2000

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An Elliptic Equation With Spike Solutions Concentrating at Local Minima of the Laplacian of the Potential, Gregory S. Spradlin

Submissions from 1996

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An Almost Periodic Function of Several Variables With No Local Minimum, Gregory S. Spradlin