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.

#### Submissions from 2018

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

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

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

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

#### Submissions from 2017

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

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

Differential Equations of Dynamical Order, Andrei Ludu and Harihar Khanal

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

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

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

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

Almost-BPS Solutions in Multi-Center Taub-NUT, C. Rugina and A. Ludu

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

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

Thermoelastic Waves in Microstructured Solids, Arkadi Berezovski and Mihhail Berezovski

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

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

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

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

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

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

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

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

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

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

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

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

#### Submissions from 2015

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

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

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

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

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

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

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

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

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

#### Submissions from 2014

An Alternate Proof of the De Branges Theorem on Canonical Systems, Keshav R. Acharya

Self-Adjoint Extension and Spectral Theory of a Linear Relation in a Hilbert Space, Keshav R. Acharya

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

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

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

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

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

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

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

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

#### Submissions from 2013

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

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

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

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

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

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

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

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

#### Submissions from 2012

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

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

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

Vortex Patterns Beyond Hypergeometric, Andrei Ludu

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

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

#### Submissions from 2011

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

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

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

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

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

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

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

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

#### Submissions from 2010

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

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

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

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

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

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

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

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

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

#### Submissions from 2009

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

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

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

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

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

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

#### Submissions from 2008

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

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

#### Submissions from 2007

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

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

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

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

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

#### Submissions from 2006

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

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

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

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

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

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

#### Submissions from 2004

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

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

#### Submissions from 2003

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

#### Submissions from 2002

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