Professor of Mathematics and Associate Chair of the Department of Mathematics
Mathematics Department
Daytona College of Arts & Sciences
Daytona Beach campus

Areas of Expertise

1. PDEs: nonlinear evolution equations, water waves, soliton interactions, hydrodynamics and fluid mechanics
2. ODEs: nonlinear dynamical systems, bifurcation theory, integrability of Riccati and Abel equations, special functions
3. Mathematical physics, differential geometry, cosmology and inflation, nonlinear optics

Dr. Mancas  received a Ph.D. in Applied Mathematics from the University of Central Florida in May 2007 under the supervision of Dr. Roy S. Choudhury. His dissertation topic was "Dissipative Solitons in the cubic-quintic Complex Ginzburg Landau equation: Bifurcations and Spatiotemporal Structure" for which he received the Outstanding Dissertation Award.

His current areas of research  involve finding analytical solutions to nonlinear evolution equations and dynamical systems. The methods used are based primarily on bifurcation theory for dynamical systems, and techniques involving special functions and complex analysis with applications to water waves, soliton theory, biological systems, cosmology and inflation for evolution equations.

  • Ph.D. - Doctor of Philosophy in Mathematics, University of Central Florida
  • M.S. - Master of Science in Mathematical Science, University of Central Florida
  • B.S. - Bachelor of Science in Mathematics, University of Central Florida

  • MA 243HON: Calc & Analytical Geometry III

Numerical Methods in Fluids (MA 488/MA 595), Complex Analysis for Engineers (MA

443), Partial Differential Equations for Engineers (MA 442), Numerical Methods for Engineers with

MATLAB (MA 438), Linear Algebra (MA 432), Advanced Engineering Mathematics (MA 441),

Differential Equations (MA 345), Calculus with Analytic Geometry I, II and III (MA 241, MA 242

and MA 243), Analytic Trigonometry (MA 142), College Mathematics for Aviation II (MA 112)

Embry-Riddle Aeronautical University, Daytona-Beach, USA
Associate Chair Fall 2017 -- present
Professor Fall 2017 -- present

Hochschule Munchen/ Munich University of Applied Sciences, Munich, Germany
UAS7 Research Professor Fellowship Spring 2015 -- Summer 2015

Embry-Riddle Aeronautical University, Daytona-Beach, USA

Associate Professor Fall 2012 -- Summer 2017
Assistant Professor Fall 2007 -- Summer 2012

1. IPICyT, Instituto Potosino de Investigation Cientifica y Tecnologica, San Luis Potosi, Mexico,
July 2017
2. LeCosPA, Leung Center for Cosmology and Particle Astrophysics, National Taiwan University,
Taipei, December 2014
3. ICTP, International Centre for Theoretical Physics, Summer School on Cosmology, Trieste,
Italy, August 2014
4. IMECC-UNICAMP, Workshop on Nonlinear Dispersive Equations, Institute of Mathematics,
State University of Campinas, Brazil, October 2013
5. IPICyT, Instituto Potosino de Investigation Cientifica y Tecnologica, San Luis Potosi, Mexico,
August 2013
6. Secondary Calculus, Levi-Civita Institute, Dififety School, July 2011
7. Classical and Quantum Integrable Models, EPSRC/ London Mathematical Society, University
of Kent, UK, July 2010
8. Universita degli Studi di Milano, Italy, Dipartimento di Filologia Moderna, Italian language
and culture summer scholarship, May -- July 2006
9. NSF--UCF, 3D Optical Memory, Ecole Normale Superieur, Paris, France, May -- September

1. External (funded) (total $104,000)‚Äč
#1 MUAS, Hochschule Munchen/Munich University of Applied Sciences -- Visiting Research
Fellowship, March-August 2015, $18,000
#2 GFS Corp, Efficiency of a Diffuser -- CoPI, Summer 2012-2013, $31,000, with A. Ludu (PI)
#3 NASA-FSGC, Florida Space Grant Consortium, Aerodynamic Stability of Satellites
in Elliptic Low Earth Orbits -- PI, Fall 2009 -- Spring 2010, $20,000, with B. Udrea (CoPI)
#4 UCF,  Undergraduate to graduate fellowship,  Fall 2002 -- Fall 2004, $20,000
#5 NSF, International research fellowship -- College of Optics and Photonics, (CREOL) and Ecole Normale Superieur, Paris, France, May -- August 2001, $15,000

2. Internal (funded) (total $233,500)
#1 IGNITE-ERAU, Soliton Ship -- Faculty adviser to build an efficient soliton ship with
Honors College students, Summer 2014, $10,000
#2 ERAU, Nonlinear Waves Lab (NLWL3) -- to build a wave tank 32' x 4' x 4', President's
Office, Spring 2014, $136,000, with A. Ludu
#3 ERAU Faculty Internal Research Award,  An Investigation on the Nature of Micro
Cavitation Bubbles on the Movement of Undersea Vessels --  Summer 2013 -- Summer 2014,
#4 CNLS-2013, Summer Conference and Summer School --  Kathmandu, Nepal, Summer 2013,
$15,000, with H. Khanal (CoPI)
#5 ERAU, Nonlinear Waves Lab (NLWL2) -- to build a wave tank 16' x 4' x  4'  President's
Office, Summer 2011-Summer 2012, $35,000, with A. Ludu
#6 ERAU, Faculty Development Funding,  President's Office, Summer 2011, $3,500
#7 ERAU, Educational Technology", March 2011 to develop the Computational Math Lab (LB
120) with 8 Linux computers, and expanded later to 15 Linux computers in COAS 301.39,
#8 ERAU Faculty Internal Research Award, Chaotical and Erupting Solitons in the
Ginzburg--Landau Equation -- July 2009 -- June 2010, $7,500
#9 ERAU Faculty Internal Research Award, Spatiotemporal Structure of Dissipative Solitons
in the cubic--quintic Ginzburg--Landau equation -- July 2008 -- June 2009, $10,500