School of Mathematical Sciences
College of Science
School of Mathematical Sciences
College of Science
BS, University of Iasi (Romania); Ph.D., University of Rochester
Areas of Expertise
This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course.
This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals.
This course covers the algebra of complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy's integral theorem and integral formulas, Taylor and Laurent series, residues, and the calculation of real-valued integrals by complex-variable methods.
This course will provide a general introduction to Lebesgue measure as applied to the real numbers, real-valued functions of a real variable, and the Lebesgue integral of such functions. It also covers topics in functional analysis relevant to application of measure theory to real-world problems. Students will be expected to read and understand proofs, and to demonstrate their understanding of topics by writing their own proofs of various facts.
1 - 3 Credits
This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.
1 - 3 Credits
Felea,, R. and R. Gaburro, A. Greenleaf, C. Nolan. "Microlocal Analysis of Doppler SAR." Inverse problems and Imaging 13. 6 (2019): 1283-1307. Web.
Felea, Raluca, et al. "A Class of Singular FIOs in SAR Imaging II: Transmitter and Receiver with Different Speeds." SIAM Journal of Math Analysis 50. 1 (2018): 591-621. Print.
Felea, R., et al. "Common Midpoint Versus Common Offset Acquisition Geometry in Seismic Imaging." Inverse Problems and Imaging 10. 1 (2016): 87-102. Print.
Felea, Raluca and Cliff Nolan. "Monostatic SAR with fold/cusp singularities." Journal of Fourier Analysis and Applications 21. 4 (2015): 799-821. Print.
Felea, Raluca, Romina Gaburro, and Cliff Nolan. "Microlocal Analysis of SAR Imaging of a Dynamic Reflectivity Function." SIAM J on Math Analysis 45. 5 (2013): 2767-2789. Print.
Ambartsoumian, Gaik, et al. "A Class of Singular Fourier Integral Operators in Synthetic Aperture Radar Imaging." Journal of Functional Analysis 264. 1 (2013): 246-269. Print.
Felea, Raluca and Todd Quinto. "The Microlocal Properties of the Local 3-D SPECT Operator." SIAM J on Math Analysis 43. 3 (2011): 1145-1157. Web.
Felea, Raluca. "Generalized Radon Transform with Cusp Singuarities." Conference on Modern Challenges in Imaging In the Footsteps of Allan MacLeod Cormack. Tufts University. Boston, MA. 7 Aug. 2019. Conference Presentation.
Felea, Raluca . "Micolocal Analysis of Doppler SAR." Conference on Mathematics of Wave Phenomena. Karlsruhe Institute of Technology. Karlsruhe, Germany. 24 Jul. 2018. Conference Presentation.
Felea, Raluca . "Microlocal Analysis of Monostatic SAR and Doppler SAR." Analysis Seminar. Purdue Univ. Purdue, IN. 26 Mar. 2018. Guest Lecture.
Felea, Raluca . "FIOs with Singularities in SAR." February Fourier Talks. University of Maryland. College Park, MD. 15 Feb. 2018. Guest Lecture.
Felea, R. "The Microlocal Analysis of some Inverse Problems in Bistatic SAR." LMS-EPSRC Durham Symposium 2016: Mathematical and Computational Aspects of Maxwell's Equations. University of Durham. Durham, UK, UK. 17 Jul. 2016. Conference Presentation.
Felea, R. "Common Midpoint and Common Offset in Seismic Imaging." Inverse Problems Symposium. Virginia Military Institute. Lexington, VA. 7 Jun. 2016. Conference Presentation.
Felea, Raluca. "Monostatic SAR with inflection points." Computational and Analytical Aspects of Image Reconstruction. ICERM, Brown University. Providence, RI. 13 Jul. 2015. Keynote Speech.
Felea, Raluca. "Fourier integral operators with cusp singularities." Program on Inverse Problems. Institut Henri Poincare. Paris, France. 11 Jun. 2015. Conference Presentation.
Felea, Raluca. "Inverse problems in bistatic SAR with different speeds." Applied Inverse Problems Conference. University of Helsinki. Helsinki, Finland. 29 May 2015. Conference Presentation.
Felea, Raluca. "Microlocal analysis of FIOs with singularities." Analysis Seminar. SUNY Albany. Albany, NY. 20 May 2015. Guest Lecture.
Felea, Raluca. "Microlocal analysis in seismic imaging." Central Spring Sectional Meeting. Michigan State University. East Lansing, MI. 15 Mar. 2015. Conference Presentation.
Felea, Raluca. "Microlocal Analysis of FIOs with Fold/cusp Singularities." 30th Southeastern Analysis Meeting. Clemson University. Clemson, SC. 8 Mar. 2014. Conference Presentation.
Felea, Raluca. "Microlocal Analysis of SAR with Moving Objects." Geometry and Inverse Problems Workshop. Banff International Research Center. Banff, Canada. 17 Sep. 2013. Conference Presentation.
Raluca, Felea. "An Inverse Problem in Common Midpoint SAR Imaging." 2012 Spring Southeastern Section Meeting. University of South Florida. Tampa, FL. 10 Mar. 2012. Conference Presentation.
Felea, Raluca. "Microlocal Analysis of Common Midpoint SAR Imaging." 2012 SIAM Conference on Imaging Science. SIAM. Philadelphia, PA. 20 May 2012. Conference Presentation.
Felea, Raluca. "Microlocal Analysis of SAR Imaging with Moving Objects." Math Seminar. University of Binghampton. Binghampton, NY. 5 Dec. 2012. Guest Lecture.
Felea, Raluca. "Common Singularities in SPECT and SAR Inverse Problems." Inverse Problems Program. Isaac Newton Institute. Isaac Newton Institute, Cambridge, England. 15 Nov. 2011. Conference Presentation.
Felea, Raluca. "A Class of Singular FIOs." seminar talk. Loughborough University. Loughborough, Loughborough, England. 9 Nov. 2011. Guest Lecture.
Felea, Raluca. "Folds and Cusp Singularities in Seismic Inverse Problems." seminar talk. Limerick University. Limerick, Limerick, Ireland. 19 Oct. 2011. Guest Lecture.
Felea, Raluca. "Microlocal Analysis of the Slant-hole SPECT Operator." Medical and Seismic Imaging Workshop. University of British Columbia. Vancouver, Vancouver, Canada. 15 Jul. 2011. Conference Presentation.
Felea, Raluca. "Microlocal Analysis of FIOs with Singularities." International Conference on Microlocal Methods in Mathematical Physics and Global Analysis. Tubingen University. Tubingen, Tubingen, Germany. 16 Jun. 2011. Conference Presentation.
Felea, Raluca. "Fourier Integral Operators with Singularities." 27th South Eastern Analysis Meeting and John Conway Day. University of Florida. Gainesville, Gainesville, FL. 19 Mar. 2011. Conference Presentation.
Felea, Raluca. "Microlocal Properties of the Slant-hole SPECT Operator." Joint Mathematics Meetings. AMS. New Orleans, New Orleans, LA. 6 Jan. 2011. Conference Presentation.
External Scholarly Fellowships/National Review Committee
7/1/2011 - 7/1/2016
Felea, Raluca and Alan Greenleaf. “FIOs with open umbrellas and seismic inversion for cusp caustics.” Mathematics Research Letters, 17.5 (2010): 867-886. Print. *
Felea, Raluca. “FIOs with open umbrellas. Special section on harmonic analysis and PDEs.” 2010 Spring Western Section Meeting. Albuquerque, NM. 17-18 April 2010. Presentation.
Felea, Raluca. “FIOs with fold and cusp singularities. Special Session on Inverse Problems, Riemann-Hilbert Problems, and NonlinearDispersive Equations.” 2010 Spring Southeastern Sectional Meeting. Lexington, KY. 27-28 March 2010.Presentation.