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Clelland, Jeanne Professor

Positions

Research Areas research areas

Research

research overview

  • Dr. Clelland's research uses methods from geometry to study a variety of problems in differential equations, including differential equations that arise naturally in various contexts in differential geometry. Her recent and current research in this area includes the study of Backlund transformations for hyperbolic partial differential equations, dynamic equivalence and dynamic feedback linearization for control systems, and isometric immersion of Riemannian manifolds, among other topics. More recently, Dr. Clelland has begun studying the mathematics of redistricting, and in particular, mathematical methods for identifying and analyzing gerrymandering, with a particular focus on Colorado's Congressional and State Legislative district plans.

keywords

  • Geometry of differential equations, Exterior differential systems, Cartan's method of moving frames, Backlund transformations, Geometry of control systems, Dynamic equivalence for control systems, Isometric embeddings of Riemannian manifolds, Darboux integrability, Mathematics of redistricting and elections

Publications

selected publications

Teaching

courses taught

  • MATH 2001 - Introduction to Discrete Mathematics
    Primary Instructor - Spring 2019 / Fall 2019
    Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
  • MATH 3430 - Ordinary Differential Equations
    Primary Instructor - Spring 2018 / Fall 2019
    Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.
  • MATH 4230 - Differential Geometry of Curves and Surfaces
    Primary Instructor - Fall 2018 / Fall 2020
    Introduces the modern differential geometry of plane curves, space curves, and surfaces in 3-dimensional space. Topics include the Frenet frame, curvature and torsion for space curves; Gauss and mean curvature for surfaces; Gauss and Codazzi equations, and the Gauss-Bonnet theorem. Same as MATH 5230.
  • MATH 4470 - Partial Differential Equations
    Primary Instructor - Spring 2020 / Spring 2021
    Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods. Same as MATH 5470.
  • MATH 4810 - Special Topics in Mathematics
    Primary Instructor - Fall 2020
    Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 5810.
  • MATH 5230 - Differential Geometry of Curves and Surfaces
    Primary Instructor - Fall 2018 / Fall 2020
    Introduces the modern differential geometry of plane curves, space curves, and surfaces in 3-dimensional space. Topics include the Frenet frame, curvature and torsion for space curves; Gauss and mean curvature for surfaces; Gauss and Codazzi equations, and the Gauss-Bonnet theorem. Same as MATH 4230.
  • MATH 5470 - Partial Differential Equations
    Primary Instructor - Spring 2020 / Spring 2021
    Studies initial boundary and eigenvalue problems for the wave, heat and potential equations. Solution by separation of variables, Green's function, and variational methods. Department enforced prerequisite: MATH 3430 or MATH 5430. Instructor consent required for undergraduates. Same as MATH 4470.
  • MATH 5810 - Special Topics in Mathematics
    Primary Instructor - Fall 2020
    Covers various topics not normally covered in the curriculum. Offered intermittently depending on student demand and availability of instructors. May be repeated up to 7 total credit hours. Same as MATH 4810.
  • MATH 6230 - Introduction to Differential Geometry 1
    Primary Instructor - Spring 2018 / Spring 2019
    Introduces topological and differential manifolds, vector bundles, differential forms, de Rham cohomology, integration, Riemannian metrics, connections and curvature. Department enforced prerequisites: MATH 2130 and MATH 4001. Instructor consent required for undergraduates.

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