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Fornberg, Bengt

Professor Emerita/Emeritus

Positions

Research Areas research areas

Research

research overview

  • Prof. Fornberg's work is focused on radial basis function (RBF) based numerical methods, applicable to a wide range of PDEs, arising for example in the geosciences and for wave propagation. He has also recently developed methods for numerical quadrature, for solving the PainlevĂ© equations, and for computations in the complex plane.

keywords

  • Numerical methods for ODEs and PDEs, quadrature, complex variables, analytic functions, finite differences, spectral methods, radial basis function methods, computational fluid dynamics, PainlevĂ© equations

Publications

selected publications

Teaching

courses taught

  • APPM 2360 - Introduction to Differential Equations with Linear Algebra
    Primary Instructor - Fall 2018 / Fall 2019
    Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Credit not granted for this course and both MATH 2130 and MATH 3430.
  • APPM 4360 - Methods in Applied Mathematics: Complex Variables and Applications
    Primary Instructor - Spring 2023
    Introduces methods of complex variables, contour integration and theory of residues. Applications include solving partial differential equations by transform methods, Fourier and Laplace transforms and Reimann-Hilbert boundary-value problems, conformal mapping to ideal fluid flow and/or electrostatics. Same as APPM 5360.
  • APPM 4380 - Modeling in Applied Mathematics
    Primary Instructor - Fall 2020
    An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics may include: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Recommended prerequisites: APPM 3310 and APPM 4350 and APPM 4650. Same as APPM 5380.
  • APPM 4660 - Intermediate Numerical Analysis 2
    Primary Instructor - Spring 2020
    Continuation of APPM 4650. Examines numerical solution of initial-value problems and two-point boundary-value problems for ordinary differential equations. Also looks at numerical methods for solving partial differential equations. Department enforced prerequisite: knowledge of a programming language. Same as MATH 4660.
  • APPM 5380 - Modeling in Applied Mathematics
    Primary Instructor - Fall 2020
    An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics may include: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Department enforced prerequisites: APPM 2350 or MATH 2400 and APPM 2360. Recommended prerequisites: APPM 3310 and APPM 4350 and APPM 4650. Same as APPM 4380.
  • APPM 5610 - Numerical Analysis 2
    Primary Instructor - Spring 2019
    Numerical linear algebra, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Department enforced prerequisite: APPM 5600 or MATH 5600.
  • APPM 7400 - Topics in Applied Mathematics
    Primary Instructor - Spring 2018 / Spring 2020 / Spring 2021
    Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours.
  • MATH 5610 - Numerical Analysis 2
    Primary Instructor - Spring 2019
    Solution of linear systems, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Department enforced prerequisite: MATH 5600 or APPM 5600. Instructor consent required for undergraduates.

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