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Mathematical Methods in Engineering I

Mark J. McCready
Organization: University of Notre Dame
Department: Department of Chemical Engineering
Education level


Development of a comprehensive, but introductory, understanding of linear analysis as applied to algebraic and differential systems. This is done by applying the general solution methods, inverse operators and spectral expansions, to a variety of problems chosen for either their physical or mathematical interest.

    * Mathematical Methods in Chemical Engineering by Varma and Morbidelli Oxford (1997) * Principles and Techniques of Applied Mathematics by Friedman Dover (1990) * Foundations of Applied Mathematics by Greenberg Prentice-Hall (1978)

This is an applied math course that is intended to serve the dual role of being the only graduate mathematics class for many chemical engineers (suggesting a need for breadth) but just the first of many others (suggesting a need for some depth) It is application motivated and problem based. Proofs are done only when they give special insight.

Topics include a comprehensive introduction to linear algebra, a selected treatment of ordinary differential equations as they apply to important problems in engineering and science and a brief introduction to partial differential equations that arise in science and engineering. Every attempt is made to unify the linear operator concept throughout the topics of this course.

Linear algebra:
  • Basic linear algebra
  • Applications of linear algebra
  • Linear spaces and linear operators
  • Algebraic eigenvalue problems

Linear ordinary differential equations:
  • Initial value problems
  • Boundary value problems
  • Differential eigenvalue problems

Partial Differential Equations:
  • Order and classifications
  • Separation of variables
  • Similarity solutions
  • Finite Fourier Transform

*Engineering > Chemical Engineering