Part-Time Programs in Engineering and Applied Science, Johns Hopkins University

Linear Algebra and Differential Equations
505.119

Course Description
This course explores basic concepts of linear algebra, matrix theory, and differential equations as they relate to and are applied in engineering and science. Systems of linear equations, vector spaces, linear transformations, linear independence and bases, matrices, and eigenvalues and eigenvectors are studied, as well as first- and higher-order linear differential equations and systems. 

Syllabus

  1. First Order Differential  Equations: Introduction, Separation of Variables, First Order Linear Equations.
  2. Higher Order Differential Equations: Spring Models, a Strategy, Homogeneous Linear Equations with Real Roots, Complex Roots.
  3. Nonhomogeneous Linear Equations: Undetermined Coefficients, Variation of Parameters, Applications.
  4. General Properties: Determinants, Wronskians, Linear Independence of Functions. Test I
  5. Linear Systems of Algebraic Equations: Row Reduced Echelon Form, Vectors and Linear Independence of Vectors.
  6. Matrix Algebra, Matrix Equations, Systems of First Order Linear Differential Equations.
  7. Solutions of Homogeneous Systems of First Order Ordinary Differential Equations, Eigen-Values and Eigen-Vectors.
  8. Homogeneous Systems with Constant Coefficients and Real Eigenvalues, and Complex Eigenvalues.
  9. Non-homogeneous Systems, Variation of Parameters, and Applications. Test II
  10. Vector Spaces: Definitions, Subspaces, Spanning Sets.
  11. Linear Independence and Bases, Dimension.
  12. Linear Transformations, Invertible Matrices.
  13. Application of Linear Transformations to Ordinary Differential Equations, Systems of Differential Equations, and Systems of Linear Algebraic Equations.
  14. Test III

Instructor
James M. D'Archangelo received his Ph.D. in mathematics from Johns Hopkins University in 1973. Dr. D'Archangelo has been a professor of mathematics at the United States Naval Academy from 1973.
E-mail the instructor.

Textbook
Differential Equations with Linear Algebra by Z. H. Nitecki and M. M. Guterman

Return to Undergraduate Engineering Courses | General Engineering | Part-Time Engineering

Fall 1998