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MATH 327. Differential Equations with Linear Algebra

Credits: 4
Department: Mathematics
Description: Matrices and matrix operations, Gaussian elimination, determinants, Euclidean n-space and subspaces, dependence, eigenvalues, eigenvectors, diagonalization. Separable and first-order linear equations, second-order linear equations having constant coefficients, applications, systems of linear ODE's with constant coefficients, nonhomogenous linear systems, Laplace transforms.
Prerequisites: MATH 222
Semester Offered:
  • Fall
  • Spring
Grading Method: ABCDF

Student Learning Outcomes

1. Perform elementary row operations on matrices; determine and analyze solutions of a system of linear equations.
2. Perform matrix arithmetic, calculate determinants, and determine inverses to given matrices.
3. Compute the eigenvalues and eigenvectors of a matrix and diagonalize matrices.
4. Identify Euclidean spaces and subspaces.
5. Distinguish between dependent and linearly independent sets of vectors.
6. Recognize various types of differential equations and execute an appropriate method to arrive at an analytical or approximate solution.
7. Solve systems of linear first-order differential equations.
8. Use Laplace transforms to solve differential equations.
9. Apply appropriate technology to analyze differential equations.
10. Communicate quantitative ideas clearly and accurately.

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