Matrix Methods and ODEs MATH 3513

Upon successful completion of this course, the student will be able to:

• Carry out matrix algebra operations.
• Solve systems of linear equations using Cramers', Gauss-Jordan and inversion of matrices.
• Use matrix differentiation to linearize matrices of functions for position estimates.
• Solve vector problems involving distance and direction in 2D and 3D space.
• Calculate eigenvalues and eigenvectors and use them to find the magnitude and directions of the semi-major and semi-minor axes of error ellipses.
• Calculate and apply quadratic forms.
• Describe vector spaces, real and complex, and look at projections from one space to another.
• Relate the ellipse of error to the bivariate normal distribution and link to the covariance matrix.
• Formulate the initial value and boundary value problems of differential equation theory.
• Set up and interpret models of practical engineering problems using differential equations.
• Solve separable and linear first-order differential equations in practical problems.
• Solve first-, second- and higher-order ordinary differential equations and investigate the properties of the solutions.
• Reduce higher-order differential equations to an equivalent system of first-order differential equations.
• Solve homogeneous higher-order linear differential equations with constant coefficients using eigenvalue methods.
• Use the methods of undetermined coefficients and variation of parameters to extend this to the inhomogeneous case.

Effective as of Fall 2024