## MAT 2330 Differential Equations & Linear Algebra

Ordinary differential equations of first and second order including, the Laplace transform, numerical approximation methods and applications. Vectors in Rn, systems of linear equations, systems of differential equations, matrices, linear transformations, subspaces, dimension and rank, coordinate vectors, determinants, eigenvalues, eigenvectors and abstract vector spaces.

Division: Science, Mathematics and Engineering
Department: Mathematics
Repeatable Credit: No
Offered Online: Yes

Prereqs: MAT 2280 AND with a grade of C or better or satisfactory score on math placement test

#### Outcomes

• Demonstrate the ability to solve ordinary first order differential equations (including those that are separable, linear, or exact), and higher order equations using separation of variables, integrating factors, total differentials, substitutions, undetermined coefficients, variation of parameters, and Laplace Transforms. Use Laplace transforms and other methods to solve systems of differential equations.
• Demonstrate the ability to model real world applications with differential equations including series circuits, dynamic mixtures, population growth, Newton's Law of Cooling, driven and undriven spring/mass systems and others.
• Demonstrate the ability to approximate solutions to differential equations and initial value problems using direction fields, Euler methods and the Runge-Kutta method.
• Demonstrate the ability to solve linear systems of equations using Gauss-Jordan elimination and the inverse matrix method. Determine a basis and dimension for a vector space as well as the range, kernel, rank, nullity, and matrix representation of a linear transformation between vector spaces. Determine the results of basic matrix and vector operations as well as determine eigenvalues and eigenvectors of a matrix and then use them to diagonalize the matrix.

#### Credit Hours: 5

Classroom Hours: 5