MAT 282 - Differential Equations w/Linear Algebra
First and second order differential equations. Matrices, determinants, eigenvalues and eigenvectors, and systems of linear equations. Linear independence, the Wronskian, and differential operators. Homogeneous and nonhomogeneous linear differential equations with constant coefficients. Methods of undetermined coefficients, and variation of parameters. Systems of linear differential equations, Laplace transforms, and power series solutions.
Prerequisite: MAT 182 Calculus II or equivalent
4 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Recognize and solve first and second order differential equations.
2. Extend the methods for first and second order differential equations to nth order differential equations, where applicable.
3. Solve a system of linear equations using elementary row operations and, when it exists, the inverse matrix for the system.
4. Understand the concept of a vector space and subspace.
5. Determine if a set of vectors is linearly independent.
6. Calculate and use the Wronskian.
7. Calculate eigenvalues and find the associated eigenvectors.
8. Use eigenvalues and matrix methods to solve a system of linear differential equations.
9. Use Laplace transforms to solve nth order linear initial-value problems and systems of linear differential equations.
10. Use power series to solve differential equations.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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