Course Syllabus

MATH 2250 Linear Algebra and Differential Equations

Course Description

This course explores principles of linear algebra and solving ordinary differential equations. Linear algebra topics will include systems of linear equations, matrix operations, vector spaces, eigenvectors, and diagonalization. Differential equations topics include ODEs, basic numerical methods, systems of first-order DEs, and Laplace transforms.Students in STEM majors should consult their program to determine if this course is required or the Math 2270 (Linear Algebra) & Math 2280 (Differential Equation) sequence is preferred.

Justification

This class is required for students in many engineering and science majors. The course lays a foundation in linear algebra and differential equations for students entering science-related fields. Knowledge and ability to solve systems of linear equations and differential equations are crucial to success in many engineering, mathematics, and science courses at the upper-division level.Currently some STEM programs allow this combination class while other STEM programs prefer Linear Algebra (Math 2270) and/or Differential Equations (Math 2280) as separate courses.

Student Learning Outcomes

1. Upon successful completion of this course, students will be able to solve foundational linear algebra problems (systems of equations, matrix operations, vectors and vector spaces)
2. Upon successful completion of this course, students will be able to solve problems involving eigensystems (diagonalization of matrices, systems of first-order DEs)
3. Upon successful completion of this course, students will be able to solve first-order and higher-order differential equations (including real-world applications)
4. Upon successful completion of this course, students will be able to apply Laplace transforms to solve differential equations
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Course Content

Linear Algebra topics will include systems of linear equations and their solutions; matrix operations and arithmetic; determinants and matrix inverses; vectors and vector spaces, including bases; eigenvalues, eigenvectors, and diagonalizationDifferential Equation topics will include mathematical modeling using differential equations; first-order differential equations and solution techniques; higher-order differential equations and solution techniques; introduction to numerical solutions (Euler’s Method); solving systems of (first-order) differential equations; Laplace transforms.