Course Syllabus

MATH 2250 Linear Algebra and Differential Equations

Course Description

This course explores methods of solving ordinary differential equations which describe much of the physical phenomena in our world. Linear algebra topics will include systems of linear equations, matrix operations, vector spaces, and eigensystems. The course examines techniques for solving linear and nonlinear first-order differential equations as well as higher-order linear equations. Other topics will include initial-value problems, Laplace transforms, numerical methods, and modeling.

The course is designed for students with majors in specific engineering and science disciplines. Students with majors in other science and engineering disciplines, and students with a mathematics major should take Math 2270 (Linear Algebra) and Math 2280 (Differential Equations) instead of Math 2250.

Justification

This class is required for students in specific engineering and science majors, such as chemistry, mechanical engineering, and civil engineering, at the senior institutions of Utah, particularly Utah State University, University of Utah, and Weber State University. 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 most of Utah's universities provide two routes for students needing linear algebra and differential equations. Students majoring in mathematics, computer science, software engineering, electrical engineering, etc. must take Linear Algebra (Math 2270) and/or Differential Equations (Math 2280) as separate courses. Students studying chemistry, mechanical engineering, civil engineering, etc. typically take Math 2250 (Linear Algebra & Differential Equations) as a combination class.

Student Learning Outcomes

1. Solve foundational linear algebra problems.
2. Use standard methods to solve differential equations.
3. Utilize differential equations to model and solve typical physical phenomena.
4. 
   

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 diagonalization

Differential 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

The problem-solving techniques taught in the course have been developed by people from a variety of languages and backgrounds. The methods learned apply to real-world problems across the world.