Course Syllabus
Course: MATH 2250
Division: Natural Science and Math
Department: Mathematics
Title: Linear Algebra and Differential Equations
Semester Approved: Summer 2022
Five-Year Review Semester: Spring 2027
End Semester: Spring 2028
Catalog 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.
Semesters Offered: Fall, Spring
Credit/Time Requirement: Credit: 4; Lecture: 4; Lab: 0
Prerequisites: MATH 2210
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:
Solve foundational linear algebra problems. A student's understanding will be assessed with quizzes, homework, and exams.
Use standard methods to solve differential equations. A student's understanding will be assessed with quizzes, homework, and exams.
Utilize differential equations to model and solve typical physical phenomena. A student's understanding will be assessed with quizzes, homework, and exams.
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.
Key Performance Indicators:
Students will demonstrate competency of the Student Learning Outcomes by:
Homework 10 to 20%
Midterm Tests 30 to 60%
Quizzes and/or Oral Presentations 0 to 20%
Comprehensive Final Exam 15 to 30%
Representative Text and/or Supplies:
The text will be selected by the instructor with departmental approval. A representative textbook is "Differential Equations and Linear Algebra" by C. Henry Edwards and and David E. Penney, current edition.
Students should also have access to a graphing calculator (TI 83/84 or equivalent).
Pedagogy Statement:
During lecture and interactive class discussions, students are encouraged to ask and help answer questions about how to apply problem-solving techniques. This helps all students have multiple opportunities to understand the techniques.
Instructional Mediums:
Lecture
Maximum Class Size: 40
Optimum Class Size: 25
