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Course Syllabus

Course: MATH 2280

Division: Natural Science and Math
Department: Mathematics
Title: Differential Equations

Semester Approved: Spring 2023
Five-Year Review Semester: Fall 2027
End Semester: Fall 2028

Catalog Description: This is a course which covers methods of solving ordinary differential equations. The class is designed to meet the needs of math, engineering, and certain science majors. Included in the class are techniques for finding solutions to linear and nonlinear first-order differential equations as well as higher-order linear equations with constant and variable coefficients. Laplace transforms, power series solutions, and several numerical approximation methods are also addressed. Some mathematical modeling of differential equations is included.

Semesters Offered: Fall, Spring
Credit/Time Requirement: Credit: 3; Lecture: 3; Lab: 0

Prerequisites: Math 2210 (can be taken concurrently)

Justification: This class is required for students majoring in mathematics, several engineering fields, and some physical sciences (physics, etc.). The material from this course is a basic foundation and problem-solving tool for students entering science-related fields. This course is designed to be fully transferable to USU, U of U, Weber, SUU, and Utah Tech (all public senior institutions in Utah).


Student Learning Outcomes:
Students will be able to use standard methods to solve a variety of differential equations, including Laplace transformations and power series solutions. A student's understanding will be assessed with quizzes, homework, presentations and/or exams.

Students will be able to solve problems and apply mathematical models relating to standard differential equation concepts, including Laplace transformations. A student's understanding will be assessed with quizzes, homework, presentations and/or exams.

Students will be able to generalize and approximate solutions to differential equations using numerical methods. A student's understanding will be assessed with quizzes, homework, presentations and/or exams.


Content:
This course will address a variety of theoretical and real-world problems, including:Mathematical modeling using differential equationsFirst-order differential equations and solution techniquesHigher-order differential equations and solution techniquesIntroduction to numerical solutions (Euler’s, Heun's, RK4 methods)Laplace transformsPower series methodsContributions of mathematicians/scientists from various backgrounds will be highlighted.

Key Performance Indicators:
Students will demonstrate competency of the Student Learning Outcomes by:

Homework 10 to 20%

Midterm/Unit Tests 30 to 60%

Quizzes and/or Oral Presentations 0 to 20%

Comprehensive Final Exam 15 to 30%


Representative Text and/or Supplies:
Differential Equations and Linear Algebra, current edition, by Edwards and Penney

Students may use technology in the form of graphing calculators, spreadsheets, etc.


Pedagogy Statement:
During lectures and interactive class discussions, students are encouraged to ask and help answer questions about how to apply problem-solving techniques. Many problems have various solution pathways and different problem-solving methods from diverse students will be recognized and valued.

Instructional Mediums:
Lecture

Maximum Class Size: 30
Optimum Class Size: 24