# Math 320: Linear Algebra and Differential Equations ## Affiliation

Name: Frank Rooney
SCID: College of Letters & Science
Department: Mathematics
Course Name: Math 320: Linear Algebra and Differential EquationsCourse Objectives:
CO1: Students will be able to model physical situations using differential equations.
CO2: Students will solve model differential equations and use the solutions to predict the behavior of the system modeled.
CO3: Students will be able to appreciate, understand, and construct mathematical proof.
CO4: Students will understand when and how to apply the tools of linear algebra.Course Units:
Unit One: First Order Ordinary Differential Equations
Unit Two: Linear Equations & Matrix Algebra
Unit Three: Vector Spaces & Linear Transformations
Unit Four: Higher Order Linear Differential Equations
Unit Five : Systems of Differential EquationsUnit Objectives:
Unit One : First Order Linear Differential Equations
UO1: Students will be able classify the types of differential equation.
UO2: Students will be able to recognize the class differential equations that can be solved in closed form and use the correct integration method to find the solution.
UO3: Students will be able to use qualitative/geometric methods to analyze the behavior of solutions.
UO4: Students will be able to use approximate methods of solution when other solution techniques are inapplicable.
UO5: Students will be able to model physical situations using differential equations.
UO6: Students will be able to solve model differential equations and interpret the solutions in terms of the situation that was modeled by the differential equation.

## Activity One

Activity:
Description: Reading : An introduction to Differential Equations & partial derivatives
Quiz; Short quiz on the reading
Modality: Online
Activity Sequence: Pre-class
Required Knowledge: Derivatives from calculus 1
Time on Task: Approximately 15-20 minutes
Objectives Supported: UO1
Horton Type: Absorb
Bloom’s Level: Remember
Evidence: Quiz results
Pedagogical Role: Knowledge check for in class activities
Social Role: NA
Managerial Role: NA
Technical Role: Canvas

## Activity Two

Activity:
Description: 1. Introduce the concept of an Initial Value Problem
2. State the Existence Uniqueness Theorem 3. Apply the theorem to application problems
Modality: Lecture
Activity Sequence: Break the lecture up for 2-3 knowledge checks (pair-share)
Required Knowledg: Pre-class reading and integration methods from calculus 2
Time on Task: 1 hour 15 minutes
Objectives Supported: UO1
Horton Type: Absorb/Do
Bloom’s Level: Remember/Understand
Evidence: Class feedback & Homework
Pedagogical Role: Understand the topics listed above
Social Role: NA
Managerial Role: NA
Technical Role: NA

## Activity Three

Activity:
Description:Reading : Review of integration using partial fractions
Quiz : Short quiz on the reading
Modality: Online
Activity Sequence: Pre-class
Required Knowledge: Integration techniques from calculus 2
Objectives Supported: UO1,UO2
Horton Type: Absorb/Do
Bloom’s Level: Remember/Understand
Evidence: Quiz result
Pedagogical Role: Knowledge check for in class activities
Social Role: NA
Managerial Role: NA
Technical Role: Canvas

## Activity Four

Activity:
Description: 1. Define a separable equation
2. Solve separable ODEs from population dynamics, chemistry and physics
Modality: Lecture
Activity Sequence: Break the lecture up for 2-3 knowledge checks (pair-share)
Required Knowledge: Pre-class reading and integration methods from calculus 2
Time on Task: 1 hour 15 minutes
Objectives Supported: UO1, UO2, UO5, UO6
Horton Type: Absorb/Do
Bloom’s Level: Remember/Understand
Evidence: Class feedback & Homework
Pedagogical Role: Understand the topics listed above
Social Role: NA
Managerial Role: NA
Technical Role: NA

## Activity Five

Activity:
Description:Short reflection
Modality: Written by students
Activity Sequence: At the end of class
Required Knowledge: NA