What This Document Is
This document is a worksheet designed for Cornell University’s Calculus For Engineers (MATH 1910) course. It focuses on extending the application of SIR (Susceptible-Infected-Recovered) models – a common epidemiological modeling technique – to represent the evolution of a new product’s adoption within a population. The worksheet presents scenarios and asks students to apply rate equations to model and analyze product diffusion.
Why This Document Matters
This worksheet is valuable for engineering students learning to apply calculus to real-world modeling problems. It bridges theoretical concepts from the course with practical applications in areas like marketing, public health, or technology adoption. Students will use this to practice translating a dynamic process into mathematical equations and interpreting the results. It’s typically used as an in-class activity or homework assignment to reinforce understanding of differential equations and modeling techniques.
Common Limitations or Challenges
This worksheet focuses on applying existing models rather than deriving them from first principles. It assumes a foundational understanding of differential equations and the basic SIR model. The worksheet provides scenarios, but doesn’t offer complete solutions or detailed explanations of the underlying mathematical principles. Students will still need to consult course lectures, textbooks, and potentially utilize software like Matlab to fully explore the concepts.
What This Document Provides
The worksheet includes three main exercises:
* A scenario involving a new product launch, requiring students to determine transmission and attrition coefficients based on provided data.
* Analysis of graphs depicting SIR model behavior with varying attrition rates, asking students to identify the curves representing susceptible, infected, and recovered populations and explain the impact of different attrition coefficients.
* A modified SIR model where rejected users can become potential users again, prompting students to adjust the equations and predict the effects on model behavior.
This preview does *not* include solutions to the problems, detailed explanations of the mathematical derivations, or the Matlab charting component mentioned in the document.
