These labs attempt to help students learn Calculus from the context of applications and mathematical modeling; thus, giving the student another viewpoint from which to appreciate calculus.

Downloads

• Full Manual (PDF)
• Supporting excel files for Lab 8 and Lab 9

The labs can be divided into three groupings

• Limits of sequences: Labs 1, 2, and 3
• Modeling the spread of the flu in a closed population with rate equations (DE's). Labs 4, 5, 6 ,and 7
• Modeling the use of natural gas consumption with integrals Labs 8, and 9.

• Lab Introductions: Notes to the instructor and students.
• Lab 1 Introduction to Excel: Introduces Excel that will be used through out the labs. Sets students up for creating spread sheets for recursive sequences.
• Lab 2 Sequences and Limits: Explores limits of sequences numerically by introducing the concept behind Cauchy sequences.
• Lab 3 More on Sequences: Show the students that there is a large variety of phenomena that can happen even with simple recursive sequences.
• Lab 4 Sequences from a Flu Epidemic: This is a data collection lab where students simulate a flu epidemic by ``encountering'' other students and rolling a dice to see if they ``catch'' the flu. This can be thought of as a ``research'' lab where students become familiar with the process they will be asked to model.
• Lab 5 Building the Model: This lab walks students through reasoning that leads them to an SIR model for the spread of the flue. That is a system of nonlinear differential equations based on mass action kinetics.
• Lab 6 Exploring the SIR Model: This Lab explains Euler's method for solving the non-linear differential equations that the student derived in lab 5 for the flu epidemic. It is best if this can be covered approximately at the same time as differentials during the regular class.
• Lab 7 There and Back Again: This lab explores the effect of varying the step size in Euler's method on the numerical simulation and brings back the idea of limits introduced in labs 2 and 3.
• Lab 8 How Much Heat?: This lab Introduces a model that can be used to estimate natural gas consumption. It uses Newton's law of cooling and a few simple assumptions. Also lab 8 introduces numerical integration and hints at similarities of this with Euler's method.
  • Supporting excel file for Lab 8
• Lab 9 How much Natural Gas?: This lab brings together Euler's method and numerical integration through the fundamental theorems of Calculus.
  • Supporting excel file for Lab 9