Mathematics 481: Mathematical Modeling II Assignment 1

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Mathematics 481: Mathematical Modeling II

Assignment 1

Introduction to Modeling and Simulation

Credit weight: 10% of the final grade

Due: Week 2, after completing Unit 1

Total: 20 marks

Instructions

Complete question 6 of the eText Section 2.1 Problems.

The purpose of the exercise is to begin to build an appreciation for the process of modeling. The given problem is purposely vague, which allows you the freedom either to specify a particular system of interest to study or, alternatively, to choose to maintain a level of generality so your model might be broadly applied across systems. Approach the problem by following these steps:

i.    Clearly define the problem that you will model, providing context as to why the problem is both interesting and important.

ii.  Describe how you will simplify the system of study by making explicit assumptions.

Assumptions play an important part in all models. A mathematical model is a representation that allows you to analyze and study a system of interest, particularly the causal mechanisms that result in given outcomes of that system.

An important part of model development is ensuring there is no room for misinterpretation. This ensures that others can verify your analysis of the model. It also allows others to then extend the model by relaxing or altering its assumptions, thus expanding on our understanding of the system.

iii. Define any variables that will be used in your model. For example, N (t ) = number of units produced in year t ,

c = cost per unit,

r = revenue per unit,

d = demand in year t ,

etc.

iv. Provide both a textual and a mathematical description of your model, explaining how the model tracks the system of study.

This step helps you to ensure that your mathematical description of the model aptly captures the system as it is described.

This assignment is designed as a learning experience and is meant to be challenging. As such, feel free to contact your tutor for help or guidance as needed.

Format

Prepare your response to the question as a typed document with all mathematical statements properly formatted (see Assessments in the Course Orientation for information about formatting). Your response should include the following elements:

•   Problem identification – 4 marks

•   Statement of assumptions – 4 marks

•   Identification and classification of variables – 4 marks

•   Description of model – 4 marks

•   Presentation/communication – 4 marks