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Math 121 Mathematical Modeling and the Environment
2008-03-03
Mathematical Modeling and the Environment
COURSE GOALS/OBJECTIVES:
Exploration of linear, power, exponential, logistic, logarithmic, and difference equations using data analysis. Students will create mathematical models from environmentally themed data sets to better understand different types of relationships between variables. Quantitative reasoning will be heavily emphasized. Graphing calculator required.
COURSE CONTENT:
Chapter 4 Linear Functions and Regression
Modeling with Linear Functions
Units of Measure in Linear Equations
Dependent versus Independent Variables
Graphing Linear Functions
Approximating Almost-Linear Data Sets
The straight-edge method
Least Squares Regression
The Correlation Coefficient
Correlation Fallacies
Chapter 5 Exponential Functions and Regression
Exponential Rates and Multipliers
The General Exponential Model
Finding Exponential Functions-The More General Case
Solving Exponential Equations
Doubling Times and Half-Lives
Approximating Almost-Exponential Data Sets
Chapter 6 Power Functions
Basic Power Functions
Solving Power Equations
Approximating Power-Like Data
Power Law Distributions and Fractals
Chapter 7 Introduction to Difference Equations
Sequences and Notation
Modeling with Difference Equations
Linear Difference Equations
Exponential Difference Equations
Why Use Difference Equations?
Affine Difference Equations
Chapter 8 Affine Solution Equations and Equilibrium Values
The Solution Equation to the Affine Model
Equilibrium Values
Classification of Equilibrium Values
Chapter 9 Logistic Growth, harvesting and Chaos
Modeling Logistic Growth with Difference Equations
Logistic Equilibrium Values
Harvest Models
Periodic Behavior
Chaotic Behavior
Optional:
Systems of Difference Equations
Exponential Change and Stable Age Distributions
REQUIRED EVALUATION METHODS: Written exams, quizzes, homework, class participation.
TEXT BOOKS:
Greg Langkamp and Joseph Hull
Quantitative Reasoning and the Environment: Mathematical Modeling in Context,1st edition,
Prentice Hall, 2007.
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