Course Description
Mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real-world data and phenomena. The investigation and analysis of applied problems and questions, and of effective communication of quantitative concepts and results.
Athena Title
Intro to Mathematical Modeling
Equivalent Courses
Not open to students with credit in MATH 1101E
Semester Course Offered
Offered fall, spring and summer
Grading System
A - F (Traditional)
Course Objectives
This course is an introduction to mathematical modeling based on the use of elementary functions to describe and explore real world data and phenomena. Linear, polynomial, exponential, and logistic models are examined and in course projects are applied to real world data. Throughout the course spreadsheet and calculator technology is used to implement, examine, and validate these models. Students are expected to create and interpret data and phenomena. This is an important aspect of modern living.
Topical Outline
1. Modeling with Linear Functions, Tables, Graphs, and Formulas. Definition of function, domain and range, functions defined by tables, graphs and formulas, average rate of change, increasing and decreasing functions. Constant rate of change and linear growth, equations of lines, linear functions, piecewise-linear functions. Fitting linear models to data. 2. Modeling Natural Growth. Percentage increase and decrease, simple interest, exponential functions and their graphs. Natural growth and decline, fitting exponential growth models to data, Newton's law of cooling. 3. Modeling Growth with Quadratic, Exponential, and Logarithmic Functions. Compound interest, credit card interest. Continuous compound interest. Quadratic functions, graphs, maxima and minima and applications. Fitting quadratic models to data. Using Excel to fit population data using linear, quadratic, and exponential models. 4. Polynomial Models and Linear Systems. Polynomial functions and graphs, solving polynomial equations. Setting up a system of equations, solving pairs of linear equations by substitution, elimination, determinants, and matrices.
General Education Core
CORE I: FoundationSyllabus