The Art of Polynomial Interpolation

• Introduction
• Techniques
• Chapter One - Elimination (Substitution) Interpolation
• Chapter One - Practice Exercises
• Chapter Two - Newton's Divided Difference Interpolation
• Chapter Two- Practice Exercises
• Chapter Three- Quadratic Spline Interpolation
• Chapter Three- Practice Exercises
• Chapter Four - Least Squares Regression
• Chapter Four- Practice Exercises
• Chapter Five- Measuring the Least Squares Fit/Exponential Least Squares Regression
• Chapter Five- Practice Exercises
• Chapter Six - Approximation with Taylor Series
• Chapter Six- Practice Exercises
• Chapter Seven - Taylor Series Remainder Test
• Chapter Seven- Practice Exercises
• Solutions to Selected Practice Exercises
• Acknowledgments
• About the Author
• Versioning History

The inspiration for this text grew out of a simple question that emerged over a number of years of teaching math to Middle School, High School and College students.

Practically speaking, what is the origin of a particular polynomial?

So much time is spent analyzing, factoring, simplifying and graphing polynomials that it is easy to lose sight of the fact that polynomials have a wealth of practical uses. Exploring the techniques of interpolating data allows us to view the development and birth of a polynomial. This text is focused on laying a foundation for understanding and applying several common forms of polynomial interpolation. The principal goals of the text are:

1. Breakdown the process of developing polynomials to demonstrate and give the student a feel for the process and meaning of developing estimates of the trend (s) a collection of data may represent.
2. Introduce basic matrix algebra to assist students with understanding the process without getting bogged down in purely manual calculations. Some manual calculations have been included, however, to assist with understanding the concept.
3. Assist students in building a basic foundation allowing them to add additional techniques, of which there are many, not covered in this text.