The Art of Polynomial Interpolation / Stuart Murphy.

Format:

Book

Author/Creator:

Murphy, Stuart, author.

Series:

Open textbook library

Language:

English

Subjects (All):

Polynomials.

Mathematics--Textbooks.

Mathematics.

Physical Description:

1 online resource (84 pages).

Place of Publication:

[Place of publication not identified] : Pennsylvania State University, [date of publication not identified]

Summary:

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: 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. 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. Assist students in building a basic foundation allowing them to add additional techniques, of which there are many, not covered in this text.

Contents:

Introduction

Techniques

Chapter One

Elimination (Substitution) Interpolation

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.

Notes:

Description based on: online resource; title from PDF information screen (Open textbook library, viewed May 05, 2023).