The Art of Polynomial Interpolation by Stuart Murphy
The Art of Polynomial Interpolation - Table of Contents
PART I: INTERPOLATION & SPLINES
- 1. Elimination (Substitution) Interpolation
- 2. Newton's Divided Difference Interpolation
- 3. Quadratic Spline Interpolation
- 4. Linear Least Squares Regression
PART II: REGRESSION & TAYLOR SERIES
- 5. Exponential Least Squares Regression
- 6. Approximation with Taylor Series
- 7. Taylor Series Remainder Test
- 8. Solutions to Selected Practice Exercises
What You Will Learn in The Art of Polynomial Interpolation
The Art of Polynomial Interpolation by Stuart Murphy is a practical, mathematically accessible textbook that guides students and self-learners through the fundamental techniques of numerical approximation, data modeling, and curve fitting. Published as a step-by-step instructional resource, this comprehensive volume covers direct substitution elimination, Newton's divided difference interpolation formulas, piece-wise quadratic spline construction, linear and exponential least squares regression, goodness-of-fit measurement, Taylor series expansion approximations, and Taylor polynomial remainder error estimates with exceptional clarity.
Designed for undergraduate students, data analysts, engineers, and applied mathematicians, this foundational text prioritizes clear hand calculations and algorithmic intuition over overly abstract real analysis proofs. Murphy details worked step-by-step examples for constructing divided difference tables, solving tridiagonal systems for quadratic splines, fitting nonlinear exponential data via log transformations, and bounding truncation errors with the Taylor remainder theorem. Whether you are developing numerical algorithms, analyzing scientific data, or reviewing practice exercise solutions for exams, this book offers an indispensable roadmap.
Recognized for its beginner-friendly pedagogy and hands-on mathematical focus, it stands as one of the best introductory numerical interpolation books for self-study. By connecting discrete data points to continuous mathematical functions, it serves as an essential tool for mastering polynomial interpolation and curve fitting with confidence.
Book Details & Specifications
Title:
The Art of Polynomial Interpolation by Stuart Murphy
Publisher:
Pennsylvania State University
Year:
2022
Pages:
90
Type:
PDF
Language:
English
ISBN-10 #:
3659781754
ISBN-13 #:
978-3659781759
License:
CC BY-NC 4.0
Amazon:
Amazon
About the Author: Stuart Murphy
The author Stuart Murphy
is a mathematician and educator with experience teaching at multiple levels and a background in industry. He combines practical knowledge with clear instruction, focusing on making complex mathematical concepts approachable and relevant. His book "The Art of Polynomial Interpolation" introduces students to "Polynomial Interpolation" using clear explanations and step-by-step methods. Incorporating "Numerical Methods", basic matrix algebra, and hands-on exercises, it emphasizes "Applied Learning" and real-world data applications.
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