First Semester in Numerical Analysis with Julia, 2020a

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CONTENTS 3 5 Approximation Theory 177 5.1 Discrete least squares .............................. 177 5.2 Continuous least squares ............................. 197 5.3 Orthogonal polynomials and least squares ................... 199 References 216 Index 217
Preface This book is based on my lecture notes for a junior level undergraduate course in Numerical Analysis. As the title suggests, the content is the standard material covered in the first semester of Numerical Analysis classes in the colleges in the United States. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The book presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). Incorporating coding and computing within the main text was my primary objective in writing this book. The simplicity of Julia allows bypassing the pseudocode, and writing a computer code directly after the description of a method. It also minimizes the distraction the presentation of a computer code might cause to the flow of the main narrative. The Julia codes are written without much concern for efficiency; the priority is to write codes that follow the derivations presented in the text. The Julia software is free, under an MIT license, and can be downloaded at https://julialang.org. While writing this book, I badly needed a comic relief, and created a character, a college student, who makes an appearance in each chapter. The character hopefully brings some humor and makes Numerical Analysis more interesting to her fellow students! I thank my daughter Arya Ökten, a college student majoring in applied mathematics herself, who graciously agreed to let the character use her name! I also thank her for reading parts of the earlier drafts and making the drawings in the book. I thank my colleague Paul Beaumont who introduced me to Julia. I thank Sanghyun Lee who used the book in his Numerical Analysis class and suggested several clarifications and corrections that improved the book. I thank my colleagues Steve Bellenot, Kyle Gallivan, Ahmet Göncü, and Mark Sussman for helpful discussions during the writing of the book. Thanks to Steve for inspiring the example Arya and the letter NUH in Section 3.4, and thanks to Ahmet for his help with the modeling of weather temperature data example in Section 5.1. The book was supported by an Alternative Textbook Grant from the Florida 4
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Chapter 5 Approximation Theory 5.1
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CHAPTER 5. APPROXIMATION THEORY 180
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Index Absolute error, 38 Beasley-Sp
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INDEX 220 Chebyshev, 203 Julia code
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First Semester in Numerical Analysis with Julia, 2020a

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