First Semester in Numerical Analysis with Julia, 2020a

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Chapter 2 Solutions of equations: Root-finding Arya and the mystery of the Rhind papyrus College life is full of adventures, some hopefully of intellectual nature, and Arya is doing her part by taking a history of science class. She learns about the Rhind papyrus; an ancient Egyptian papyrus purchased by an antiquarian named Henry Rhind in Luxor, Egypt, in 1858. Figure 2.1: Rhind Mathematical Papyrus. (British Museum Image under a Creative Commons license.) The papyrus has a collection of mathematical problems and their solutions; a translation is given by Chace & Manning [2]. The following is Problem 26, taken from [2]: 51
CHAPTER 2. SOLUTIONS OF EQUATIONS: ROOT-FINDING 52 A quantity and its 1/4 added together become 15. What is the quantity? Assume 4. \1 4 \1/4 1 Total 5 As many times as 5 must be multiplied to give 15, so many times 4 must be multiplied to give the required number. Multiply 5 so as to get 15. \1 5 \2 10 Total 3 Multiply 3 by 4. 1 3 2 6 \4 12 The quantity is 12 1/4 3 Total 15 Arya’s instructor knows she has taken math classes and asks her if she could decipher this solution. Although Arya’s initial reaction to this assignment can be best described using the word "despair", she quickly realizes it is not as bad as she thought. Here is her thought process: the question, in our modern notation is, find x if x + x/4 =15. The solution starts with an initial guess p =4. It then evaluates x + x/4 when x = p, and finds the result to be 5: however, what we need is 15, not 5, and if we multiply both sides of p + p/4 =5by 3, we get (3p)+(3p)/4 =15. Therefore, the solution is 3p =12.
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First Semester in Numerical Analysi
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Page 5 and 6: Contents 1 Introduction 5 1.1 Revie
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CHAPTER 3. INTERPOLATION 102 Exampl
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CHAPTER 3. INTERPOLATION 104 Exerci
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CHAPTER 3. INTERPOLATION 120 Exerci
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CHAPTER 3. INTERPOLATION 122 yi yi+
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CHAPTER 3. INTERPOLATION 126 In [2]
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CHAPTER 3. INTERPOLATION 140 Recrea
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CHAPTER 4. NUMERICAL QUADRATURE AND
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Chapter 5 Approximation Theory 5.1
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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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