First Semester in Numerical Analysis with Julia, 2020a

Contents
1 Introduction 5
1.1 Review of Calculus ................................ 5
1.2 Julia basics .................................... 8
1.3 Computer arithmetic ............................... 28
2 Solutions of equations: Root-finding 50
2.1 Error analysis for iterative methods ....................... 53
2.2 Bisection method ................................. 54
2.3 Newton’s method ................................. 59
2.4 Secant method .................................. 69
2.5 Muller’s method .................................. 72
2.6 Fixed-point iteration ............................... 76
2.7 High-order fixed-point iteration ......................... 84
3 Interpolation 87
3.1 Polynomial interpolation ............................. 88
3.2 High degree polynomial interpolation ...................... 106
3.3 Hermite interpolation ............................... 111
3.4 Piecewise polynomials: spline interpolation ................... 119
4 Numerical Quadrature and Differentiation 140
4.1 Newton-Cotes formulas .............................. 140
4.2 Composite Newton-Cotes formulas ....................... 146
4.3 Gaussian quadrature ............................... 151
4.4 Multiple integrals ................................. 158
4.5 Improper integrals ................................ 166
4.6 Numerical differentiation ............................. 167
2