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Welcome to First Semester in Numerical Analysis with Python
Preface
Chapter 1 Introduction
1.1 Review of Calculus
1.2 Python basics
1.3 Computer arithmetic
Chapter 2 Solutions of Equations: Root-finding
2.1 Error analysis for iterative methods
2.2 Bisection method
2.3 Newton’s method
2.4 Secant method
2.5 Muller’s method
2.6 Fixed-point iteration
2.7 High-order fixed-point iteration
Chapter 3 Solutions to Linear Systems
3.1 Gaussian elimination
3.2 Iterative methods for solving linear systems
3.3 Cholesky decomposition
Chapter 4 Interpolation
4.1 Polynomial interpolation
4.2 High degree polynomial interpolation
4.3 Hermite interpolation
4.4 Piecewise polynomials: spline interpolation
Chapter 5 Numerical Quadrature and Differentiation
5.1 Newton-Cotes formulas
5.2 Composite Newton-Cotes formulas
5.3 Gaussian quadrature
5.4 Multiple integrals
5.5 Improper integrals
5.6 Numerical differentiation
Chapter 6 Approximation Theory
6.1 Discrete least squares
6.2 Continuous least squares
6.3 Orthogonal polynomials and least squares
Chapter 7 Numerical Optimization
7.1 Golden-section search
7.2 Derivative-based optimization
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