Numerical-Analysis-I

Course contents for Numerical Analysis I (MATH 4650/5660 at CU Denver)

Chapter 1--Introduction

Review of Calculus

Python basics

Computer arithmetic

Chapter 2--Solutions of equations: Root-finding

Error analysis for iterative methods

Bisection method

Newton’s method

Secant method

Muller's method

Fixed-point iteration

High-order fixed-point iteration

Chapter 3--Solutions to linear systems

Gaussian Elimination

Iterative methods for solving linear systems

Cholesky decomposition

Chapter 4--Interpolation

Polynomial interpolation

High degree polynomial interpolation

Hermite interpolation

Piecewise polynomials: spline interpolation

Chapter 5--Numerical Quadrature and Differentiation

Newton-Cotes formulas

Composite Newton-Cotes formulas

Gaussian quadrature

Multiple integrals

Improper integrals

Numerical differentiation

Chapter 6--Approximation Theory

Discrete least squares

Continuous least squares

Orthogonal polynomials and least squares

Chapter 7--Numerical optimization

Golden-section search

Derivative-based optimization

Latex Plug-in

To display the math environment correctly, the Jupyter notebook plug-in (some) LaTeX environments for Jupyter notebook needs to be installed.

Creative Commons License Information

First Semester in Numerical Analysis with Python by Yaning Liu and Giray Okten is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Based on a work at https://github.com/CU-Denver-MathStats-OER/Numerical-Analysis-I.

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Numerical-Analysis-I

Chapter 1--Introduction

Review of Calculus

Python basics

Computer arithmetic

Chapter 2--Solutions of equations: Root-finding

Error analysis for iterative methods

Bisection method

Newton’s method

Secant method

Muller's method

Fixed-point iteration

High-order fixed-point iteration

Chapter 3--Solutions to linear systems

Gaussian Elimination

Iterative methods for solving linear systems

Cholesky decomposition

Chapter 4--Interpolation

Polynomial interpolation

High degree polynomial interpolation

Hermite interpolation

Piecewise polynomials: spline interpolation

Chapter 5--Numerical Quadrature and Differentiation

Newton-Cotes formulas

Composite Newton-Cotes formulas

Gaussian quadrature

Multiple integrals

Improper integrals

Numerical differentiation

Chapter 6--Approximation Theory

Discrete least squares

Continuous least squares

Orthogonal polynomials and least squares

Chapter 7--Numerical optimization

Golden-section search

Derivative-based optimization

Latex Plug-in

Creative Commons License Information

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