\[\newcommand{\vect}[1]{\mathbf{#1}} \newcommand{\uvect}[1]{\hat{#1}} \newcommand{\abs}[1]{\lvert#1\rvert} \newcommand{\norm}[1]{\lVert#1\rVert} \newcommand{\I}{\mathrm{i}} \newcommand{\ket}[1]{\left|#1\right\rangle} \newcommand{\bra}[1]{\left\langle#1\right|} \newcommand{\braket}[1]{\langle#1\rangle} \newcommand{\Braket}[1]{\left\langle#1\right\rangle} \newcommand{\op}[1]{\mathbf{#1}} \newcommand{\mat}[1]{\mathbf{#1}} \newcommand{\d}{\mathrm{d}} \newcommand{\D}[1]{\mathcal{D}[#1]\;} \newcommand{\pdiff}[3][]{\frac{\partial^{#1}#2}{\partial{#3}^{#1}}} \newcommand{\diff}[3][]{\frac{\d^{#1} #2}{\d{#3}^{#1}}} \newcommand{\ddiff}[3][]{\frac{\delta^{#1} #2}{\delta{#3}^{#1}}} \newcommand{\floor}[1]{\left\lfloor#1\right\rfloor} \newcommand{\ceil}[1]{\left\lceil#1\right\rceil} \DeclareMathOperator{\Tr}{Tr} \DeclareMathOperator{\erf}{erf} \DeclareMathOperator{\erfi}{erfi} \DeclareMathOperator{\sech}{sech} \DeclareMathOperator{\sn}{sn} \DeclareMathOperator{\cn}{cn} \DeclareMathOperator{\dn}{dn} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\order}{O} \DeclareMathOperator{\diag}{diag} \newcommand{\mylabel}[1]{\label{#1}\tag{#1}} \newcommand{\degree}{\circ} \]
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Physics 581: Physics Inspired Computational Techniques

Contents:

  • Getting Started
  • Syllabus
    • Prerequisites and Resources
    • Assignment Instructions
  • Prerequisites and Resources
  • Readings
    • Plotting
  • Assignments
    • Assignment Instructions
    • Assignment 0: Introduction
    • Assignment 1: Monty Hall etc.
    • Assignment 2: IVPs and ODEs
    • Assignment 4: Chaos and Lyapunov Exponents
    • Assignment 5: Modeling Data
  • API Reference
    • phys_581_2021
      • assignment_0
      • assignment_1
        • derivative
        • lambertw
        • play_monty_hall
        • zeta
      • assignment_2
        • solve_ivp_abm
        • solve_ivp_euler
        • solve_ivp_rk4
        • step_rk45
        • OdeResult
      • assignment_4
        • compute_lyapunov
      • plotting
        • corner_plot

Other Content:

  • Notes
    • Globally Convergent Newton’s Method
    • Model Fitting
    • Model Fitting Details
    • Model Fitting E.g. 1: Cosine
    • Model Fitting E.g. 1: Cosine
    • Model Fitting E.g. 1b: MCMC
    • Random Variables
  • Project Ideas
  • Instructor Notes
  • CoCalc
  • Class Log

Includes (for autobuild):

  • Physics 581: Physics Inspired Computational Techniques
Theme by the Executable Book Project

Notes

Notes¶

  • Globally Convergent Newton’s Method
    • Polynomial Inversion
  • Model Fitting
    • Single Value
    • Curve Fitting
    • The Main Point
    • Summary
  • Model Fitting Details
    • Independently Distributed Errors
    • Parameter Uncertainties (Covariance)
    • Confidence Levels
    • The Geometry of Data Fitting
    • Complete Example
  • Model Fitting E.g. 1: Cosine
    • Linear Gaussian Approximation
    • Non-Gaussian Errors
    • References
  • Model Fitting E.g. 1: Cosine
    • Linear Gaussian Approximation
    • Non-Gaussian Errors
    • References
  • Model Fitting E.g. 1b: MCMC
    • References
  • Random Variables
    • Function of a Random Variable
    • Sum of Independent Random Variables
    • Product of Independent Random Variables
    • Chi-Squared Distribution

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Globally Convergent Newton’s Method

By Michael McNeil Forbes
© Copyright 2021, Michael McNeil Forbes.