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    "Advanced Mathematics for Nuclear Chemical Engineering August 2020 UMass Lowell; Prof. V. F. de Almeida **06Aug2020**\n",
    "\n",
    "# 03. Non-Linear Algebra\n",
    "$  \n",
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    "---\n",
    "## Table of Contents<a id=\"toc\"></a>\n",
    "* [Non-Linear System of Algebraic Equations](#nlinalg)\n",
    " - Newton's method, Jacobian matrix, iterative algorithm\n",
    "* [Non-Linear Least-Squares Method](#nllsq)\n",
    " - Incomplete Newton's method\n",
    "---"
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    "## [Non-Linear System of Algebraic Equations](#toc)<a id=\"nlinalg\"></a>\n",
    "\n",
    "The course notes in [ChEn-3170-nonlinalg-a](https://studentuml-my.sharepoint.com/:o:/g/personal/valmor_dealmeida_uml_edu/EsURG6azFKdHg13aiJdg0X8Bwn1JHj9ziyIz3bXrr2CjRw?e=P2EkeB), [ChEn-3170-nonlinalg-b](https://studentuml-my.sharepoint.com/:o:/g/personal/valmor_dealmeida_uml_edu/Et5dh9qx7wlIhSwTMHlUejoBEmLfisX9lBT-wHs5zVttgQ?e=WhR37k), and [ChEn-3170-nonlinalg-c](https://studentuml-my.sharepoint.com/:o:/g/personal/valmor_dealmeida_uml_edu/Ei3KyNR90cVBnzOTgU04-1YBlN77e7yejChMxKWtZD3jtg?e=3N7UQF) progressively cover basic elements of Newton's method for non-linear system of algebraic equations as applied to chemical reactions in equilibrium. These elements apply equaly well to general system of non-linear algebraic equations. Computational examples are found in [ChEn-3170 Notebook 13](https://nbviewer.jupyter.org/github/dpploy/chen-3170/blob/master/notebooks/13-nonlinear-root-finding.ipynb), [ChEn-3170 Notebook 14](https://nbviewer.jupyter.org/github/dpploy/chen-3170/blob/master/notebooks/14-single-reaction-equilibrium.ipynb) and [ChEn-3170 Notebook 15](https://nbviewer.jupyter.org/github/dpploy/chen-3170/blob/master/notebooks/15-multiple-reactions-equilibrium.ipynb)."
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    "## [Non-Linear Least-Squares Method](#toc)<a id=\"nllsq\"></a>\n",
    "\n",
    "The non-linear least-squares method handles cases when the relationship between parameters is non-linear. Similarly to its linear counterpart, it has widespread applications in engineering and science.\n",
    "\n",
    "The non-linear least-squares method is an example of the usage of Newton's method for non-linear algebraic equations. Notes can be found in [ChEn-3170-nllsq](https://studentuml-my.sharepoint.com/:o:/g/personal/valmor_dealmeida_uml_edu/EqGM1mM9GghIl0bfPiav20QBf77_wXh_9dyOBNoPu75znA?e=WDILM4), and examples in [ChEn-3170 Notebook 16](https://nbviewer.jupyter.org/github/dpploy/chen-3170/blob/master/notebooks/16-non-linear-lsq-arrhenius-data-fit.ipynb)"
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