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122 lines
2.7 KiB
Text
122 lines
2.7 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Mechanica"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"### Quiz Notations and Products\n",
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"\n",
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":::{card} Exercise 1\n",
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"What is the type of the result of the product?\n",
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"\n",
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"$\\mathit{v}_i \\cdot \\mathit{A}_{ij} \\cdot \\mathit{w}_j$\n",
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"\n",
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"\n",
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"```{admonition} Solution\n",
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":class: tip, dropdown\n",
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"Scalar\n",
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"```\n",
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":::\n",
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"\n",
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":::{card} Exercise 2\n",
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"How would you write the product\n",
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"\n",
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"$\\mathit{v}_i \\cdot \\mathit{A}_{ij} \\cdot \\mathit{w}_j$\n",
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"\n",
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"in matrix/vector notation?\n",
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"```{admonition} Solution\n",
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":class: tip, dropdown\n",
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"$\\mathbf{v}^T \\cdot \\mathbf{A} \\cdot \\mathbf{w}$\n",
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"```\n",
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":::\n",
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"\n",
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":::{card} Exercise 3\n",
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"What is the type of the result of the following product?\n",
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"\n",
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"$\\mathit{v}_i \\cdot \\mathit{w}_j$\n",
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"```{admonition} Solution\n",
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":class: tip, dropdown\n",
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"Second order tensor\n",
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"```\n",
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":::\n",
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"\n",
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":::{card} Exercise 4\n",
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"How would you write the product\n",
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"\n",
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"$\\mathit{A}_{ij} \\cdot \\mathit{v}_{i}$\n",
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"\n",
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"in matrix vector notation?\n",
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"```{admonition} Solution\n",
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":class: tip, dropdown\n",
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"$\\mathbf{A}^T \\cdot \\mathbf{v}$\n",
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"```\n",
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":::\n",
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"\n",
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":::{card} Exercise 5\n",
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"How would you write the result of the product\n",
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"\n",
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"$\\mathit{v}_{i} \\cdot \\mathit{w}_{j}$\n",
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"\n",
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"in matrix vector notation?\n",
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"```{admonition} Solution\n",
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":class: tip, dropdown\n",
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"$\\mathbf{v} \\cdot \\mathbf{w}^T$\n",
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"```\n",
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":::\n",
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"\n",
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":::{card} Exercise 6\n",
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"How would you write the product\n",
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"\n",
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"$\\mathbf{A} \\cdot \\mathbf{B}^T$\n",
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"\n",
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"in index notation?\n",
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"```{admonition} Solution\n",
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":class: tip, dropdown\n",
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"$\\mathit{A}_{ik} \\cdot \\mathit{B}_{jk}$\n",
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"```\n",
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":::"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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},
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"codemirror_mode": {
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},
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