docs(intro): fix minor notation issue
"Differential equations can be divided into 2 types: ordinary differential equations (ODEs) and partial differential equations (PDEs).\n",
"\n",
"### Ordinary Differential Equations\n",
- "An ordinary differential equation (ODE) is an differential equation that contains only one independent variable (a scalar). Let $t \\in \\mathbb{R}$ be the independent variable and $x(t): \\mathbb{R} \\mapsto \\mathbb{R}$ be a function of $t$. An ordinary differential equation of order $n$ takes the form:\n",
+ "An ordinary differential equation (ODE) is an differential equation that contains only one independent variable (a scalar). Let $t \\in \\mathbb{R}$ be the independent variable and $x: \\mathbb{R} \\to \\mathbb{R}$ be a function of $t$. An ordinary differential equation of order $n$ takes the form:\n",
"\n",
"$$F(t, x, \\frac{dx}{dt}, \\frac{d^2x}{dt^2}, \\ldots, \\frac{d^nx}{dt^n}) = 0,$$\n",
"\n",
"\n",
"### System of Ordinary Differential Equations\n",
"\n",
- "A number of coupled differential equations form a system of equations. Let $t \\in \\mathbb{R}$ be the independent variable and $\\vec{x}(t): \\mathbb{R} \\mapsto \\mathbb{R^m}$ be a function of $t$. A system of ordinary differential equations of order $n$ takes the form:\n",
+ "A number of coupled differential equations form a system of equations. Let $t \\in \\mathbb{R}$ be the independent variable and $\\vec{x}: \\mathbb{R} \\to \\mathbb{R^m}$ be a function of $t$. A system of ordinary differential equations of order $n$ takes the form:\n",
"\n",
"$$F(t, \\vec{x}, \\frac{d\\vec{x}}{dt}, \\frac{d^2\\vec{x}}{dt^2}, \\ldots, \\frac{d^n\\vec{x}}{dt^n}) = \\vec{0},$$\n",
"\n",
"![case2](case2.png)\n",
"*Figure 2: Comparing analytical and ANN-based solutions of Poisson's equation.*"
]
+ },
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+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
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