typos Lec 5

Author: 5trobl

Lecture-5-Sympy.ipynb

@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Sympy - Symbolic algebra in Python"
+    "# SymPy - Symbolic algebra in Python"
    ]
   },
   {
@@ -261,7 +261,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The imaginary unit is denoted `I` in Sympy. "
+    "The imaginary unit is denoted `I` in SymPy. "
    ]
   },
   {
@@ -462,7 +462,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "SymPy uses a library for artitrary precision as numerical backend, and has predefined SymPy expressions for a number of mathematical constants, such as: `pi`, `e`, `oo` for infinity.\n",
+    "SymPy uses a library for arbitrary precision as numerical backend, and has predefined SymPy expressions for a number of mathematical constants, such as: `pi`, `e`, `oo` for infinity.\n",
     "\n",
     "To evaluate an expression numerically we can use the `evalf` function (or `N`). It takes an argument `n` which specifies the number of significant digits."
    ]
@@ -629,7 +629,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can also combine numerical evolution of expressions with NumPy arrays:"
+    "We can also combine numerical evaluation of expressions with NumPy arrays:"
    ]
   },
   {
@@ -692,7 +692,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "However, this kind of numerical evolution can be very slow, and there is a much more efficient way to do it: Use the function `lambdify` to \"compile\" a Sympy expression into a function that is much more efficient to evaluate numerically:"
+    "However, this kind of numerical evaluation can be very slow, and there is a much more efficient way to do it: Use the function `lambdify` to \"compile\" a SymPy expression into a function that is much more efficient to evaluate numerically:"
    ]
   },
   {
@@ -779,7 +779,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "One of the main uses of an CAS is to perform algebraic manipulations of expressions. For example, we might want to expand a product, factor an expression, or simply an expression. The functions for doing these basic operations in SymPy are demonstrated in this section."
+    "One of the main uses of an CAS is to perform algebraic manipulations of expressions. For example, we might want to expand a product, factor an expression, or simplify an expression. The functions for doing these basic operations in SymPy are demonstrated in this section."
    ]
   },
   {
@@ -919,7 +919,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The opposite a product expansion is of course factoring. The factor an expression in SymPy use the `factor` function: "
+    "The opposite of product expansion is of course factoring. To factor an expression in SymPy use the `factor` function: "
    ]
   },
   {
@@ -1589,7 +1589,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can evaluate sums and products using the functions: 'Sum'"
+    "We can evaluate sums using the function `Sum`:"
    ]
   },
   {