Change derivative in comments to use prime symbol.

markrogoyski · Sep 8, 2016 · f94ecfe · f94ecfe
1 parent ae04047
commit f94ecfe
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Showing 3 changed files with 14 additions and 14 deletions.
diff --git a/src/NumericalAnalysis/NumericalDifferentiation/FivePointFormula.php b/src/NumericalAnalysis/NumericalDifferentiation/FivePointFormula.php
@@ -34,7 +34,7 @@ class FivePointFormula extends NumericalDifferentiation
      *   - If the 3rd point is our $target, use the Midpoint Formula:
      *
      *              1                                         h⁴
-     *     f'(x₀) = - [f(x₀-2h)-8f(x₀-h)+8f(x₀+h)-f(x₀+2h)] - - f⁽⁵⁾(ζ₁)
+     *     f′(x₀) = - [f(x₀-2h)-8f(x₀-h)+8f(x₀+h)-f(x₀+2h)] - - f⁽⁵⁾(ζ₁)
      *             12h                                        30
      *
      *         where ζ₁ lies between x₀ - 2h and x₀ + 2h
@@ -43,7 +43,7 @@ class FivePointFormula extends NumericalDifferentiation
      *   - Note that when the 3rd point is our $target, we use a negative h.
      *
      *              1                                                        h⁴
-     *     f'(x₀) = - [-25f(x₀)+48f(x₀+h)-36f(x₀+2h)+16f(x₀+3h)-3f(x₀+4h)] + - f⁽⁵⁾(ζ₀)
+     *     f′(x₀) = - [-25f(x₀)+48f(x₀+h)-36f(x₀+2h)+16f(x₀+3h)-3f(x₀+4h)] + - f⁽⁵⁾(ζ₀)
      *             12h                                                       5
      *
      *         where ζ₀ lies between x₀ and x₀ + 4h
@@ -88,7 +88,7 @@ public static function differentiate($target, $source, ... $args)
          *   - If the 3rd point is our $target, use the Midpoint Formula:
          *
          *              1                                         h⁴
-         *     f'(x₀) = - [f(x₀-2h)-8f(x₀-h)+8f(x₀+h)-f(x₀+2h)] - - f⁽⁵⁾(ζ₁)
+         *     f′(x₀) = - [f(x₀-2h)-8f(x₀-h)+8f(x₀+h)-f(x₀+2h)] - - f⁽⁵⁾(ζ₁)
          *             12h                                        30
          *
          *         where ζ₁ lies between x₀ - 2h and x₀ + 2h
@@ -97,7 +97,7 @@ public static function differentiate($target, $source, ... $args)
          *   - Note that when the 3rd point is our $target, we use a negative h.
          *
          *              1                                                        h⁴
-         *     f'(x₀) = - [-25f(x₀)+48f(x₀+h)-36f(x₀+2h)+16f(x₀+3h)-3f(x₀+4h)] + - f⁽⁵⁾(ζ₀)
+         *     f′(x₀) = - [-25f(x₀)+48f(x₀+h)-36f(x₀+2h)+16f(x₀+3h)-3f(x₀+4h)] + - f⁽⁵⁾(ζ₀)
          *             12h                                                       5
          *
          *         where ζ₀ lies between x₀ and x₀ + 4h

diff --git a/src/NumericalAnalysis/NumericalDifferentiation/SecondDerivativeMidpointFormula.php b/src/NumericalAnalysis/NumericalDifferentiation/SecondDerivativeMidpointFormula.php
@@ -31,9 +31,9 @@ class SecondDerivativeMidpointFormula extends NumericalDifferentiation
      *
      * Second Derivative Midpoint Formula:
      *
-     *           1                                h²
-     * f''(x₀) = - [f(x₀-h) - 2f(x₀) + f(x₀+h)] - - f⁽⁴⁾(ζ)
-     *           h²                               12
+     *          1                                h²
+     * f″(x₀) = - [f(x₀-h) - 2f(x₀) + f(x₀+h)] - - f⁽⁴⁾(ζ)
+     *          h²                               12
      *
      *     where ζ lies between x₀ - h and x₀ + h
      *
@@ -71,9 +71,9 @@ public static function differentiate($target, $source, ... $args)
         $h = ($sorted[2][$x] - $sorted[0][$x]) / 2;
 
         /*
-         *           1                                h²
-         * f''(x₀) = - [f(x₀-h) - 2f(x₀) + f(x₀+h)] - - f⁽⁴⁾(ζ)
-         *           h²                               12
+         *          1                                h²
+         * f″(x₀) = - [f(x₀-h) - 2f(x₀) + f(x₀+h)] - - f⁽⁴⁾(ζ)
+         *          h²                               12
          *
          *     where ζ lies between x₀ - h and x₀ + h
          */

diff --git a/src/NumericalAnalysis/NumericalDifferentiation/ThreePointFormula.php b/src/NumericalAnalysis/NumericalDifferentiation/ThreePointFormula.php
@@ -34,7 +34,7 @@ class ThreePointFormula extends NumericalDifferentiation
      *   - If the 2nd point is our $target, use the Midpoint Formula:
      *
      *              1                     h²
-     *     f'(x₀) = - [f(x₀+h)-f(x₀-h)] - - f⁽³⁾(ζ₁)
+     *     f′(x₀) = - [f(x₀+h)-f(x₀-h)] - - f⁽³⁾(ζ₁)
      *              2h                    6
      *
      *         where ζ₁ lies between x₀ - h and x₀ + h
@@ -43,7 +43,7 @@ class ThreePointFormula extends NumericalDifferentiation
      *   - Note that when the 3rd point is our $target, we use a negative h.
      *
      *              1                               h²
-     *     f'(x₀) = - [-3f(x₀)+4f(x₀+h)-f(x₀+2h)] + - f⁽³⁾(ζ₀)
+     *     f′(x₀) = - [-3f(x₀)+4f(x₀+h)-f(x₀+2h)] + - f⁽³⁾(ζ₀)
      *              2h                              3
      *
      *         where ζ₀ lies between x₀ and x₀ + 2h
@@ -86,7 +86,7 @@ public static function differentiate($target, $source, ... $args)
          * If the 2nd point is our $target, use the Midpoint Formula:
          *
          *          1                     h²
-         * f'(x₀) = - [f(x₀+h)-f(x₀-h)] - - f⁽³⁾(ζ₁)
+         * f′(x₀) = - [f(x₀+h)-f(x₀-h)] - - f⁽³⁾(ζ₁)
          *          2h                    6
          *
          *     where ζ₁ lies between x₀ - h and x₀ + h
@@ -95,7 +95,7 @@ public static function differentiate($target, $source, ... $args)
          * Note that when the 3rd point is our $target, we use a negative h.
          *
          *          1                               h²
-         * f'(x₀) = - [-3f(x₀)+4f(x₀+h)-f(x₀+2h)] + - f⁽³⁾(ζ₀)
+         * f′(x₀) = - [-3f(x₀)+4f(x₀+h)-f(x₀+2h)] + - f⁽³⁾(ζ₀)
          *          2h                              3
          *
          *     where ζ₀ lies between x₀ and x₀ + 2h