From e7d1fc677180bd6cf07745dc18057483970e6e1a Mon Sep 17 00:00:00 2001 From: Tom Malone Date: Sun, 21 Feb 2016 21:59:25 -0500 Subject: [PATCH] Added more information to introduction to Numerical Integration. --- .../Approximate_Integration-checkpoint.ipynb | 4 +++- 07_Integration_Techniques/Approximate_Integration.ipynb | 4 +++- 2 files changed, 6 insertions(+), 2 deletions(-) diff --git a/07_Integration_Techniques/.ipynb_checkpoints/Approximate_Integration-checkpoint.ipynb b/07_Integration_Techniques/.ipynb_checkpoints/Approximate_Integration-checkpoint.ipynb index a724164..d34f747 100644 --- a/07_Integration_Techniques/.ipynb_checkpoints/Approximate_Integration-checkpoint.ipynb +++ b/07_Integration_Techniques/.ipynb_checkpoints/Approximate_Integration-checkpoint.ipynb @@ -14,7 +14,9 @@ "\n", "You can _approximate_ definite integrals using simple, arithmetic methods similar to __Riemann Sums.__\n", "\n", - "Essentially, these methods provide approximate values of the area under a curve between two endpoints (the limits of integration).\n", + "Essentially, _these methods provide an approximate value for the area under a curve between two endpoints_ (the limits of integration). The methods work on any type of functions, regardless of whether or not an antiderivative of the function can be found.\n", + "\n", + "In many scenarios in science & engineering, the resulting approximations are close enough to fulfill project requirements. Additionally, methods exist for controlling the accuracy of/error in the resulting approximate values.\n", "\n", "#### Examples\n", "These functions cannot be integrated using the techniques of integration we've learned:\n", diff --git a/07_Integration_Techniques/Approximate_Integration.ipynb b/07_Integration_Techniques/Approximate_Integration.ipynb index a724164..d34f747 100644 --- a/07_Integration_Techniques/Approximate_Integration.ipynb +++ b/07_Integration_Techniques/Approximate_Integration.ipynb @@ -14,7 +14,9 @@ "\n", "You can _approximate_ definite integrals using simple, arithmetic methods similar to __Riemann Sums.__\n", "\n", - "Essentially, these methods provide approximate values of the area under a curve between two endpoints (the limits of integration).\n", + "Essentially, _these methods provide an approximate value for the area under a curve between two endpoints_ (the limits of integration). The methods work on any type of functions, regardless of whether or not an antiderivative of the function can be found.\n", + "\n", + "In many scenarios in science & engineering, the resulting approximations are close enough to fulfill project requirements. Additionally, methods exist for controlling the accuracy of/error in the resulting approximate values.\n", "\n", "#### Examples\n", "These functions cannot be integrated using the techniques of integration we've learned:\n",