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 # <span style="color:rgb(213,80,0)">Numerical Methods with Applications</span>
 
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-[![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) or [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=README.mlx)
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-![MATLAB Versions Tested](https://img.shields.io/endpoint?url=https%3A%2F%2Fraw.githubusercontent.com%2FMathWorks-Teaching-Resources%2FNumerical-Methods-with-Applications%2Frelease%2FImages%2FTestedWith.json)
-
-**Curriculum Module**
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-_Created with R2021b. Compatible with R2021b and later releases._
-
+
+[![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) or [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=README.mlx)
+
+![MATLAB Versions Tested](https://img.shields.io/endpoint?url=https%3A%2F%2Fraw.githubusercontent.com%2FMathWorks-Teaching-Resources%2FNumerical-Methods-with-Applications%2Frelease%2FImages%2FTestedWith.json)
+
+**Curriculum Module**
+
+_Created with R2021b. Compatible with R2021b and later releases._
+
 # Information
 
 This curriculum module contains interactive [MATLAB® live scripts](https://www.mathworks.com/products/matlab/live-editor.html) that teach fundamental concepts and basic terminology related to designing and implementing numerical methods related to interpolation, numerical integration and differentiation, and numerical solutions to ordinary and partial differential equations.
@@ -53,30 +53,30 @@ MATLAB® is used throughout. Tools from the Symbolic Math Toolbox™ are used fr
 
 # Scripts
 ## [**Interpolation.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=Interpolation.mlx) 
-| <img src="Images/hand.png" width="171" alt="hand.png"> <br>  | **In this script, students will...** <br> <br>-  define interpolation and explain how it is different from regression and extrapolation <br> <br>-  demonstrate multiple solutions to an interpolation problem, even when interpolating by polynomials <br> <br>-  implement three different interpolation functions <br>  | **Applications** <br> <br>-  Drawing a smooth rendition of their hand <br> <br>-  Tracking the path of a cyclone <br> **Scaffolded Template Scripts** <br> [<samp>linInterp.m</samp>](./FunctionLibrary/linInterp.m) <br> [<samp>pcHInterp.m</samp>](./FunctionLibrary/pcHInterp.m) <br> [<samp>pcSpline.m</samp>](./FunctionLibrary/pcSpline.m) <br>   |
+| <img src="Images/hand.png" width="171" alt="hand.png"> <br>  | **In this script, students will...** <br> <br>-  define interpolation and explain how it is different from regression and extrapolation <br>-  demonstrate multiple solutions to an interpolation problem, even when interpolating by polynomials <br>-  implement three different interpolation functions <br>  | **Applications**  <br>-  Drawing a smooth rendition of their hand <br>-  Tracking the path of a cyclone <br><br> **Scaffolded Template Scripts** <br> [<samp>linInterp.m</samp>](./FunctionLibrary/linInterp.m) <br> [<samp>pcHInterp.m</samp>](./FunctionLibrary/pcHInterp.m) <br> [<samp>pcSpline.m</samp>](./FunctionLibrary/pcSpline.m) <br>   |
 | :-- | :-- | :-- |
 
 ## Supporting Scripts
 -  [<samp>Hand.mlx</samp>](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=Hand.mlx) 
 -  [<samp>TrackStorms.mlx</samp>](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=TrackStorms.mlx) 
 ## [**NumericalDerivatives.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=NumericalDerivatives.mlx) 
-| <img src="Images/NoisyDerivative.png" width="171" alt="NoisyDerivative.png"> <br>  | **In this script, students will...** <br> <br>-  determine numerical derivative approximations formulas <br> <br>-  use Taylor's theorem to calculate the order of the error for a numerical approximation to a derivative <br> <br>-  demonstrate how numerical derivatives can magnify approximation errors <br>  | **Applications** <br> <br>-  Numerical solutions to differential equations <br>   |
+| <img src="Images/NoisyDerivative.png" width="171" alt="NoisyDerivative.png"> <br>  | **In this script, students will...** <br> <br> -  determine numerical derivative approximations formulas <br>-  use Taylor's theorem to calculate the order of the error for a numerical approximation to a derivative <br> -  demonstrate how numerical derivatives can magnify approximation errors <br>  | **Applications** <br>-  Numerical solutions to differential equations <br>   |
 | :-- | :-- | :-- |
 
 ## [**NumericalIntegration.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=NumericalIntegration.mlx) 
-| <img src="Images/BakerLakeSR.png" width="171" alt="BakerLakeSR.png"> <br>  | **In this script, students will...** <br> <br>-  implement Euler's method, Gaussian 2\-point approximations, and Simpson's rule for numerical integration <br> <br>-  explain why higher\-order approximations may not be appropriate in applications <br>  | **Applications** <br> <br>-  Measure the area of a lake <br> **Scaffolded Template Scripts** <br> [<samp>eulerMethod.m</samp>](./FunctionLibrary/eulerMethod.m) <br> [<samp>gauss2pt.m</samp>](./FunctionLibrary/gauss2pt.m) <br> [<samp>simpsonsRule.m</samp>](./FunctionLibrary/simpsonsRule.m) <br>   |
+| <img src="Images/BakerLakeSR.png" width="171" alt="BakerLakeSR.png"> <br>  | **In this script, students will...** <br> <br> -  implement Euler's method, Gaussian 2\-point approximations, and Simpson's rule for numerical integration <br> -  explain why higher\-order approximations may not be appropriate in applications <br>  | **Applications** <br> -  Measure the area of a lake <br><br> **Scaffolded Template Scripts** <br> [<samp>eulerMethod.m</samp>](./FunctionLibrary/eulerMethod.m) <br> [<samp>gauss2pt.m</samp>](./FunctionLibrary/gauss2pt.m) <br> [<samp>simpsonsRule.m</samp>](./FunctionLibrary/simpsonsRule.m) <br>   |
 | :-- | :-- | :-- |
 
 ## Supporting Scripts
 -  [<samp>MeasureLakeArea.mlx</samp>](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=MeasureLakeArea.mlx) 
 ## [**NumericalODEs.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=NumericalODEs.mlx) 
-| <img src="Images/image_6.png" width="171" alt="image_6.png"> <br>  | **In this script, students will...** <br> <br>-  implement Euler's method for first\-order initial value problems <br> <br>-  calculate the error of their numerical solution <br> <br>-  implement a trapezoidal method <br> <br>-  implement a four\-step Runge\-Kutta method <br> <br>-  compare results with the built\-in MATLAB solver <samp>ode45</samp> <br>  | **Applications** <br> <br>-  Model a pendulum with increasingly realistic assumptions <br> **Scaffolded Template Scripts** <br> [<samp>eulerMethodDE.m</samp>](./FunctionLibrary/eulerMethodDE.m) <br> [<samp>rk4.m</samp>](./FunctionLibrary/rk4.m) <br>   |
+| <img src="Images/image_6.png" width="171" alt="image_6.png"> <br>  | **In this script, students will...** <br> <br> -  implement Euler's method for first\-order initial value problems <br> -  calculate the error of their numerical solution <br> -  implement a trapezoidal method <br>-  implement a four\-step Runge\-Kutta method <br> -  compare results with the built\-in MATLAB solver <samp>ode45</samp> <br>  | **Applications** <br> -  Model a pendulum with increasingly realistic assumptions <br><br> **Scaffolded Template Scripts** <br> [<samp>eulerMethodDE.m</samp>](./FunctionLibrary/eulerMethodDE.m) <br> [<samp>rk4.m</samp>](./FunctionLibrary/rk4.m) <br>   |
 | :-- | :-- | :-- |
 
 ## Supporting Scripts
 -  [<samp>PendulumModels.mlx</samp>](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=PendulumModels.mlx) 
 ## [**NumericalPDEs.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=NumericalPDEs.mlx) 
-| <img src="Images/heatSoln.gif" width="171" alt="heatSoln.gif"> <br>  | **In this script, students will...** <br> <br>-  identify errors from discretizing the problem and from discretizing the method and choose appropriate parameters to minimize overall error <br> <br>-  explain the importance of stability when choosing a numerical method <br> <br>-  implement explicit, implicit, and Crank\-Nicolson methods to solve a 1\-D heat equation <br>  | **Applications** <br> <br>-  Solve a heat equation <br> **Scaffolded Template Scripts** <br> [<samp>explicitPDE.m</samp>](./FunctionLibrary/explicitPDE.m) <br> [<samp>implicitPDE.m</samp>](./FunctionLibrary/implicitPDE.m) <br> [<samp>cnPDE.m</samp>](./FunctionLibrary/cnPDE.m) <br>   |
+| <img src="Images/heatSoln.gif" width="171" alt="heatSoln.gif"> <br>  | **In this script, students will...** <br> <br> -  identify errors from discretizing the problem and from discretizing the method and choose appropriate parameters to minimize overall error <br> -  explain the importance of stability when choosing a numerical method <br> -  implement explicit, implicit, and Crank\-Nicolson methods to solve a 1\-D heat equation <br>  | **Applications** <br> -  Solve a heat equation <br><br> **Scaffolded Template Scripts** <br> [<samp>explicitPDE.m</samp>](./FunctionLibrary/explicitPDE.m) <br> [<samp>implicitPDE.m</samp>](./FunctionLibrary/implicitPDE.m) <br> [<samp>cnPDE.m</samp>](./FunctionLibrary/cnPDE.m) <br>   |
 | :-- | :-- | :-- |
 
 # License
@@ -102,4 +102,5 @@ Looking for more? Find an issue? Have a suggestion? Please contact the [MathWork
 
  *©* Copyright 2024 The MathWorks™, Inc
 
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