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# Numerical Methods with Applications
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[](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) or [Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/numerical-methods-with-applications&project=NumericalMethods.prj)
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[](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) or [Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj)
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**Curriculum Module**
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_Created with R2021b. Compatible with R2021b and later releases._
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These scripts do not assume knowledge of analytic solutions to ordinary or partial differential equations.
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## Details ##
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**NavigationOverview.mlx**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/numerical-methods-with-applications&project=NumericalMethods.prj&file=NavigationOverview.mlx)
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**NavigationOverview.mlx**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=NavigationOverview.mlx)
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This script brings together links and short descriptions of the content in the recommended order of use.
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## ##
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**Interpolation**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/numerical-methods-with-applications&project=NumericalMethods.prj&file=interpolation.mlx)
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**Interpolation**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=interpolation.mlx)
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This folder includes the interactive example script `interpolation.mlx` that guides students through building
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their own data set(s) using `hand.mlx` and writing their own linear interpolation function and piecewise cubic
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Hermite interpolation function. The laboratory script `trackStorms.mlx` allows students to apply the scripts
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- Demonstrate multiple solutions to an interpolation problem, even when interpolating by polynomials.
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## ##
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**Derivatives**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/numerical-methods-with-applications&project=NumericalMethods.prj&file=approximatingDerivatives.mlx)
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**Derivatives**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=approximatingDerivatives.mlx)
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This folder includes the interactive example script `approximatingDerivatives.mlx` that introduces the
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method of Taylor series approximation to create and analyze numerical approximations to derivatives of
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different orders.
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- Demonstrate how numerical derivatives can magnify approximation errors.
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## ##
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**Integrals**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/numerical-methods-with-applications&project=NumericalMethods.prj&file=numericalIntegration.mlx)
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**Integrals**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=numericalIntegration.mlx)
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This folder includes the interactive example script `numericalIntegration.mlx` that guides students
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through building functions to compute forward and backward Euler method approximations, a 2-point
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Gaussian approximation, and a Simpson's rule approximation. The laboratory script `measureLake.mlx`
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- Explain why higher-order approximations may not be appropriate in applications.
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## ##
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**Ordinary Differential Equations**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/numerical-methods-with-applications&project=NumericalMethods.prj&file=diffEqs.mlx)
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**Ordinary Differential Equations**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=diffEqs.mlx)
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This folder includes the interactive example script `diffEqs.mlx` that guides students through
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implementing an Euler method solver and a four-step Runge-Kutta method solver, and comparing the
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results of their implementations to the built-in solver `ode45`. The laboratory script
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- Implement a four-step Runge-Kutta method.
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## ##
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**Partial Differential Equations**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/numerical-methods-with-applications&project=NumericalMethods.prj&file=partialDiffEqs.mlx)
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**Partial Differential Equations**[Open in MATLAB Online](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=partialDiffEqs.mlx)
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This folder includes the interactive example script `partialDiffEqs.mlx` that guides students
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through an exploration of explicit, implicit, and mixed methods for numerically solving
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first-order ordinary differential equations. The activity script `implementExplicitSolver.mlx`
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