You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Copy file name to clipboardExpand all lines: README.md
+16-15Lines changed: 16 additions & 15 deletions
Display the source diff
Display the rich diff
Original file line number
Diff line number
Diff line change
@@ -1,15 +1,15 @@
1
1
2
2
# <spanstyle="color:rgb(213,80,0)">Numerical Methods with Applications</span>
3
3
4
-
5
-
[](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) or [](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=README.mlx)
_Created with R2021b. Compatible with R2021b and later releases._
12
-
4
+
5
+
[](https://www.mathworks.com/matlabcentral/fileexchange/111490-numerical-methods-with-applications) or [](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Numerical-Methods-with-Applications&project=NumericalMethods.prj&file=README.mlx)
_Created with R2021b. Compatible with R2021b and later releases._
12
+
13
13
# Information
14
14
15
15
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
| <imgsrc="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> |
56
+
| <imgsrc="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> |
| <imgsrc="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> |
63
+
| <imgsrc="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> |
| <imgsrc="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> |
67
+
| <imgsrc="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> |
| <imgsrc="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> |
73
+
| <imgsrc="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> |
| <imgsrc="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> |
79
+
| <imgsrc="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> |
80
80
| :-- | :-- | :-- |
81
81
82
82
# License
@@ -102,4 +102,5 @@ Looking for more? Find an issue? Have a suggestion? Please contact the [MathWork
0 commit comments