OverviewThis article describes the HTML notebook format, and is primarily intended for front-end applications using or embedding R, or other users who are interested in reading and writing documents using the R Notebook format.R Notebooks are HTML documents with data written and encoded in such a way that:. The source.Rmd document can be recovered, and.
Chunk outputs can be recovered.To generate an R Notebook, you can use rmarkdown::render and specify the htmlnotebook output format in your document’s YAML metadata. Documents rendered in this form will be generated with the.nb.html file extension, to indicate that they are HTML notebooks.To ensure chunk outputs can be recovered, the elements of the R Markdown document are enclosed with HTML comments, providing more information on the output. For example, chunk output might be serialized as:
Parsing R NotebooksThe rmarkdown::parsehtmlnotebook function provides an interface for recovering and parsing an HTML notebook.
Mathematica LabsThis is where my students can come to download the labs we will be doingin class. I have also added some more general labs that others might findinteresting.
This is a work 'in progress', so I am open to suggestionsfor other topics, improvements on these labs, and corrections.Before you begin - Check out my. The labs at the top of the list require version 6 (or higher) of Mathematica to work. They may work in earlier versions, but I doubt it. Calculus IV - Spring 2013. Lab 1: Functions, Graphs, and IntegralsThe composition of functions of more than one variable, functions as arguments, ParametricPlot3D, restrictions on functions. Using Mathematica to help you visualize and compute double and triple integrals. ( - 3.4 megabyte file).
Lab 2a: Non-Cartesian Coordinate Systems - Part aUsing a change of coordinates to evaluate integrals over difficult regions of integration. Mathematica's built-in non-Cartesian coordinate systems and how to visualize them. Calculus III - Fall 2012. Lab 1: Curves and SurfacesCurves and curvature. Functions of 2 variables and limits.
Notebook Spring Vector Png
6 megabyte file.). Lab 2a: Surfaces and OptimizationSurfaces in spherical and cylindrical coordinates. Calculus III - Fall 2011. Lab 1: Curves, Surfaces, and OptimizationCurves and curvature. Functions of 2 variables, cylindrical and spherical coordinates, and limits. Optimization and constrained optimization. 6 megabyte file.)Calculus IV - Spring 2009.
Lab 1a: Functions, Graphs, and Integrals - Part aThe composition of functions of more than one variable, functions as arguments, ParametricPlot3D, restrictions on functions. ( - 1.6 megabyte file) If you downloaded the original version of this, I have deleted one of the last graphing problems (the one in parametric cylindrical coordinates), so be sure you double-check.
Lab 1b: Functions, Graphs, and Integrals - Part bUsing Mathematica to help you visualize and compute double and triple integrals. ( - 1.6 megabyte file). Lab 2a: Non-Cartesian Coordinate Systems - Part aUsing a change of coordinates to evaluate integrals over difficult regions of integration. Mathematica's built-in non-Cartesian coordinate systems and how to visualize them. ( - 5.6 megabyte file. A much smaller file with the output deleted can be downloaded, if you have a slowish connection.
You will need to re-execute everything.). Lab 2b: Non-Cartesian Coordinate Systems - Part bUsing a change of coordinates to evaluate integrals over difficult regions of integration. Mathematica's built-in non-Cartesian coordinate systems and how to work with them. ( - 2 megabyte file.). Lab 3: IntegrationNothing very deep here; just some different types of integrals (path, line, surface, etc.) to work. You must also identify which can be worked using the different integral theorems we have studied and verify the theorems are indeed true on these. Calculus IV - Spring 2008.
Lab 1a: Functions, Graphs, and Integrals - Part aThe composition of functions of more than one variable, functions as arguments, ParametricPlot3D, restrictions on functions. ( - 1.6 megabyte file) If you downloaded the original version of this, I have deleted one of the last graphing problems (the one in parametric cylindrical coordinates), so be sure you double-check. Lab 1b: Functions, Graphs, and Integrals - Part bUsing Mathematica to help you visualize and compute double and triple integrals. ( - 1.6 megabyte file). Lab 2a: Non-Cartesian Coordinate Systems - Part aUsing a change of coordinates to evaluate integrals over difficult regions of integration. Mathematica's built-in non-Cartesian coordinate systems and how to visualize them.
( - 5.6 megabyte file. A much smaller file with the output deleted can be downloaded, if you have a slowish connection. You will need to re-execute everything.). Lab 2b: Non-Cartesian Coordinate Systems - Part bUsing a change of coordinates to evaluate integrals over difficult regions of integration.
Mathematica's built-in non-Cartesian coordinate systems and how to work with them. ( - 2 megabyte file.). Lab 3: IntegrationNothing very deep here; just some different types of integrals (path, line, surface, etc.) to work. You must also identify which can be worked using the different integral theorems we have studied and verify the theorems are indeed true on these. Labs below this line were written for version 5/5.1/5.2 of Mathematica; they may or may not work with the current version 6. Differential Equations - Summer 2007.
Lab 0 - Using Mathematica to Solve Differential EquationsThis isn't really a true lab, but it is an introduction to how to use Mathematica to solve differential equations and systems of differential equations. Use this for reference and to do the other labs. Warning: This explanation isn't complete, though it should have plenty of information in it to get you started (you won't need all of it right away). ( / - 6 Megabyte file / - much smaller file, but you have to execute the commands to see the output). Lab 1 - Equilibrium behavior, sensitivity to initial conditions, and an example of population growthThis lab covers techniques for analyzing autonomous equations, investigating the sensitivity of a first order equation to initial conditions and how that effects approximation methods, and investigates another model of population growth. ( / )Calculus IV - Spring 2007.
Lab 1: Limits and FunctionsLimits of functions of two variables, the composition of functions of more than one variable, functions as arguments, ParametricPlot3D, and graphing too many dimensions. ( / - 6 megabyte file / - much smaller file, but you have to execute the commands to see the output).
Lab 2: Non-Cartesian Coordinate SystemsHow to work in non-Cartesian coordinate systems. This examines graphing, differential operators, integration, and Mathematica's built-in support for doing these things in different non-Cartesian coordinate systems. ( / / - If you download the short form, you should go to the Kernal menu, choose Evaluation, and then Evaluate Notebook.)Differential Equations - Summer 2006.
Lab 0 - Using Mathematica to Solve Differential EquationsThis isn't really a true lab, but it is an introduction to how to use Mathematica to solve differential equations and systems of differential equations. Use this for reference and to do the other labs. Warning: This explanation isn't complete, though it should have plenty of information in it to get you started (you won't need all of it right away). ( / - 6 Megabyte file / - much smaller file, but you have to execute the commands to see the output). Lab 1 - Equilibrium behavior, sensitivity to initial conditions, and an example of population growthThis lab covers techniques for analyzing autonomous equations, investigating the sensitivity of a first order equation to initial conditions and how that effects approximation methods, and investigates another model of population growth. ( / )Calculus IV - Spring 2006.
Lab 1: Limits and FunctionsLimits of functions of two variables, the composition of functions of more than one variable, functions as arguments, and ParametricPlot3D. ( / ). Lab 2: Non-Cartesian Coordinate SystemsHow to work in non-Cartesian coordinate systems. This examines graphing, differential operators, integration, and Mathematica's built-in support for doing these things in many different non-Cartesian coordinate systems.
( / / - If you download the short form, you should go to the Kernal menu, choose Evaluation, and then Evaluate Notebook.)Differential Equations - Summer 2005. Lab 0 - Using Mathematica to Solve Differential EquationsThis isn't really a true lab yet, but it is an introduction to how to use Mathematica to solve differential equations and systems of differential equations. Use this for reference and to do the other labs. Warning: This explanation isn't complete, though it should have plenty of information in it to get you started (you won't need all of it right away). ( / - 6 Megabyte file / - much smaller file, but you have to execute the commands to see the output). Lab 1 - Equilibrium behavior, sensitivity to initial conditions, and an example of population growthThis lab covers techniques for analyzing autonomous equations, investigating the sensitivity of a first order equation to initial conditions and how that effects approximation methods, and investigates another model of population growth.
( / )Calculus IV - Spring 2005. Lab 1: Limits and FunctionsLimits of functions of two variables, the composition of functions of more than one variable, functions as arguments, and ParametricPlot3D. ( / ).
Lab 2: Non-Cartesian Coordinate SystemsHow to work in non-Cartesian coordinate systems. This examines graphing, differential operators, integration, and Mathematica's built-in support for doing these things in many different non-Cartesian coordinate systems. ( / / - If you download the short form, you should go to the Kernal menu, choose Evaluation, and then Evaluate Notebook.)Calculus IV - Fall 2004.
Lab 1: Limits and FunctionsLimits of functions of two variables, the composition of functions of more than one variable, functions as arguments, and ParametricPlot3D. ( / ). Lab 2: Non-Cartesian Coordinate SystemsHow to work in non-Cartesian coordinate systems. This examines graphing, differential operators, integration, and Mathematica's built-in support for doing these things in many different non-Cartesian coordinate systems. ( / / - If you download the short form, you should go to the Kernal menu, choose Evaluation, and then Evaluate Notebook.). Lab 3: Vector IntegrationNothing very deep here; just some different types of integrals (path, line, surface, etc.) to work.
You must also identify which can be worked using the different integral theorems we have studied and verify the theorems are indeed true on these. ( / )Differential Equations - Summer 2004. Lab 0 - Using Mathematica to Solve Differential EquationsThis isn't really a true lab yet, but it is an introduction to how to use Mathematica to solve differential equations and systems of differential equations. Use this for reference and to do the other labs.
Warning: This explanation isn't complete, though it should have plenty of information in it to get you started (you won't need all of it right away). ( / - 6 Megabyte file / - much smaller file, but you have to execute the commands to see the output). Lab 1 - Equilibrium behavior, sensitivity to initial conditions, and an example of population growthThis lab covers techniques for analyzing autonomous equations, investigating the sensitivity of a first order equation to initial conditions and how that effects approximation methods, and investigates another model of population growth. ( / )Calculus II - Spring 2004. Extra credit labFinding Taylor series expansions of a function and the error introduced by using a finite Taylor polynomial. ( / )Calculus IV - Spring 2004.
Lab 1: Limits and FunctionsLimits of functions of two variables, the composition of functions of more than one variable, and ParametricPlot3D. ( / ). Lab 2: Non-Cartesian Coordinate SystemsHow to work in non-Cartesian coordinate systems. This examines graphing, differential operators, integration, and Mathematica's built-in support for doing these things in many different non-Cartesian coordinate systems. ( / / - If you download the short form, you should go to the Kernal menu, choose Evaluation, and then Evaluate Notebook.). Lab 3: Vector IntegrationNothing very deep here; just some different types of integrals (path, line, surface, etc.) to work.
You must also identify which can be worked using the different integral theorems we have studied and verify the theorems are indeed true on these. ( / )Differential Equations - Summer 2003. Lab 0 - Using Mathematica to Solve Differential EquationsThis isn't really a true lab yet, but it is an introduction to howto use Mathematica to solve differential equations and systems of differentialequations. Use this for reference and to do the assignement I announcedin class. I hope to have a real lab or three for you soon, but we'llsee how time goes.
Warning: This explanation isn't complete, thoughit should have plenty of information in it to get you started. (/ ). Lab 1 - Damped Harmonic Oscillation with a Driving ForceThis is just the assignment I gave in class on Wednesday, but fleshedout a little. It asks you to give graphical examples of resonance, beating,and the 3 different types of damping for a driven, damped harmonic oscillator.( / )General labs - I hope to add more of thesesoon. Lab 1: The Rule of Three and Other Oddities (some CollegeAlgebra content, some Calculus level content)This lab introduces the Rule of Three which has been a populareducational idea over the last few years. The idea is that you approachproblems from three different perspectives: numerically, graphically,and symbolically. In seeing the same problem from three different 'angles',you sometimes develop a better feel for how the problem works.
WhileI think this idea can be abused, it does offer a useful approach tosome types of problems. This lab investigates some simple examples thatutilize this approach. Some of the later labs make use of these ideasin a less formal way, but with more sophistication. WARNING: THIS LABIS NOT COMPLETE YET.
USE AT YOUR OWN RISK. (/ ). Lab 2: Curve Fitting Population Growth Data (College Algebra andabove level)This lab investigates fitting several different curves to some dataon the population of the U.S. It compares the different 'fits'and considers what happens when more data is available.
(/ ). Lab 3: Numerical Integration and Error Approximation (CalculusII and above level)This lab investigates the simpler methods of approximating a definiteintegral numerically (left-hand sum, right-hand sum, Trapezoid Rule,Midpoint Rule, and Simpson's Rule) and the errors in these methods asa function of the number of subdivisions.
(/ ). Lab 4: Error Approximation in Taylor Series (Calculus II and abovelevel)This lab investigates using a finite Taylor polynomial to approximatea function. In particular, it exames how to find the domain for a Taylorpolynomial of given degree such that its error will be within a desiredrange. It also investigates the case where you need to find how manyterms of a Taylor series to use to approximate a function to withina desired error tolerance over a given interval. (/ )Calculus IV - Spring 2002. Lab 1: Limits and FunctionsLimits of functions of two variables, the composition of functionsof more than one variable, and ParametricPlot3D.
(/ ). Lab 2: Non-Cartesian Coordinate SystemsThis lab discusses how to visualize non-Cartesian coordinate systemsin 3 dimensions. It also discusses the functions Mathematica has built-into handle this. There is some discussion of integration in these coordinatesystems as well. (/ - I havedeleted all the output in the notebook to save space. After you downloadthis file, you should go to the Kernal menu, choose Evaluation,and then Evaluate Notebook.).
Lab 3: Vector IntegrationThis is actually a pretty short lab (since we are short on timedue to the technical problems we had before we got the Mathematica updataearlier in the semester). I simply ask students to work the integralsfrom the last test in Mathematica. (/ )Calculus III - Spring 2001. Lab 1: Polar and Parametric EquationsLab 1 comes in two parts:. 1a - Polar Equations:Finding points of intersection of two polar graphs, finding thearea between two polar graphs, and finding the arc-length of a polargraph.
(/ ). 1b - Parametric Equations:Use parametric equations to take a closer look at the cycloid, epicycloid,and the hypocycloid.
(/ ). Lab 2: 3-Dimensional GraphsLab 2 comes in two parts:. 2a - CurvesCurvature and its relationship to the graph.
Curves on a surface.( / ). 2b - Surfaces:Functions of two variables. Graphs in spherical and cylindricalcoordinates. Limits of functions of two variables.
(/ ). Lab 3: Optimization - Optimization without constraints, curvefitting using the method of least squares, and optimization with constraints.( / )Calculus III - Fall 2000. Lab I - Polar and Parametric Equations (including a closerlook at the cycloid, epicycloid, and hypocycloid). Lab 2 - 3-Dimensional Graphs: Curves and Surfaces. Lab 3 - Optimization (constrained and unconstrained, with a lookat fitting a curve to experimental data) These will be added as I finish them.