The week long Analyzing COVID-19 Data Study Group (6) covered the of analysis, visualization and modeling of COVID-19 pandemic data using various Wolfram COVID-19 resources, the NY Times COVID-19 Dataset, and a patient data set. The daily study sessions demonstrated techniques to analyze patient data, virus genetic sequences, and model the pandemic using epidemic data. The figure below shows the COVID-19 Death Rate per 100,000 people by state based on the April 11, 2021 update of the *Epidemic Data for Novel Coronavirus COVID-19 dataset*, for example.

# Category Archives: Mathematica

# Wolfram U Daily Study Group: System Modeling

The two week long System Modeling Study Group (5) uses the Wolfram System Modeler: An Introduction course as part of the day lectures. The Wolfram System Modeler is a separate application and is based on the open source Modelica language. In the study group, we simulated chemical reactions, thermal conductivity of walls, the electro-mechanics of a joystick, a DC motor, and a heater, for example. The System Modeler uses the Functional Mock-up Interface (FMI) and can interface with more that 150 tools. We installed StandardFirmata into an Arduino to demonstrate a control applications with System Modeler.

# Wolfram U Daily Study Group: Calculus

The three week Calculus Study Group (4) uses the Introduction to Calculus self study course as part of the daily lectures and covers functions, limits, differential calculus, and integral calculus. This course is a good way to prepare for AP Calculus and is a great refresher on the topic.

The functions 3^{x}, the derivative of 3^{x}, e^{x}, the derivative of e^{x}, and 2^{x}, the derivative of 2^{x} are shown in the plot on the left in the figure below to show the awesome properties of e^{x}, for example. The derivative of e^{x} is e^{x} so the slope anywhere on the line is just the value of the function at that point.

The tangent line and normal line are shown in the plot on the right for e^{x}=3. This point was chosen as an example. The functions used to create the tangent and normal lines are as follows.

- f(x)=e
^{x} - Tangent(x)=f′(x)(x−x0)+f(x0) at x0=3
- Normal(x)=(−1/f′(x))(x−x0)+f(x0) at x0=3

The area under e^{x} to x0=3 can be found by integrating the curve from −∞ to 3 and is e^{3}. Thus, the area under the curve is also the value of the function at that point.

To receive a program completion certificate you must pass three quizzes.

# Wolfram U Introduction to Notebooks

The three week Introduction to Notebooks Study Group (3) covered notebooks, machine learning, and image processing. Daily study group lectures included content from Wolfram courses and live instructor instruction that varied from week to week and included:

- Week 1: Introduction to Notebooks covered styling, formatting and creating interactive documents.
- Week 2: Machine Learning covered classification, regression, cluster analysis and anomaly detection.
- Week 3: Image processing covered digital image processing, image representation, and classical operations on images.

I used the image processing tools to find clusters in a photograph of an Arduino MKR WiFi 1010 board, colorized the clusters, and add colorized text to make a composite illustration that demonstrates the use of these features.

To receive a course completion certificate you must pass three quizzes.

# Wolfram Technology Level 1 Certificate

I received my Wolfram Technology Level 1 Certificate for demonstrating proficiency in the Wolfram Language Programming Fundamentals! To receive the Level 1 certificate, students needed to complete and pass a 20 question exercise. Each question required you to write a program to solve a problem described in the question. Most questions gave hints on what functions should be used to solve the problem.

So, now it get interesting because the exercises run on the Wolfram cloud and the answers are graded by an auto-grader. Basically, we need to convince a bot that we can program. There are multiple correct ways to solve the problem, but the auto-grader doesn’t like just any solution so it might take 3 or more program submission to get a pass on a question. The auto-grader seems to prefer efficient code so you can have the correct from of the program, but auto-grader will reject it until you submit the more or most efficient answer.

Some questions specified the use of random integers or random selections. The auto-grader did not seem to be able to accommodate program answers that produce random outputs. Several other questions seemed to give the auto-grader problems, and it’s unclear why. The answers to these seven questions were submitted to the study group staff by email and graded by hand.

# Wolfram Language Programming Fundamentals Certificate

My efforts to improve my Wolfram Language skills continues with the Wolfram U daily study group on the the Wolfram Language Programming Fundamentals. This Study group ran four days a week in May 2020 and required passing four quizzes. Again, thanks to Wolfram for running the program.

# Wolfram Language Introduction Certificate

I’ve been working to improve my Wolfram Language skills by taking the Wolfram U study group on the introduction to the Wolfram Language that is integral to Mathematica. The Study group ran four days a week in April 2020 and required passing four quizzes. Thanks to Wolfram for running the program.

# Introduction to Mathematica® for Physicists

Springer has made Introduction to Mathematica® for Physicists available for free on its website. The book uses Mathematica 9 to describe physics topics that include:

- Trigonometric functions
- Quantum Oscillators
- Spherical Harmonics
- Adding Angular Momenta in Quantum Mechanics
- Quantum Nonlinear Oscillators
- Riemann Curvature Tensors
- Multi-ζ Functions
- Geometric Optics
- Cyclohexane configurations

# Fluid simulator

Wolfram has posed a pretty cool web based fluid simulator. Wolfram’s blog describes how they visualized the fluid flow simulation. The source is available on GitHub.

# Graphene FET Toy Physics Model

This graphene FET toy physics model is primarily based on the graphene physics described in the paper *Electronic transport in two dimensional graphene* by S. D. Sarma et. al. and from materials properties data found in a number of sources (see the **Description** tab for the details). I’d appreciate any comments on errors, problems, inaccuracies, or how to make this model better.

The **IV Model** tab allows you to selected the gate dielectric, dielectric thickness, mobility, gate voltage, phonon energy of the dielectric, drain-source voltage, drain-source length and width, and the resulting IV curve is plotted for these parameters.

The **Performance Table** tab shows a summary of the graphene FET performance based on the selected values on the IV Model tab.

The **Materials Properties** Tab shows the dielectric constant, breakdown voltage, and optical phonon energy for each gate dielectric that can be selected in the IV Model tab.

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