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.
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 3x, the derivative of 3x, ex, the derivative of ex, and 2x, the derivative of 2x are shown in the plot on the left in the figure below to show the awesome properties of ex, for example. The derivative of ex is ex 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 ex=3. This point was chosen as an example. The functions used to create the tangent and normal lines are as follows.
- 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 ex to x0=3 can be found by integrating the curve from −∞ to 3 and is e3. 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.
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.
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