Our goal in Unit 1 is to make learners comfortable with Python by using it as a graphing calculator. In later units/volumes we will dive into more advanced numerical techniques.
Below are the specific skills that we introduce in Unit 1 of Volume 1 and where they are introduced.
In addition to these skills, there are Python examples that demonstrate how more advanced numerical techniques might be advantageous.
The purpose of these are to be demonstrations rather than give the reader more to have to learn.
Unit 1 Python Skills
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Scientific notation (Section 1.2)
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Printing and f-strings (Section 1.6)
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Variables, Arithmetic, and Plotting with Matplotlib (Section 1.7.1 - Using Computing Tools)
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Using NumPy arrays to represent vectors (Section 2.2)
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Using arrays to do vector algebra (Section 2.3)
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Computing dot products and magnitudes in Python (Section 2.4)
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Using functions to represent mathematical functions (Section 3.1)
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Euler's method in 1 dimension (Section 3.7)
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Euler's method in multiple dimensions (Section 4.6)
Additional Demonstrations in Unit 1
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Numerical Derivatives (Section 3.2)
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Computing a second derivative numerically (Section 3.3)
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Euler's method example in 1D (Section 3.6)
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Dampened harmonic oscillator (Section 5.7)
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Circular and non-circular orbits with 2D Euler's method (Section 6.3)
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Felix Baumgartner (Section 6.4)