58 lines
1.7 KiB
Markdown
58 lines
1.7 KiB
Markdown
---
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title: Homework 1
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allDay: true
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date: 2024-09-18
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endDate: 2024-09-19
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completed: false
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type: single
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---
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# Instructions
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Please do a written solution for problems 1 and 2. We will review them on Monday, Sept 16 in class prior to the assignment being due.
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Please upload a Jupyter Notebook for problems 3 and 4.
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Problems 1 and 2 are worth 10 points each, problems 3 and 4 are worth 15 points each.
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# Written Problems
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## Problem 1
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Please find the general solution of
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$$
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\bf{\dot{X}} =
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\begin{bmatrix}
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-1 & 5 & 2\\
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4 & -1 & -2\\
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0 & 0 & 6
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\end{bmatrix}
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\bf{X}
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$$
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## Problem 2
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Please find the general solution of
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$$
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\bf{\dot{X}} =
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\begin{bmatrix}
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-6 & 5 \\
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-5 & 4 \\
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\end{bmatrix}
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\bf{X}
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$$
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# Python Problems
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## Problem 3
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The Archimedes Spiral can be plotted by taking all the positive whole numbers (e.g.j = 0, 1, 2, 3, 4, 5, ...) and putting them into the format $n = (j,j)$ , and plotting them in polar coordinates where the first term, $n_1$, is the radius, and the second term, $n_2$, is the angle in radians.
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### Part A
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You need to plot the first 1000 terms in a scatter plot. In addition, we would like to only look at the top right quadrant! What you're going for is shown in Figure 1.
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### Part B
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You need to plot the first 25 terms, looking at th eentire polar plot (all quadrants, and then, put a *smooth* line through it. What you're going for is shown in Figure 2.)
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Hint: [This will be a useful reference](https://matplotlib.org/stable/gallery/pie_and_polar_charts/index.html)
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---
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**Documentation**
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- [<] ME2016-HW1 📅 2024-09-18
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- [<] Problem 1 ⏳ 2024-09-16
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- [<] Problem 2 ⏳ 2024-09-16
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- [<] Problem 3
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- [<] Part A ⏳ 2024-09-16
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- [<] Part B ⏳ 2024-09-16
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- [<] Problem 4
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- [<] Part B ⏳ 2024-09-16
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