Order of Magnitude Reasoning in Qualitative Differential Equations
Order of Magnitude Reasoning in Qualitative Differential Equations
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In our eReader you can find the full English version of the book. Read Order of Magnitude Reasoning in Qualitative Differential Equations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Order of Magnitude Reasoning in Qualitative Differential Equations
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By variance bound, Av must be ZERO. By vari- ance over time, therefore, AT" = -| — r = ZERO. Applying variance over time in the other \dv\ direction, Ax = LTdx = ZERO. So we have a complete description of Al: Al: [x] = MEDIUM dx = ZERO Ax = ZERO [v] = ZERO av = -SMALL Av = ZERO AT- = ZERO Let A2 be the next state. Since [x] = MEDIUM and Ax = ZERO in Al, by variance at state change [x] must be MEDIUM in A2. By mean value from zero and continuity, [v] must be —SMALL. From the differential equatio...ns, dx and dv must both be —SMALL. We cannot determine the variances or duration until we look at the next state.
Let A3 be the next state. In A3, either [x], [v], dx or dv must change. In fact, since the differential equations determine dx and dv from [x] and [v], either [x] or [v] must change. By mean value at non-zero and continuity, we must either have [v] change to —MEDIUM, or have [x] change to SMALL or both. We will consider each of these in turn: Suppose that [v] changes to -MEDIUM in A3.
What to read after Order of Magnitude Reasoning in Qualitative Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by Ernest Davis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
By variance bound, Av must be ZERO. By vari- ance over time, therefore, AT" = -| — r = ZERO. Applying variance over time in the other \dv\ direction, Ax = LTdx = ZERO. So we have a complete description of Al: Al: [x] = MEDIUM dx = ZERO Ax = ZERO [v] = ZERO av = -SMALL Av = ZERO AT- = ZERO Let A2 be the next state. Since [x] = MEDIUM and Ax = ZERO in Al, by variance at state change [x] must be MEDIUM in A2. By mean value from zero and continuity, [v] must be —SMALL. From the differential equatio...ns, dx and dv must both be —SMALL. We cannot determine the variances or duration until we look at the next state.
Let A3 be the next state. In A3, either [x], [v], dx or dv must change. In fact, since the differential equations determine dx and dv from [x] and [v], either [x] or [v] must change. By mean value at non-zero and continuity, we must either have [v] change to —MEDIUM, or have [x] change to SMALL or both. We will consider each of these in turn: Suppose that [v] changes to -MEDIUM in A3.
What to read after Order of Magnitude Reasoning in Qualitative Differential Equations?
You can find similar books in the "Read Also" column, or choose other free books by Ernest Davis to read onlineMoreLess
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