Cocalc Chapter 7 Tutorial Ipynb

This tutorial will show you how to use the included Simulation class to simulate node dynamics by specifying a graph, the initial state of the nodes, and node state transitions. Included with these tutorials is a simulation.py file that contains a Simulation class. This class will allow us to skip the details of writing a simulation, allowing us to concentrate on the interesting parts. A simulation is made up of three main parts: The graph on which to simulate node dynamics This one is easy, we just need a NetworkX Graph instance.

For this example we'll use a random graph. You can run the following cell multiple times if you wish, until you get a graph that looks good: Master Stokes' theorem connecting surface integrals to line integrals through computational practice with curl calculations and circulation analysis. This comprehensive Jupyter notebook demonstrates oriented surfaces with boundary curves, curl interpretation, and applications to electromagnetic theory and fluid dynamics. CoCalc's SageMath environment offers 3D visualization of surfaces and boundaries, symbolic curl computation, and theorem verification tools, enabling students to understand the deep relationship between circulation around boundaries and curl through surfaces. This notebook contains Chapter 7 from the main Advanced Calculus with SageMath notebook.

For the complete course, please refer to the main notebook: Advanced Calculus with SageMath.ipynb This relates the circulation of a vector field around a closed curve to the flux of its curl through any surface bounded by that curve. STOKES’ THEOREM\displaystyle \textbf{STOKES' THEOREM}STOKES’ THEOREM Python Machine Learning 3rd Edition by Sebastian Raschka, Packt Publishing Ltd. 2019 Code Repository: https://github.com/rasbt/python-machine-learning-book-3rd-edition

Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s). The use of watermark is optional. You can install this Jupyter extension via For more information, please see: https://github.com/rasbt/watermark. If all ccc's are zero, a set of vectors {v1,v2,...,vp}\{v_1, v_2,...,v_p\}{v1​,v2​,...,vp​} is said to be linearly independent, if the equation

If any of ci≠0c_i\neq 0ci​=0, the set of vectors is linearly dependent. Determine if v1,v2,v3{v}_1, {v}_2, {v}_3v1​,v2​,v3​ are linearly independent. v1=[123]T,v2=[456]T, and v3=[210]T {v}_{1}=\left[\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right]^T, {v}_{2}=\left[\begin{array}{l} 4 \\ 5 \\ 6 \end{array}\right]^T, \text { and } {v}_{3}=\left[\begin{array}{l} 2 \\ 1 \\ 0 \end{array}\right]^T v1​=​123​​T,v2​=​456​​T, and v3​=​210​​T The common way of testing linear combination is to construct augmented matrix and calculate the reduced form, for example ([10−2001100000], (0, 1))\displaystyle \left( \left[\begin{matrix}1 & 0 & -2 & 0\\0 & 1 & 1 & 0\\0 & 0 & 0 & 0\end{matrix}\right], \ \left( 0, \ 1\right)\right)​​100​010​−210​000​​, (0, 1)​ Assume the following situation.

From an experiment we have gathered following data: We want to use the data as an input to a simulation. However, as visible, the data is noisy and thus may lead to instability of our simulation. First we will load modules supporting this tutorial. Note that you should install matplotlib first if not already happenend, as only this tutorial needs matplotlib. For usage of ebcpy, you don't need it. Let's specify the path to our measurement data and load it.

If you're familiar with python and DataFrames, you will ask yourself: Why do I need the TimeSeriesData-Class? We implemented this class to combine the powerful pandas.DataFrame class with new functions for an easy usage in the context of Building Energy Systems for three main reasons: Most data in our case is Time-Dependent, therefore functions for easy conversion between seconds (for simulation) and Timestamps (for measurements) is needed By the end of this lecture you will be able to: Perform 1-Dimensional interpolating functions using interp1d and InterpolatedUnivariateSpline inside the scipy library Use the different interpolation kinds available for the interp1d method

Change the polynomial degree of an InterpolatedUnivariateSpline function. Use the numeric differentiation and integration methods available from InterpolatedUnivariateSpline Often when looking at a network, we want to find the most "important" nodes, for some definition of important. The most basic measure of centrality is the degree, or number of links attached to a node. Let's look at the Enron executive email graph: Edge lists are a simple, plain text format for storing graphs.

Since this simple file format doesn't contain information about data types, all node names are assumed to be strings by default. When the node names are given by integers, as they are in this example, we should specify the nodetype=int keyword argument to avoid confusion with the node names. We're going to make use of Python's built-in max function in order to find the node with the highest degree. First, let us recall what the max function does. At its most basic, the max function returns the "greatest" item in a sequence: Parameters: used to discrabe a probability distribution, e.g.

mean, variance, etc. Statistics: a function of random sample of a distribution, i.e. randomly choose some samples from a distribution. Estimate: guess the parameter by the statistics. Estimate bias: bias(θ^)=E(θ^)−θbias(\hat{\theta}) = E(\hat{\theta})-\thetabias(θ^)=E(θ^)−θ, if bias=0bias = 0bias=0, we call this estimate unbias estimate. Estimate variance: Var(θ^)Var(\hat{\theta})Var(θ^) is the same with the definition of variance.

By the end of this lecture you will be able to: Define variables and differentiate between global and local variables. Identify and use different object types in python. Use some of the python's default functions and define your own functions. Introduction to numpy and matplotlib libraries

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