Vector Addition

Two vectors of the same size can be added together by adding their corresponding elements, to form another vector of the same size, called the sum of the vectors. \[ \begin{bmatrix} 0 \\ 7 \\ 3 \end{bmatrix} + \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} = \begin{bmatrix} 1 \\ 9 \\ 3 \end{bmatrix} \] Likewise, for substraction, the difference of two vectors is \[ \begin{bmatrix} 1 \\ 9 \end{bmatrix} - \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 0 \\ 8 \end{bmatrix} \] …

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Vectors Examples

An \(n\)-vector can be used to represent \(n\) quantities or values in an application. A 2-vector can be used to represent a position in a 2-dimensional (2-D) space. A 3-vector can be used to represent a location in a 3-dimensional (3-D) space. Each entry of the vector gives a coordinate. When a vector is used to represent a displacement in space, it is typically drawn as an arrow. from mpl_toolkits import mplot3d import matplotlib. …

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Vectors

A vector is an ordered finite list of numbers. They’re normally written as vertical arrays, surrounded by squared or curved brackets. \[ \begin{pmatrix} -1.1 \\ 0.0 \\ 3.6 \\ -7.2 \end{pmatrix} \] or \[ \begin{bmatrix} -1.1 \\ 0.0 \\ 3.6 \\ -7.2 \end{bmatrix} \] The elements (or entries, coefficients, components) of a vector are the values in the array. The size (or dimensions, or length) of the vector is the number of elements it contains; an \(n\)-dimensional vector (or n-vector) is a vector with \(n\) elements in it. …

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Double Integrals

The integration of a function of two variables is called iterated integration. The following is an example of a double integral: \[\int_3^6 \int_{-1}^2 10xy^2 dxdy\] Because integrals can be thought of as “undoing” differentiation, the double integral can be interpreted as undoing a second partial derivative of a function. from sympy.abc import x, y from sympy import * expr = 10 * x * y**2 integrate(expr, (x, -1, 2), (y, 3, 6)) ## 945

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