mathematical tools

to the derivative of the scalar y-to-column vector x,The y is biased for the elements of each x without transpose.DY/DX = [Dy/dx (IJ)]Important Conclusions:y = U ' XV =σσu (i) x (IJ) v (j) then Dy/dx = = UV 'y = U ' X ' XU then dy/dx = 2XUU 'y = (xu-v) ' (xu-v) then dy/dx = d (U ' X ' xu-2v ' XU + V ' V)/dx = 2XUU '-2VU ' + 0 = 2 (xu-v) U '9. Derivative of matrix Y to matrix x:Each element of Y is derivative of x, and then it is lined together to form a super matrix.Mathematical knowledge of pa

Theorem. $$\bex \int_0^1\frac{\ln^2x}{x^x}\rd xProof: By the division Integral and Fubini theorem, $$\beex \bea \int_0^1 x^m\ln^nx\rd x=\frac{( -1) ^nn!} {(m+1) ^{n+1}},\\ \int_0^1 \frac{\ln^2x}{x^x}\rd x =\int_0^1 e^{-x\ln x} \ln^2x \rd x =\int_0^1\sum_{k=0}^\infty \fra c{( -1) ^k}{k!} x^k\ln^{k+2}x\rd x\\ =\sum_{k=0}^\infty \frac{( -1) ^k}{k!} \int_0^1 x^k\ln^{k+2}\rd x =\sum_{k=0}^\infty \frac{k+2}{(k+1) ^{k+2}},\\ \int_0^1 \frac{\rd x}{x^x}=\sum_{k=0}^\ Infty \frac{1}{(k+1) ^{k+1}},\\ k+2Jul

This chapter describes several common PHP math intrinsic functions. General calculations, we can solve by operators, such as subtraction. Using PHP's mathematical calculation intrinsics can help us solve some of the more complex calculations. The following mainly covers round, floor, ceil, pow, Rand,max, Min, Decbin, Bindec, Dechex, Hexdec, decoct, Octdec function. RoundRound-Rounding the floating-point number. The round function syntax is as follows

Add mathematical formulas to the blog, and add mathematical formulas to the blogMathJax MathJax allows you to include formulas on your webpage. Whether using LaTeX, MathML, or AsciiMath symbols, these formulas are processed as HTML, SVG, or MathML symbols by javascript.Usage Add JavaScript references to the blog Add in body Effect The CSDN blog imposes only the following restrictions on javascript: R

Mathematical Analysis of scattered lists (final solution)-solving collision and mathematical analysis through the Linked List Method The specific implementation of the hash is not described much. It is an array. Each subscript stores the head pointer of the linked list of collision elements, as shown in: Next we will directly study the analysis of hash using the link method: Given a hash T with m slots tha

Algorithms-Meanings of mathematical terms and mathematical terms in discrete mathematics, and answers to discrete mathematics and Algorithms Here we will introduce two important functions in discrete mathematics: The base function and the top function. Make x a real number. The base function rounds x to an integer smaller than or equal to x and closest to x, while the top function rounds x to an integer gr

How can we improve our mathematical analysis? Original mathematical forum for Dr. scibirdThe requests from friends on the Forum tell me about my learning experience and experience in the score for your reference.First, I declare that there is no omnipotent method in the world. Any method has its limitations and applicability.The essence of what you say is a dialectical view. Similarly, if you see something

software. Finite Element Theory it must be called ANSYS, fluent, ABAQUS ..., on the circuit simulation forum, we were bustling with the following: ads, Microwave Office ,...,, in the discussion of Computational chemistry, lt; Edit gt; Gaussian lt;/edit gt;, nwchem, the ADF occupies a large area of space, I have been involved in the discussion of mathematical tools for a long time, and it is almost f

This paper summarizes and analyzes the PHP mathematical operation function. Share to everyone for your reference, specific as follows: First, the commonly used function description: Abs: Get absolute value. Acos: Gets the inverse cosine value. Asin: Get the inverse chord value. Atan: Get the tangent value. Atan2: Calculates the inverse tangent value of two numbers. Base_convert: Converts the rounding of a number. Bindec: The binary turns into

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