Canvas Widgets

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 Canvas Widgets https://labellota02.tistory.com/entry/Canvas-Widgets
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partial derivatives and Multiple integrals

 partial derivatives and Multiple integrals


Additional topics: partial derivatives 

The symbol for partial derivatives is shown in the "Mathematical Symbols” palette (∂), but it's 

not functional, i.e., it cannot be used to calculate derivatives. Use function ‘diff to calculate 

partial derivatives.


Representation of derivatives before evaluations - use apostrophes before each diff.


Multiple integrals

To see the multiple integrals before evaluations, place an apostrophe before each integrate:




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Temperature effects_maturity

  In the   CEB-FIP Model Code 90 ,   maturity   is a concept used to predict the rate at which concrete gains strength based on temperature and time.   Eq. (2.1-87)   is used to calculate the   maturity-adjusted time  $$ t_T$ $​ , which accounts for the effects of temperature on concrete's strength development. \(  S=\int d^{4} x\left(\frac{R}{2 \kappa}\right) \) begin{eqation} S=\int d^{4} x\left(\frac{R}{2 \kappa}\right) end{equation} Definition of Equation (2.1-87): The maturity-adjusted time $$tTt_T tT​$$  is calculated as: $$tT=∫t0texp⁡[QR(1T0−1T(τ))]dτt_T = \int_{t_0}^{t} \exp \left[ \frac{Q}{R} \left( \frac{1}{T_0} - \frac{1}{T(\tau)} \right) \right] d\tau tT​=∫t0​t​exp[RQ​(T0​1​−T(τ)1​)]dτ$$ Where: tTt_T tT​  = maturity-adjusted time (in days) tt t  = real elapsed time (in days) t0t_0 t0​  = start time for the calculation (usually 0) QQ Q  = activation energy for hydration process, typically around 33,500 J/mo...
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