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Algebra
Published in John Bird, Bird's Engineering Mathematics, 2021
The order of precedence is brackets, division, multiplication and addition. Hence, 3c+2c×4c+c÷(5c−8c)=3c+2c×4c+c÷−3c=3c+2c×4c+c−3c
Basic algebra
Published in John Bird, Science and Mathematics for Engineering, 2019
Sometimes addition, subtraction, multiplication, division, powers and brackets can all be involved in an algebraic expression. With mathematics there is a definite order of precedence (first met in chapter 1) which we need to adhere to. With the laws of precedence the order is: BracketsOrder (or pOwer)DivisionMultiplicationAdditionSubtraction
Algebra
Published in John Bird, Engineering Mathematics, 2017
The order of precedence is brackets, division, multiplication and addition. Hence, 3c+2c×4c+c÷(5c-8c)=3c+2c×4c+c÷-3c=3c+2c×4c+c-3c $$ \begin{aligned}&3c + 2c\times 4c + c\div (5c - 8c) \\&\quad = 3c + 2c\times 4c + c\div - 3c \\&\quad = 3c + 2c\times 4c + {\frac{{c}}{{{-}3c}}} \end{aligned} $$
Using conductive fabrics as inflation sensors for pneumatic artificial muscles
Published in Advanced Robotics, 2021
Arne Hitzmann, Yanlin Wang, Tyler Kessler, Koh Hosoda
Our setup for static testing (Figure 6) is used to measure the change in resistance over displacement, as well as conducting the breaking test to evaluate the textile adhesives. We designed a dynamic testing rig for our experiments, which allows us to measure the length changes when variably loading the muscles. For our testing, we used the FGP-5 digital force gauge from Nidec Shimpo in combination with an FGS-50E-H motorized test stand from Shimpo and a DS-025 linear encoder from Mutoh. These components allowed us to precisely evaluate the change in resistance of the different materials as they are stretched. The motorized stand we used has no position encoder itself, therefore, we added a linear encoder externally. In addition, we designed custom brackets to fix the specimen in the test stand. Our design distributed the tensile force over a larger surface to avoid the tearing of individual fibers or an uneven application of the force.
Decomposition of stochastic flow and an averaging principle for slow perturbations
Published in Dynamical Systems, 2020
Diego Sebastian Ledesma, Fabiano Borges da Silva
We observe that when the fast and slow motions are fully coupled, it is complicated to work with these equations and few results exist for this general case (see [11]). The dynamics obtained with Equations (15) and (16) are not fully coupled, but the slow-motion depends on the dynamics of as we mentioned before. So it is interesting to use a principle of averaging to obtain an approximate solution for the slow-motion . In addition, note that when the vector fields and commute, that is, the Lie brackets , for and , then , for , and therefore the equations are totally uncoupled.
Combining diagnostic testing and student mentorship to increase engagement and progression of first-year computer science students
Published in European Journal of Engineering Education, 2022
G. Knight, N. Powell, G. Woods
The topics in the mathematics intervention workshops were chosen by the LDC academic team, with resources designed and delivered by the maths mentors. The intervention workshops ran from the second-week teaching with seven weekly workshops covering order of operations, expanding brackets, factorisation, solving linear equations, straight-line geometry, solving and sketching quadratic equations, trigonometry, matrices, and vectors. These subject areas aligned with the content being delivered in the CS students’ first-year mathematics module.