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Logarithmic, exponential and hyperbolic functions
Published in Surinder S. Virdi, Advanced Construction Mathematics, 2019
Antilogarithm is the reverse of logarithm. If we know the logarithm of a number, then we can use the antilogarithm key ( ) of a scientific calculator to determine the original number. Antilogarithms can be used to simplify equations that involve logarithms, as they cancel each other out; this is illustrated in example 9.5b.
Game-based learning apps in engineering education: requirements, design and reception among students
Published in European Journal of Engineering Education, 2023
Eva Jacobs, Oliver Garbrecht, Reinhold Kneer, Wilko Rohlfs
Figure 8(a) shows a simple example in HeatQuiz App. The main screen has three areas: The task as a sketch (left), an input line like on a scientific calculator (above), and a keyboard (right) that has been customised to the question. The sketch shows two parallel walls, one is considered a black body () and the other a grey body (). In this task, the surface brightness of the red dashed surface is asked for. The student has to understand what components the heat flow consists of, express each as a formula and derive the final equation. This is one of an engineer's core competences. Each component has to be expressed by an individual mathematical term, derived from Stefan-Boltzmann's law. Here, the components are the surface's own emission and the reflected part of the other wall's surface brightness. On the solution screen (see Figure 8(b)), the user's solution (top) is compared with the correct solution (bottom). Due to the modular structure of the solution, applying the guideline is especially useful here: It makes sense to award points not only for the correct expression as a whole, but also for single correct terms. If the first term is correct, the student has understood emission; if the second term is correct, the student has understood reflection. As the equation is composed of modular components, the task requires structural insight. Transfer of learning, as required by the guidelines, is supported by perceptual learning.
Using a constraint-based expert model to provide step-level feedback for user-inputted mathematics equations
Published in International Journal of Mathematical Education in Science and Technology, 2022
In the framework of a CBT, the step selection acts as the relevance condition, and the student’s work entry acts as the satisfaction condition. The student is able to solve the equation with any sequence of steps as long as each step is performed correctly, which provides the student complete freedom in their solution path. Because the student cannot move on to the next step before the current step is applied correctly, there is no compounding of errors resulting in an incorrect final solution. Requiring the student to declare the step they are performing also allows SANYMS to determine when a student has come to the correct solution via the wrong means. The additional integration of an on-screen mathematics keyboard via the Desmos8 HTML5 graphing calculator, specifically the standalone scientific calculator9, allows students to input their equations as they would write them on paper, which minimises syntax errors. All of these components are brought together with a simple Python programming language10 Graphical User Interface (GUI), where input from the GUI and from Desmos is analysed using a computer algebra system.
Catalysis and mechanistic study of Ru(III) and Os(VIII) on the oxidation of taurine by BAT in acid and alkaline media: a kinetic modeling
Published in Inorganic and Nano-Metal Chemistry, 2021
Nathegowda Suresha, Kalyan Raj, Malini Subramanya
All kinetic runs were performed under pseudo-first order conditions of [TAU]0 ≫ [BAT]0, at 313± 0.1 K . The reactions were carried out in glass-stoppered Pyrex boiling tubes whose outer surfaces were covered black to eliminate the photochemical effects. For each run, the requisite amount of substrate, HCl and Ru(III) (in acid medium), substrate, NaOH and Os(VIII) (in basic medium), and water (to maintain total volume constant for all runs) were introduced into the tube and thermostatted at 313 ± 0.1K for thermal equilibrium. A measured amount of oxidant (BAT) also thermostatted at the same temperature was added rapidly to the above mixture to initiate the reaction. The mixture was sporadically shaken to attain uniform concentration. The progress of the reaction was monitored by pipetting 5 ml of aliquot into ice cold water (containing known amount of KI and H2SO4 solutions) at regular intervals of time and titrating against standard sodium thiosulfate solution using starch indicator near the end point to determine unreacted BAT. The reaction was followed for more than two half-lives. The pseudo-first order rate constants (k′ s−1) calculated from the linear plots of log[BAT] verses time were reproducible to ±5%. The regression analysis of experimental data was carried out using scientific calculator, from which the regression coefficient ‘r’ was calculated.