Search Results for differentiate

...Linear ODEs and Orthogonal Functions It has been recognized that the vast majority of the eigenvalue problems in physics lead to second-order differential equations with the general form ( Ince, 1927 ) (2.1) L ^ [ ϕ ] = R ( x ) , a ≤ x ≤ b , Now if the sequential...

... of constraints are needed at the end points of a wavefunction to have a legitimate solution. Differential calculus says that two BCs are actually needed, this being due to the presence of the second-order spatial derivatives in the atomic system’s Hamiltonian eigenvalue equation. The two BCs may be specified...

... and the greenhouse effect (e.g., Henriksen and Jorde, 2001; and Österlind, 2005 ). Similar results are reported consistently in different age groups by many other studies. Most students regard sunshine as a basic unit as opposed to a spectrum of frequencies; that is, they do not differentiate between UV rays...

... fields, and vector differential and integral calculus to interpret flow physics through conservation laws; using Newton's second law to the analysis of fluids at rest and in movement; applying mass, momentum, and energy conservation to steady flows; interpreting and applying laminar and turbulent flow...

... photovoltaic models by means of a hybrid differential evolution with whale optimization algorithm ,” Solar Energy   176 , 742 – 761 ( 2018 ). 10.1016/j.solener.2018.10.050 Yu , S. , Heidari , A. A. , Liang , G. , Chen , C. , Chen , H. , and Shao , Q. , “ Solar photovoltaic...

... in the literature. A recent review ( Odden and Russ, 2019 ) differentiated three different ways in which sensemaking is characterized: (1) sensemaking as a cognitive process, (2) sensemaking as discourse practice facilitated and supported by communication, and (3) factors that influence the process of sensemaking...

... into conceptions of energy being related to living and non-living things as well, upon further inspection identified the following more differentiated themes: (1) vitalism (e.g., we need energy to live), (2) activity (e.g., we need energy to exercise), (3) work (e.g., machines need energy to function, and (4...

... differentiated innovative research-based educational paths ( Fischler and Lichtfeldt 1992 ; Niedderer and Deylitz, 1998 , 1999 ; Petri and Niedderer, 1998 ; Fischler, 1999 ; Michelini et al., 2000 , 2008 , 2014a , 2014b ; Michelini, 2008 ; Michelini and Stefanel, 2008 , 2010 , 2021a , 2021b...

... they should be implemented and what kinds of support students should be provided. Student internal characteristics include their prior preparation and physics beliefs (which are shaped by differential prior support from societal stakeholders and differential opportunities due to lack of resources in addition...

... at one of the poles and a lack of charges at the other. Students who had already completed a first course in electricity and magnetism often viewed a magnet as an electrified object. This view probably arises from the poor differentiation between electric and magnetic dipoles. In the fourth model...

... of the scheme, the first and the last positions were hypothetical extensions extrapolated from the empirical work. Positions 1 through 5 describe the cognitive development, intellectual refinement toward increasing differentiation and complexity. Positions 6 through 9 describe the ethical maturation ( Table...

... in education has the potential to change the material basis of aspects of laboratory work, differentiate the character of students' experiences, enrich physics teaching and learning and promote inquiry teaching and learning. Virtual laboratories are widely used and there is extensive literature...

...” and “uncertainty” and the probabilistic nature of quantum theory Measurement of eigenstate vs uncertainty results on superposition state Operator in quantum mechanics Wave-particle dualism in the SE solution Solution of a differential equation vs eigenfunction What is a potential well? Boundary...

... differentiated according to the ways in which the different components of the practice are considered. If “enacting” alone is studied more often (about two-thirds of the studies) than the other two, “reflecting” is hardly ever treated alone. No study of the first three themes (see Table 24.1 ) deals with all...

... and calculated intensity. The strategy used by Xiong et al. (2018) was integrating differential evolution with a whale optimization algorithm. Xiong et al. (2018) stated that parameter extraction of solar photovoltaic models is a complex non-linear multivariable optimization problem...

.... Other epistemic games have been named in the literature, including ones focused on more formal methods—such as analytical derivation ( Bajracharya and Thompson, 2016 ) or the sophisticated partial derivative and differential mathematics used in thermodynamics ( Kustusch et al., 2014 )—and ones...

...${\frac{{\mathrm{}}^{}}{}]}_{\epsilon =0}<0$ Let us obtain [ ∂ 2 E w ∂ ε 2 ] by differentiating Eq. ( 8.21 ) with respect to ε. Here again, it is differentiation under the integral sign for the first term...