Related papers: Using math in physics: 5. Functional dependence
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
We report results from a study designed to identify links between undergraduate students' views about experimental physics and their engagement in multiweek projects in lab courses. Using surveys and interviews, we explored whether students…
From industry to government to academia, attracting and retaining science, technology, engineering, and mathematics majors is recognized as a key element of the 21$^{\text{st}}$ century knowledge economy. The ability to retain students…
In the talk we investigate the question of commutation of the whole-partial derivatives, which should be considered when the function, which is subjected to differentiation, has both explicit and implicit dependence. We apply the results to…
This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…
The learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which…
Friction laws, which are a key to the understanding of the diversity of earthquakes, are considered theoretically. Using dimensional analysis, the logarithmic dependence of the friction coefficient on the slip velocity and the state…
Functional data often arise from measurements on fine time grids and are obtained by separating an almost continuous time record into natural consecutive intervals, for example, days. The functions thus obtained form a functional time…
Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…
The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations…
Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their…
Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and…
Indications of a possible composition-dependent fifth force, based on a reanalysis of the E\"{o}tv\"{o}s experiment, have not been supported by a number of modern experiments. Here, we argue that searching for a composition-dependent fifth…
The likelihood function plays a crucial role in statistical inference and experimental design. However, it is computationally intractable for several important classes of statistical models, including energy-based models and simulator-based…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
Developing expertise in physics requires appropriate integration and assimilation of physics and mathematics. Instructors and students often describe physics courses in terms of their emphasis on conceptual and quantitative problem-solving.…
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
Education, science, in fact the whole society, extensively use images. Between us and the world are the visual displays. Screens, small and large, individual or not, are everywhere. Images are increasingly the 2D substrate of our virtual…