Related papers: Using math in physics: 5. Functional dependence
The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and while it…
Physics as a discipline embeds conceptual meaning about the physical world in mathematical formalism. The meaning associated with mathematical symbols depends on context, and physicists can shift conceptual meaning by manipulating those…
In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its…
Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…
In recent years, computing has become an important part of the way we teach and learn physics. Teachers, both at high school and college levels, now use computational activities in many of their courses. Physics departments are offering…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
Computation is a central aspect of 21st century physics practice; it is used to model complicated systems, to simulate impossible experiments, and to analyze mountains of data. Physics departments and their faculty are increasingly…
Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are…
Before we attempt to learn a function between two (sets of) observables of a physical process, we must first decide what the inputs and what the outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven…
In the causal learning setting, we wish to learn cause-and-effect relationships between variables such that we can correctly infer the effect of an intervention. While the difference between a cyclic structure and an acyclic structure may…
Previous research has found that introductory physics students perform far better on numeric problems than on otherwise equivalent symbolic problems. This paper describes a framework to explain these differences developed by analyzing…
A priority of physics instruction is to help students make the connection between the formulae they think they are required to memorize and the real world in which they interact every day. If you ask students to describe a situation in real…
The friction force, friction coefficients and the effects on the dynamics of particles, bodies and systems, are fundamental themes in university physics of the first cycles and also in general physics courses of upper secondary education in…
Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…
How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general "cultural"…
Almost all theories of physics have expressed physical laws by means of differential equations. One can ask: why differential equations? What is special about them? This article addresses these questions and is presented as an inquiry-based…
Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely…
The effects of the experiment itself upon the obtained results and, especially, the influence of a large number of experiments are extensively discussed in the literature. We show that the important factor that stands at the basis of these…
Nowadays the Science progress depends on the numerical calculus, due to the possibility of obtention of solutions using simulations which would be impracticable, or even impossible, to be analitically obtained. In this aspect, it becomes…
Fundamental physical constants play important role in modern physics. Studies of their variation can open an interface to new physics. An overview of different approaches to a search for such variations is presented as well as possible…