Related papers: Using math in physics -- 3. Anchor equations
Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a…
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary).…
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.
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…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and…
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
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…
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
Identifying the relevant physics principles is a central component of problem solving. A major goal of most introductory physics courses is to help students discern the deep similarities between problems based upon the physics principles so…