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Название: Physics 2000 (Parts I, II), Calsulus 2000
Автор: Huggins E.R.
ABOUT THE COURSE
Physics2000 is a college level introductory physics course that begins with special relativity, ends with quantum mechanics, and in-between covers the usual topics with a 20th century focus. This approach eliminates the great divide between classical and modern physics.
BEGIN WITH SPECIAL RELATIVITY?
Introducing Einstein’s special relativity in Chapter 1
means that you cannot rely on the usual mathematical techniques because no mathematics has been discussed yet. You have no choice but to focus on the physical ideas like the behavior of clocks and measurements of distance. The result is that you remove the mathematical fear factor usually associated with the subject. The only mathematics you need is the Pythagorean theorem.
Compare this with the standard approach
that introduces special relativity after discussing Maxwell’s equations. You have just introduced the students to integral-differential equations, you hit them with complex historical arguments about the search for ether, and then present some really weird physics. Fortunately the course is about over, so that you do not have to expect the students to get it.
END WITH QUANTUM MECHANICS?
Once you have finished with Maxwell’s wave theory of light, you can proceed directly to the photoelectric effect, and the particle nature of light. You can do this because the students already know special relativity and are fully prepared to handle the simple mechanics of photons. The contrast between light waves and light particles sets the stage for a discussion of the particle-wave nature of matter, which is at the heart of quantum mechanics.
THE PHYSICS IN-BETWEEN
Strobe photographs are used to provide an intuitive introduction to calculus concepts. Using Feynman’s recoil definition of mass, one sees from a simple thought experiment that mass must increase with velocity. The unity of electricity and magnetism is shown by deriving the magnetic force law as a relativistic correction to Coulomb’s law. The particle-wave nature of matter plays an equally important role in the text as mechanics and E&M.
THE MATHEMATICAL LEVEL?
On the bookshelves
you will find books with names like Physics for Poets, Non-Calculus Physics, College Physics, University Physics, and Physics for Scientists and Engineers. These are texts with more or less the same content, written at progressively higher mathematical levels.
We take a different approach.
The idea is to present the physics in the clearest and simplest way possible, and let the companion text Calculus2000 introduce the more complex mathematics.
Part 1 of Physics2000 uses physics to teach calculus.
The definitions of velocity and acceleration are introduced through strobe photographs. The concept of taking the limit as delta t goes to zero corresponds to turning the strobe rate all the way up. In two chapters we compare the use of calculus and the use of the computer in handling physics problems. It is not until we get to potential energy, half way through Part 1 that we begin to rely on some previous knowledge of integration.
Part 2, chapters on electricity and magnetism, do rely on calculus.
The focus is on surface and line integrals, which are discussed in detail. All the calculus needed for the entire physics course is taught in Chapter 1 of Calculus2000.
For the student with a more advanced mathematical background,
Calculus2000 takes subjects in Physics2000 to a higher mathematical level. Complex variables are used in the discussion of circuit theory, the concepts of divergence and curl lead to new insight into Maxwell’s and Schrödinger’s equations, and the final chapters of Calculus2000 provide an introduction to fluid dynamics, covering such topics as the Navier-Stokes equation, the Helmholtz theorem, and quantum vortices.