I haven't taken the required math and physics classes? Can I still apply?

Most (if not all) of our students have math, science, or engineering backgrounds. Our atmospheric science program is a very science-intensive program. We expect entering students to be comfortable with college math (topics like differential equations and statistics) and physics (thermodynamics, fluid mechanics, etc.). We've found that students who lack a strong math background (ideally including multi-variable calculus, linear algebra, and partial differential equations) tend to really struggle with the coursework. So you are unlikely to be admitted without some evidence (summer research in atmospheric science or oceanography, for example) that demonstrates your ability to do scientific work. If you really want to get a graduate degree in Atmospheric Science, it's probably best if you take a year to do some coursework and possibly gain some experience in research (working at a university, government lab, or business). Are you near a university with atmospheric science classes? Perhaps the professors know of available jobs where you could become more familiar with atmospheric science. Showing that you're already able to do a little research can go a long way to reassuring us that you'll be able to handle the research component of the degree, which is the primary component of our program. You could work for a year or two, take some classes, and then apply for grad school.

Another option is the MRM program here. Although it's called Marine Resource Management, students can do projects related to the atmosphere as well. The program requires less in the way of math and science undergrad coursework, and may be perfect for you if you are more interested in the management/policy/outreach side of the science. You can also check out the Environmental Science program, which offers a very flexible program of study. However, due to this flexibility, students must be very self-motivated to be successful in the Environmental Science program.

I'm not trying to dissuade you from pursuing atmosphere science if that is your passion. If your main goal is still focused on the science, then you really do need to take the equivalent of the required coursework before applying.