Calculus I studies fives main areas: functions and models, limits and derivatives, differentiation rules, applications of differentiation and integrals. In general, Calculus I introduces students to mathematical equations that yield the volume of solids through the manipulation of functions. This is the lowest level of Calculus and may be separated into two sections: A and B. Some physics majors may not have to take Calculus I, if they score well on AP exams before entering college.
Calculus II builds on the foundations of Calculus I by teaching more integration techniques, vectors, parametric equations and three-dimensional figures. Physics majors will typically work heavily with vectors, which are directly applicable to many physics courses. In addition, Calculus II is often taught in conjunction with certain physics courses. In Calculus II, students begin to deal with theoretical math equations, while still working with practical math equations at the same time.
Calculus III works with theoretical math and physics. Calculus III departs from a two-dimensional analysis of functions and works with three dimensions, using vectors to expand into the third dimension. In the course, force and angular velocity are studied through using vectors. Calculus III deals a lot with proving and disproving certain theorems, such as the Fundamental Theorem of Calculus or Green's Theorem. Calculus III is not always required for physics majors, but it is often a component of more rigorous programs.
Differential Equations, sometimes called "Ordinary Differential Equations" or "Diff E," studies theories and methods of solutions of equations. It looks at linear equations that have standard coefficients by using graphing and numerical methods. It also works with eigenvalues and eigenvectors. This generally represents the hardest and highest level of math for physics majors. Because much of the course work involves graphing; computers, CDs and graphing calculators are often a large component of the curriculum.