The study of Differential Equations uses quite a lot of skills and structures and methods and facts from other branches of mathematics; in fact, if you've ever wondered "when are we going to use this?" in a previous math class, the answer is very likely to be "in Math 22B." Here are some topics that will very likely be important in 22B; it would be a very good idea to review any of these that you may have forgotten.
Ideas from High School Math (maybe):
making and interpreting graphs
factoring and finding roots of a polynomial (especially quadratics, maybe cubics too)
trigonometric identities (definitions, Pythagorean, small-angle approximation, angle-sum)
hyperbolic trigonometric functions (at least know the formulas for sinh and cosh)
complex numbers
Ideas from Math 21A:
limits
continuity
derivatives of all basic functions, especially xn, ex, ln(x), sin(x), and cos(x)
product rule, quotient rule, chain rule
what the derivative tells you about a function's graph
building a linear approximation of a function at a point
Ideas from Math 21B:
integrals of all basic functions, especially xn, ex, 1/x, sin(x), and cos(x)
integration by substitution
integration by parts
partial fraction decomposition
Ideas from Math 21C:
partial derivatives
chain rule for partial derivatives
notation for sequences & series
Maclaurin series for ex, sin(x), and cos(x)
Euler's Formula for imaginary exponents
Ideas from Math 21D:
vector functions
multiple integrals
Ideas from Math 22A:
solving a system of equations with matrices
determinant of a matrix
inverse of a matrix
vector spaces
linear combinations & linear independence
eigenvalues and eigenvectors
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