Prerequisite Math Skills

### Secret Math Prereqs

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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