Preparing to study electrical engineering on Khan Academy

Math

Math fundamentals

• Equation of a line, slope, y-intercept
• Quadratic formula
• Exponents
• Radians
• Vectors, vector addition
• Solving simultaneous equations
• Complex numbers

Trigonometry

• Definitions of sine, cosine, and tangent from the sides of a triangle
  [(SOHCAHTOA)]

  SOH CAH TOA

  $\begin{array}{lll} \sin \theta = \dfrac{\text{opposite}}{\text{hypotenuse}}\qquad & \textbf S\text{ine is } \textbf O\text{pposite over } \textbf H\text{ypotenuse.} \\ \\ \cos \theta = \dfrac{\text{adjacent}}{\text{hypotenuse}} & \textbf C\text{osine is } \textbf A\text{djacent over } \textbf H\text{ypotenuse.} \\ \\ \tan \theta = \dfrac{\text{opposite}}{\phantom{0}\text{adjacent}\phantom{0}} & \textbf T\text{angent is } \textbf O\text{pposite over } \textbf A\text{djacent.} \\ \end{array}$
• For further review, see trigonometry.

A few concepts from calculus

• Limits
• Derivative
• Derivative notation:
  [Notation for differentiation]

  A derivative is always the derivative of a function with respect to a variable.

  When we write the formal definition of the derivative, we mean the derivative of the function $f(x)$f, left parenthesis, x, right parenthesis with respect to the variable $x$x.

  $\displaystyle \lim_{\Delta x \rightarrow 0} \dfrac{f(x+\Delta x) - f(x)}{\Delta x}$limit, start subscript, delta, x, right arrow, 0, end subscript, start fraction, f, left parenthesis, x, plus, delta, x, right parenthesis, minus, f, left parenthesis, x, right parenthesis, divided by, delta, x, end fraction

  One notation for derivatives is prime notation, introduced by Lagrange. The function $f'(x)$f, prime, left parenthesis, x, right parenthesis means the derivative of $f(x)$f, left parenthesis, x, right parenthesis with respect to $x$x. Read this as "f prime of $\,x$space, x." If $y = f(x)$y, equals, f, left parenthesis, x, right parenthesis, then .

  Second-order and higher derivatives have increasing number of primes. For example, the second derivative of $y$y with respect to $x$x would be written as

  $y''(x)$y, start superscript, prime, prime, end superscript, left parenthesis, x, right parenthesis

  Another very common notation was developed by Leibniz. With this notation, if $y = f(x)$y, equals, f, left parenthesis, x, right parenthesis, then the derivative of $y$y with respect to $x$x can be written as $\dfrac{dy}{dx}$start fraction, d, y, divided by, d, x, end fraction.

  Read this as "$\,dy\:dx$space, d, y, space, d, x", not "$dy$d, y over $dx$d, x".

  Leibniz notation suggests that derivatives can be treated like fractions, which is true in some circumstances. This will come up when you study the chain rule. This is also called differential notation, where $dy$d, y and $dx$d, x are called differentials.

  A variation of Leibniz's notation is written to make $\dfrac{d}{dx}$start fraction, d, divided by, d, x, end fraction look like an operator, $\dfrac{d}{dx} \,y$start fraction, d, divided by, d, x, end fraction, space, y.

  Second-order and higher derivatives using Leibniz notation borrow exponent notation:

  $\left( \dfrac{d}{dx}\right )^2 y\quad$left parenthesis, start fraction, d, divided by, d, x, end fraction, right parenthesis, start superscript, 2, end superscript, y, space means the same as $\quad \dfrac{d^2 y}{dx^2}$space, start fraction, d, start superscript, 2, end superscript, y, divided by, d, x, start superscript, 2, end superscript, end fraction

  Isaac Newton gave us dot notation where the derivative of $x$x is $\dot{x}$.

  Read this as "$x$x dot."

Calculus

• Derivative of simple functions (xⁿ where n is an integer )
• Derivative of eˣ
• Notation for integral
• Integral of xⁿ
• Evaluating definite integrals
• Derivative of sine and cosine
• Line integral

Physics

• High school physics: force, energy, and work
• Force problems using vectors: here, and here.
• Scientific notation
• Significant figures

Chemistry

• High school chemistry: elements, atoms, the electron and nucleus, mole

Classics

Summary