REE Challenge

Master the Mathematics portion - the foundation of all EE subjects!

1. Algebra and Trigonometry

Quadratic Formula

x = [-b +/- sqrt(b2 - 4ac)] / 2a

Discriminant: b2 - 4ac determines nature of roots

Trigonometric Identities

sin2(x) + cos2(x) = 1
sin(2x) = 2sin(x)cos(x)
cos(2x) = cos2(x) - sin2(x)
tan(x) = sin(x)/cos(x)

Logarithms

log(AB) = log(A) + log(B)
log(A/B) = log(A) - log(B)
log(A^n) = n x log(A)
ln(e) = 1, log10(10) = 1

2. Complex Numbers (Essential for AC!)

Forms of Complex Numbers

Rectangular: Z = a + jb
Polar: Z = r angle theta
Exponential: Z = r x e^(j theta)

Conversions

r = sqrt(a2 + b2) (magnitude)
theta = arctan(b/a) (angle)
a = r x cos(theta) (real part)
b = r x sin(theta) (imaginary part)

Operations

Add/Sub: Use rectangular form
Mult: r1r2 angle (theta1 + theta2)
Div: (r1/r2) angle (theta1 - theta2)

3. Calculus

Differentiation

d/dx(x^n) = nx^(n-1)
d/dx(sin x) = cos x
d/dx(cos x) = -sin x
d/dx(e^x) = e^x
d/dx(ln x) = 1/x

Integration

integral x^n dx = x^(n+1)/(n+1) + C
integral sin x dx = -cos x + C
integral cos x dx = sin x + C
integral e^x dx = e^x + C
integral 1/x dx = ln|x| + C

4. Differential Equations

First Order Linear DE

dy/dx + P(x)y = Q(x)

Solution using integrating factor

Second Order (Constant Coeff)

ay'' + by' + cy = 0

Characteristic equation: ar2 + br + c = 0

5. Laplace Transforms

Common Transforms

L{1} = 1/s
L{t} = 1/s2
L{e^(at)} = 1/(s-a)
L{sin(wt)} = w/(s2 + w2)
L{cos(wt)} = s/(s2 + w2)

Properties

Linearity: L{af + bg} = aL{f} + bL{g}
Differentiation: L{f'} = sF(s) - f(0)
Integration: L{integral f dt} = F(s)/s

REE Pro Tips - Mathematics

- Complex numbers are ESSENTIAL for AC circuit analysis
- Master j operator: j = sqrt(-1), j2 = -1
- Laplace transforms simplify circuit transient analysis
- Know your calculator modes (DEG vs RAD)
- Practice converting between rectangular and polar forms

Mathematics