Introductory Mathematics for Engineering Applications

Useful Mathematical Relations

Algebra and Geometry

Arithmetic Operations

Exponents and Radicals

Factoring Special Polynomials

x² − y² = (x + y) (x − y)

x³ + y³ = (x + y) (x² − xy + y²)

x³ − y³ = (x − y) (x² + xy + y²)

Quadratic Formula

If ax² + bx + c = 0. then

Lines

Equation of line with slope m and y-intercept b:

y = mx + b

Slope of line through points P₁(x₁, y₁) and P₂(x₂, y₂):

Point-slope equation of line through point P₁(x₁, y₁) with slope m:

y − y₁ = m(x − x₁)

Point-slope equation of line through point P₂(x₂, y₂) with slope m:

y − y₂ = m(x − x₂)

Distance Formula

Distance between points P₁(x₁, y₁) and P₂(x₂, y₂):

Area of a Triangle:

Equation, Area and Circumference of Circle:

Equation:

Trigonometry

Angle Measurement

π radians = 180°

s = rθ

Right-Angle Trigonometry

Trigonometric ...