Engineering

Calculus

100

Branch of mathematics concerned with the calculation of instantaneous rates of change.

Differential Calculus

200

A differential equation where the derivatives are taken with respect to only one variable.

Ordinary Differential Equation

300

Aside from 

ln | sec (x) | + C

give the other anti-derivative of tan (x) dx.

ln | cos (x) | + C

400

If y = sin x / cos x,

find y''.

y'' = 2sec² x tan x

500

A car's acceleration is given by the function a(t)=6t, m/s^2, where t is the time in seconds. The car starts from rest at t=0 and from the origin x(0)=0.

Find the original position.

x = t^3

Constants

100

The density of water in kg/m^3.

1000 kg/m^3

200

Earth's Gravitational Acceleration

9.80665 m/s^2

300

Leonhard Euler's Number

e = 2.71828 

400

The Gravitational Constant

6.67430 x 10^-11 Nm^2/kg^2

500

Stefan-Boltzman's Constant

σ = 5.67037 x 10^-8 W/(m^2 K^4)

Formulas/Equations

100

Young's Modulus formula.

Stress/Strain

200

The Ideal Gas Law equation.

PV/mRT

300

A kinematic equation that does not include acceleration, a, as its variable.

Δx = ½(Vf+Vo)t

400

The formula of the Horizontal Range in a projectile motion.

R = [v^2 sin(2θ)]/g

500

Derive a formula for velocity from the energy balance equation. (Kinetic Energy = Potential Energy)

V = √ (2gh)

Unit Conversions

100

1 inch = ____ cm

2.54

200

1 atm = ____ MPa

0.101325

300

14 kg = ____ libras

30.8647

400

1 statute mile = ___ m

1,609

500

1 kg/L = ____ lbm/ft³

62.428

Laws

100

"The acceleration of the body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body."

Newton's Second Law of Motion

200

"Energy cannot be created or destroyed; it can only be converted from one form to another."

First law of Thermodynamics

300

"Every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them."

Newton's Law of Universal Gravitation

400

"The strain of the material is proportional to the applied stress within the elastic limit of that material."

Hooke's Law

500

"An increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy."

Bernoulli's Principle