Wave equation

Solve the wave equation using d'Alembert's method (See attached file for full problem description)

Wave equations

I'm have so much trouble understanding the wave equations. The book I'm using does a terrible job at explaining this section and the example are horrible. I really would appreciate if someone could take the time and work this example problem step by step so I can get a better understanding of this. (See attached file for full problem description)

1-D heat equations

Can someone please solve this 1-D heat equation. The book I'm using doesn't explain the examples. I need all steps Please!!!! (See attached file for full problem description)

Quadratic equation

1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i). Question: In the real world, where might these so-called imaginary numbers be used? 2. When using a formula, we often know the value of one variable to a greater degree of accuracy than we know the others. In your opinion, what affect, if any, does it make on our use of a formula if we know the value of one variable to a greater degree of accuracy than another?

Computing distance

Background Information: A simple pendulum, such as a rock hanging from a piece of string or the inside of a grandfather clock, consists of a mass (the rock) and a support (the piece of string). When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and forth in a constant amount of time called the period. One period is the amount of time required for the mass to swing all the way to the other side and then swing back to its staring point. Note: we are making the simplifying assumption that our pendulum is swinging in a perfect vacuum, (i.e., there is no air resistance that will stop the pendulum). The period of a s... click for more