PROBLEM 3TWE

A constant-coefficient second-order partial differential equation of the form

can be classified using the discriminant D= b2-4ac. In particular, the equation is called

Verify that the wave equation is hyperbolic and Laplace’s equation is elliptic. It can be shown that such hyperbolic (elliptic) equations can be transformed by a linear change of variables into the wave (Laplace’s) equation. Based on your knowledge of the latter equations, describe which types of problems (initial value, boundary value, etc.) are appropriate for hyperbolic equations and elliptic equations.

Week 1 and 2 of College Pre-algebra Life Saver notes! Order of operations Remember GEMDAS 1.G rouping 2.E xponents 3.M ultiply 4.D ivide 5.A dd 6.S ubtract NOTE: when multiplying, dividing, adding, and subtracting you do it as you are reading a book; you go left to right. Important things to remember!: When there are parenthesis ( ) inside of brackets [ ] be sure to do the parenthesis inside of the brackets first. Ex: 35- [3+(9-7)-2] The first step of the problem would be what is in the parenthesis, so (9-7) then you can solve for what remains left in the larger bracket. Don't be intimidated if you see fractions! Fractions just simply mean divide | | aka absolute value is considered a grouping symbol When you have to find