1.2.1. Method

Try these first

1. 1.

   What is a Partial Differential Equation?

   Hint

   Think about the definition involving derivatives.

2. 2.

   Name a field where PDEs are used.

   Hint

   Consider any science or engineering discipline.

3. 3.

   What is a Partial Differential Equation?

   • An equation of only one variable.
   • An equation involving partial derivatives of multivariable functions.
   • A linear equation.

   Hint

   Think about the definition you have learned.

4. 4.

   True or False: You can form PDEs only by eliminating constants.

   • True
   • False

   Hint

   Consider both methods we discussed.

5. 5.

   Given z=ln(x²+y²+c), derive a PDE after eliminating constant c.

   Hint

   Challenge yourself to see how constants can be transformed away.

6. 6.

   Starting with z=f(xy)+g(x+y), derive its second-order PDE form after eliminating functions f and g.

   Hint

   Remember the application of chain rule and relationships.