Complex methods- Differentiation Flashcards
Seperate the PDE into 2 ODEs + produce a general solution.
Hint for gen. solution:
A solution depends on the constant C. The sollution of a linear PDE is given by a sum of possible choices.
Don’t forget arbitrary weigtings/constant!
Sum is over c as solns depend on const c.
What do linear PDEs obey? (should be a short answer)
What does this mean for its solutions?
Seperate this into 2 ODEs by first putting into a form (Lx + Ly) u(x,y). Find the solutions ot the ODEs and state the general solution.
Given this solution and E= 2, state the 2 possibilities/general solution.
Solve this Linear ODE
Solutions to linear ODE- What is the form when m1 != m2? (this image is answer)
Solution when m1= m2? (When roots are equal?)
Solution when m<0 ? (m is negative)?
Hint: Think about determinant/quadratic formula to help solve.
Solve this linear ODE
Solve the ODE: y’’ + 8y’ + 25 = 0
Don’t look at image until after
Try and solve this problem
Try this problem
Read about symmetries
State the starting point for the power-series method (where x0 = 0).
Attempt this example using a power series around x=0 - DON’T LOOK PAST THE INITIAL QUESTION UNTIL COMPLETION
Test whether this series converges
Test whether this series converges
State the condition for convergence of a power series
Given the solution, find the RADIUS of convergence for this series.
Don’t forget the modulus! Radius of convergence MUST be positive, similar to the radius of a circle.
Do not look beyond the question mark until complete.
If a series terminates, what does this tell you about if it converges or diverges?
