Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
9 Cards in this Set
- Front
- Back
|
How many initial values will you need if you have a nth-order differential equations that you wish to fully solve?
|
you will need n initial value conditions, starting from
y(x) = y0, y'(x) = y1, y''(x) = y2, ..., all the way to y^(n-1)(x) = y(n-1) |
|
|
What does the theory on the "Existence of a Unique Solution" say?
|
As long as the coefficients on the left hand side of the equation are all continuous. And the f(x) on the right hand side of the equation is continuous. If x = x0 is any point in this interval, then a solution y(x) of the initial-value problem (1) exist on the interval and is unique.
|
|
|
What is a boundary-value problem (BVP)?
|
A BVP is any linear equation of order two or greater in which the dependent variable y or its derivatives are specified at different points.
The different points specified are known as boundary conditions. Any solution to the differential equation must be a function that passes through these initial condition points. |
|
|
What different type of solutions can a BVP have?
|
A BVP can have Many, One, or No Solutions.
|
|
|
What does homogenous mean? What does nonhomogenous mean?
|
Homogenous means that a function equals 0. As in g(x) = 0. Nonhomogenous means that a function equals something other than 0, as in f(x) = g(x), where g(x) is not zero.
|
|
|
What is the Quadratic Equation?
|
[-b (+|-) Sqrt[b^2 - 4(a)(c)] ]/2a, when an equation is of the form
am^2 + bm + c = 0 |
|
|
How do you solve a homogenous linear equation with constant coefficients?
|
Find the roots of the equation using whatever means neccesary.
The steps are: i)make the assumption that the solution will contain r(t) = e^(mt), which mean r'(t) = m*e^(mt), etc. ii) now make the equivilant substitutions into the equation. iii) reorganize so that you have e^(mt)*G(x), find all solutions for G(x). iiii) create solution of y = {(constant 1, 2, 3,...)*e^(all the solutions you got from part iii))}. so if you found 3 solutions in iii, you should have three parts to your y = something. |
|
|
What is the function name to find roots for a polynomial equation in mathermatica? How high an order can it solve for?
|
Solve[3m^3 + 5m^2 + 10m == 0, m]
polynomial can be algebraicly solved if they are of degree less than 5 |
|
|
What is the mathematica equation for solving a differential equation?
|
DSolve[y''[x] + 2y'[x] +2y[x] == 0, y[x], x]
|
