Karteikarten
basic de notions
Karten in diesem Stapel (15)
- 1What is a differential equation?any equation which contains derivatives, either ordinary derivatives or partial derivatives.
- 2What is the order of a differential equation?the largest derivative present in the differential equation
- 3What is an ordinary differential equation?abbreviated by ode, differential equation that has ordinary derivatives in it.
- 4What is a partial differential equation?abbreviated by pde, differntial equation that has partial derivatives in it
- 5What is a linear differntial equation?Looks like a n-th degree function but with derivates instead of x
There are no products of the function - 6What is solution to a differential equation?A solution to a differential equation on an interval α < t < β is any function y(t)
which satisfies the differential equation in question on the interval α < t < β
. It is important to note that solutions are often accompanied by intervals and these intervals can impart some important information about the solution. - 7What are initial conditions?Initial Condition(s) are a condition, or set of conditions, on the solution that will allow us to determine which solution that we are after.
- 8What is an initial value problem?An Initial Value Problem (or IVP) is a differential equation along with an appropriate number of initial conditions.
- 9What is the interval of validity for an IVP with initial condition(s)?is the largest possible interval on which the solution is valid and contains t0
- 10What is the general solution?the most general form that the solution can take and doesn’t take any initial conditions into account.
- 11What is the actual solution?the specific solution that not only satisfies the differential equation, but also satisfies the given initial condition(s).
- 12What is the explicit solution?any solution that is given in the form y=y(t). In other words, the only place that y
actually shows up is once on the left side and only raised to the first power - 13What is the implicit solution?any solution that isn’t in explicit form. Note that it is possible to have either general implicit/explicit solutions and actual implicit/explicit solutions.
- 14Given a differential equation will a solution exist?Not all differential equations will have solutions so it’s useful to know ahead of time if there is a solution or not.
This question is usually called the existence question in a differential equations course. - 15If a differential equation does have a solution how many solutions are there?it is possible for a differential equation to have more than one solution. We would like to know how many solutions there will be for a given differential equation.
This question is usually called the uniqueness question in a differential equations course.
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- differential equations Karteikarten am basic de notions, erstellt von Mircea Chira am 29/12/2019.
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- Mircea Chira
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