Podcast
Questions and Answers
Which type of differential equation is defined by a linear polynomial in the unknown function and its derivatives?
Which type of differential equation is defined by a linear polynomial in the unknown function and its derivatives?
- Quadratic equation
- Linear equation
- Ordinary differential equation (correct)
- Partial differential equation
What is the term used to describe differential equations that may be with respect to more than one independent variable?
What is the term used to describe differential equations that may be with respect to more than one independent variable?
- Quadratic equations
- Ordinary differential equations
- Partial differential equations (correct)
- Linear equations
Which of the following is an example of a linear differential equation?
Which of the following is an example of a linear differential equation?
- $y'' + 2xy' - 3y = 0$ (correct)
- $y' + \sin(x)y = 0$
- $y^2 + 3y' - 4x = 0$
- $y''' + y'' - 2y' + y = 0$
In a linear differential equation, the functions $a_0(x), a_1(x), ..., a_n(x)$ and $b(x)$ can be any type of functions.
In a linear differential equation, the functions $a_0(x), a_1(x), ..., a_n(x)$ and $b(x)$ can be any type of functions.
What is the general form of a linear differential equation?
What is the general form of a linear differential equation?
Which of the following statements about Fourier series is true?
Which of the following statements about Fourier series is true?
Why are Fourier series useful in analyzing functions?
Why are Fourier series useful in analyzing functions?
What type of functions have Fourier series that converge to the original function?
What type of functions have Fourier series that converge to the original function?
What did Joseph Fourier use Fourier series for?
What did Joseph Fourier use Fourier series for?
Why can't Fourier series be used to approximate arbitrary functions?
Why can't Fourier series be used to approximate arbitrary functions?
