Mathematics Flashcards
What is the axis of symmetry in standard form for a parabola?
X = -b/2a
What is the general equation of a circle?
x²+y²+Cx+Dx+E=0
Which of the following is a conic section?
A. Circle
B. Parabola
C. Ellipse
D. All of the Above
D. All of the Above
Explanation: Circles, parabolas, ellipses, and hyperbolas are the conic sections.
Which class of numerical methods are inherently stable for all step sizes?
Answer: Implicit methods
What is the equation for volume of a sphere?
Answer: V = (4/3)*πr3
The method of __________ transforms can be used to solve a linear ordinary differential equation with constant coefficients.
Answer: Laplace
The focus of points whose sum of distances from two foci is constant is known as an:
Answer: ellipse.
The focus of points whose difference of distances from two foci is constant is known as an:
Answer: hyperbola.
Which of the following describes an unknown function that depends on more than one independent variable?
A. Partial differential equation
B. Derivative equation
C. Differential equation
D. First-order linear equation
Answer: A
Explanation: When an unknown function depends on more than one independent variable, the equation is called a partial differential equation (PDE).
Which of the following is a first-order linear homogenous equation?
A. yʹʹ + 3y = 0
B. yʹ + 3y^2 = 0
C. yʹ + 3y = 0
D.yʹʹ + 3y^2 = 0
Answer: C
Explanation: yʹ + 3y = 0 is a first-order linear homogenous equation.
What is the dimension of the null space of a full rank matrix of size (n by n)?
Answer: 0
Explanation: The dimension of the null space of a full rank matrix of size (n by n) is 0.
Explanation: If a matrix has a full rank, the dimension of the null space is 0 by the rank-nullity theorem.
Describe (don’t calculate) the output of the following algorithm:
num = 0;
for i = 1:100
num = num + 1;
end
Return num
Answer: The algorithm provides the sum of the first 100 integers.
Find the center of the circle with the following equation: (x – 3)^2 + (y – 2)^2 = 15.
Answer: 3, 2
Explanation: The center of a circle is the point (h,k) which is (3,2) in this case.
The following scheme below is used to numerically solve the ODE (dy/dx)=f(x)
yi+1=yi+hf(xi)
What is the scheme called?
Answer: Euler (or Forward Euler) Method
If the adjacent and hypotenuse are known on a right triangle, the tangent function can be used to solve for the angle. True or false?
Answer: False
Explanation: If the adjacent and hypotenuse are known on a right triangle, the cosine function can be used to solve for the angle.
