Ph.D. QUALIFYING EXAM DIFFERENTIAL EQUATIONS Spring, 2004
... 1. Consider the differential equation with initial condition dx/dt = F (t, x), x(a) = x0 ∈ Rn where x(t) = (x1 (t), x2 (t), . . . , xn (t))T and F (t, x) = (F1 (t, x), F2 (t, x), . . . , Fn (t, x))T . Suppose F (t, x) is continuous for a ≤ t ≤ b and x ∈ Rn and satisfies a Lipschitz condition |F (t, ...
... 1. Consider the differential equation with initial condition dx/dt = F (t, x), x(a) = x0 ∈ Rn where x(t) = (x1 (t), x2 (t), . . . , xn (t))T and F (t, x) = (F1 (t, x), F2 (t, x), . . . , Fn (t, x))T . Suppose F (t, x) is continuous for a ≤ t ≤ b and x ∈ Rn and satisfies a Lipschitz condition |F (t, ...
MATH 495
... Let R be a ring; an element x in R is said to be idempotent if x 2 x . How many idempotent elements does the ring ℤ20 contain? ...
... Let R be a ring; an element x in R is said to be idempotent if x 2 x . How many idempotent elements does the ring ℤ20 contain? ...
Moghadam
... Course Description: This course is designed to acquaint business students with mathematical techniques which are useful in business and management. Topics include Basic Algebra, Functions, Mathematics of Finance, Systems of Linear Equations, Linear Programming, Probability and Data Description. Gene ...
... Course Description: This course is designed to acquaint business students with mathematical techniques which are useful in business and management. Topics include Basic Algebra, Functions, Mathematics of Finance, Systems of Linear Equations, Linear Programming, Probability and Data Description. Gene ...
![m1-] 63 NOTE ON THE NUMBER OF LINEARLY INDEPEND](http://s1.studyres.com/store/data/012997862_1-d2f38d28dd32ef9691afaab3955d0a2a-300x300.png)
hw2
... Problem 1: Consider that somebody has both a die and a coin. Each time, he can choose to roll the die or to flip the coin. The decision is based on a Bernoulli distribution. The observed number for flipping the coin is either 0 or 1, and the observed number for rolling the die is either 0, 1, 2, 3, ...
... Problem 1: Consider that somebody has both a die and a coin. Each time, he can choose to roll the die or to flip the coin. The decision is based on a Bernoulli distribution. The observed number for flipping the coin is either 0 or 1, and the observed number for rolling the die is either 0, 1, 2, 3, ...
