y = mx + b Slope-Intercept Form of a Linear Equation The solution is (2, 5) The solution is (4, 2) The system has no solution

Slope-Intercept Form of a Linear Equation

The ones that can be converted unto a higher order differential equation, single one what does it mean if there is at least one f(t) that is nonzero? How do you check is the solutions to the matrix equation are linearly independent? How is the wronskian for the solution vectors different from previous use of wronskian? What type of systems are we focusing on here?

What type of systems are we focusing on here?

The condition is that the highest order derivative needs to be able to be written in terms of components of the dependent, independent variables and their lower order derivatives What's condition for a system to be able to be converted into a single linear differential equation? What does the wronskian have to equal for all t values to be linearly independent? What is the term f(t) in the system represent? Consider the principle of superposition for corresponding homogenous equation

What's condition for a system to be able to be converted into a single linear differential equation?

To be able to use them to solve first order systems How do you check is the solutions to the matrix equation are linearly independent? What does the solution vector function satisfy? What's the focus with matrices for? Consider the principle of superposition for corresponding homogenous equation

What's the focus with matrices for?

Matrices of functions, where each cell is a funtion How do you check is the solutions to the matrix equation are linearly independent? What type of matrices can be used to express a system as? Consider the principle of superposition for corresponding homogenous equation For homogenous equation matrix, what happens to the linear combination of the solutions if they are all linearly independent?

What type of matrices can be used to express a system as?

When all the functions in its entry can be differentiated or integrated How do you solve a non homo matrix equation? What does the solution vector function satisfy? When is a function matrix differentiable or integrable? What's condition for a system to be able to be converted into a single linear differential equation?

When is a function matrix differentiable or integrable?

By deriving each of its entries What's the focus with matrices for? What is the column vector f(t) full of? How do you find the derivative of a function matrix? What type of matrices can be used to express a system as?

How do you find the derivative of a function matrix?

It's a x prime = p_11(t)x_1 + ... + p_1n(t)x_n + f_1(t) What does the system we are converting look like? What's the focus with matrices for? What does the solution vector function satisfy? How is the wronskian for the solution vectors different from previous use of wronskian?

What does the system we are converting look like?

It represents the hon-homogenous part of the equation What is the term f(t) in the system represent? How is the wronskian for the solution vectors different from previous use of wronskian? What is the solution like? What's the focus with matrices for?

What is the term f(t) in the system represent?

X prime = P(t) x + F(t) What is the solution like? What type of matrices can be used to express a system as? what does it mean if there is at least one f(t) that is nonzero? What does the Matrix differential equation that is equivalent to that system look like?

What does the Matrix differential equation that is equivalent to that system look like?

It's made of column vectors for X and X prime and f(t) and a full matrix with p(t) what does it mean if there is at least one f(t) that is nonzero? How do you solve a non homo matrix equation? What's the focus with matrices for? What is the matrix differential equation made of?

What is the matrix differential equation made of?

find a g(n) such that f(n) infinity (f(n) / g(n)) = 0 or C prove If 𝑑(𝑛) is 𝑂(𝑓(𝑛)) and 𝑒(𝑛) is 𝑂(𝑔(𝑛)), then 𝑑(𝑛) + 𝑒(𝑛) is 𝑂(𝑓(𝑛) +𝑔(𝑛)) log b (a) = c if how to find if f(n) is O(g(n)) (2 ways) log (ac) is equiv to

how to find if f(n) is O(g(n)) (2 ways)

can prove by multiplying d(n) <= f(n) by constant a and setting ac = c so that ????????(????) <= ????(????) prove that if 𝑑(𝑛) is 𝑂(𝑓(𝑛)), then 𝑎𝑑(𝑛) is 𝑂(𝑓(𝑛)) what is c and n0 how to find if f(n) is Ω(g(n)) (2 ways) growth rate functions

prove that if 𝑑(𝑛) is 𝑂(𝑓(𝑛)), then 𝑎𝑑(𝑛) is 𝑂(𝑓(𝑛))

can prove by adding inequalities d(n) <= c1f(n) and e(n) <= c2g(n) to get d(n) + e(n) <= c1c2 f(n)+g(n) what is c and n0 log (a^c) is equiv to how to find if f(n) is O(g(n)) (2 ways) prove If 𝑑(𝑛) is 𝑂(𝑓(𝑛)) and 𝑒(𝑛) is 𝑂(𝑔(𝑛)), then 𝑑(𝑛) + 𝑒(𝑛) is 𝑂(𝑓(𝑛) +𝑔(𝑛))

prove If 𝑑(𝑛) is 𝑂(𝑓(𝑛)) and 𝑒(𝑛) is 𝑂(𝑔(𝑛)), then 𝑑(𝑛) + 𝑒(𝑛) is 𝑂(𝑓(𝑛) +𝑔(𝑛))

similar technique to prev prove If 𝑑(𝑛) is 𝑂(𝑓(𝑛)) and 𝑒(𝑛) is 𝑂(𝑔(𝑛)), then 𝑑(𝑛) + 𝑒(𝑛) is 𝑂(𝑓(𝑛) +𝑔(𝑛)) prove If 𝑑(𝑛) is 𝑂(𝑓(𝑛)) and 𝑒(𝑛) is 𝑂(𝑔(𝑛)), then 𝑑(𝑛)𝑒(𝑛) is𝑂(𝑓(𝑛)𝑔(𝑛)) log (a^c) is equiv to log b (a) is equiv to

prove If 𝑑(𝑛) is 𝑂(𝑓(𝑛)) and 𝑒(𝑛) is 𝑂(𝑔(𝑛)), then 𝑑(𝑛)𝑒(𝑛) is𝑂(𝑓(𝑛)𝑔(𝑛))

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