Lectures 12-16

Question 1

ODE 45

Answer 1

applies a variable-step classical Runge-Kutta method that is h^4 accurate. Should be the first method to try

Question 2

ode23

Answer 2

used for solving moderatley “stiff” equations (example - mass spring dampening with a high spring constant)

Question 3

ode15s

Answer 3

should be used for solving stiff equations - potentially less acccurate

Question 4

What is the set up for an ode

Answer 4

[x,y]=ode45(‘myfunc’,tspan,y1)
y1 = initial value
tspan = vector limiting the domain for the problem (need to define)(vector)

Question 5

What are some causes of not being a linear equation?

Answer 5

squared term

two variables multiplied together

Question 6

What are the three possible outcomes when solving a linear equation?

Answer 6

1. there is a unique solution
2. there is a non-unique solution (family of solutions)
3. there is no explicit solution

Question 7

What are the commands do to A^-1 of the equation Ax=b?

Answer 7

x=inv(A)*b

x=A\b

Question 8

What does a unique solution to a system require?

Answer 8

the existence of the inverse A^-1

Question 9

Rank

Answer 9

the total number of linearly independent rows in a matrix

Question 10

Singular

Answer 10

when a matrix has linearly dependent rows

Question 11

What is another code of inv if the the solution is NaN or Inf

Answer 11

pinv(A)

Question 12

sample set

Answer 12

a population , numerical sequence of probability and statitics

Question 13

mean

Answer 13

average of a sample set, the function ‘ mean ‘ is used

Question 14

median

Answer 14

the value which separates a sample set between a lower half and an upper half. matlab code = median

Question 15

standard deviation

Answer 15

the neighborhood about the mean value which captures 68% of the population

Question 16

probability distributioin

Answer 16

the relative likelihood (as a ratio) of obtaining a specified outcome, x

Question 17

uniform distribution

Answer 17

all outcomes are equally probable

Question 18

normal distribution

Answer 18

a bell curve probability distribution; the further the outcome is from the mean, the less probable

Question 19

cumulative probability

Answer 19

the cumulative (integrated) likelihood of obtaining a specified range of outcomes

Question 20

rand

Answer 20

generates a random real number on the open interval (0,1)

Question 21

rand(m,n)

Answer 21

generates an m x n array of random numbers

Question 22

randi(imax,m,n)

Answer 22

generates an m x n array of random integers between 1 and imax

Question 23

randn

Answer 23

generates a random real number using a normal probability distribution

Question 24

randn(m,n)

Answer 24

generates an m x n array of random numbers using a normal distribution

Question 25

round(x)

Answer 25

rounds x towards the nearest integer

Question 26

fix(n)

Answer 26

round x toward zero

Question 27

hist(x,n)

Answer 27

plots a histogram where x is the sample and n is the number of bins

Question 28

calculates histogram data

Answer 28

[z,y]=hist(x,n)

Question 29

bar(y,z)

Answer 29

draws a bar graph that looks like a histogram (especially if y and z are determined using hist command)

Question 30

How do you create a bar graph with the probability of rolling a die (with 6 different sides) with an input for a number of rolls.

Answer 30

n=input('number of rolls')
b=1:6 %possible sides of the die
dievalue=randi(6,1,n)
[z,y]=hist(dievalue,b)
bar(y,z)