Intro to ChemE Final Flashcards
Bisection Method Flow Diagram
- keep upper half of range
**low = mid **
Newton’s Method Flow Diagram
- define converge tolerance tol
Newton’s Method Flow Diagram
- calculate slope fpr(x)
x=x-f(x)/fpr(x)
calculate f(x)
Syntax to create an nxn identity matrix and an identity matrix the same size as matrix A
eye(n)
eye(size(A))
Bisection Method Flow Diagram
- input lower and upper limits low and high
To return an answer for an array function use
Ctrl + Shift + Enter
Excel command for inverse
minverse
For an undetermined system, what methods will not work
Matrix inverse method and Cramer’s method
MATLAB command for inverse
inv
Excel command for determinate
mdeterm
Newton’s Method Flow Diagram
- output root x
Using the Exponential Function to describe data
y=b(10)mx and its equivalent form y=bemx give a straight line when plotted on a semilog plot whose y axis is logarithmic
Syntax and solution output for pseudoinverse method
x=pinv(A)*b
minimum norm solution
Using the Power Function to describe data
y=bxm gives a straight line when plotted on log-log axes
If you attempt to solve a _____ using the inv command, MATLAB displays _____
If you attempt to solve a singular problem using the inv command, MATLAB displays an error message
Using the Linear Function to describe data
y=mx+b gives a straight line when plotted on a rectilinear axes. its slope is m and its intercept is b
Newton’s Method Flow Diagram
- while abs(f(x)) > tol
If the number of equations equals the number of unknowns and if |A| ≠ 0 then _____
If the number of equations equals the number of unknowns and if |A| ≠ 0 then the equation set has a solution and it is unique
In subplot, what is the variable p
The variable p tells MATLAB to place the output of the plot command following the subplot command into the pth pane
Bisection Method
if signs are different (negative product) you should eliminate the _____ of the interval
if signs are different (negative product) you should eliminate the UPPER HALF of the interval
MATLAB command for determinate
det
Excel command for transpose
transpose
Bisection Method Flow Diagram
- mid = (high + low) ÷ 2
evaluate function at lower limit and midpoint
fl=f(low) fm=f(mid)
Bisection Method Flow Diagram
- fl × fm > 0
MATLAB command to obtain several smaller subplots in the same figure
Syntax
subplot
subplot(m,n,p)
Bisection Method Flow Diagram
- display root (mid)
Bisection Method Flow Diagram
- keep lower half of range
high = mid
Excel command for multiplication
mmult
Syntax to create a nxn matrix of zeros and an mxn matrix of zeros
zeros(n) and zeros(m,n)
Bisection Method
if signs are same (positive product) you should eliminate the _____ of the interval
if signs are same (positive product) you should eliminate the LOWER HALF of the interval
Newton’s Method Flow Diagram
- input initial guess x
calculate f(x)
MATLAB commands for generating plots
loglog(x,y)
semilogx(x,y)
semilogy(x,y)
Bisection Method Flow Diagram
- while high-low > 2 × tolerance
The left-division method is based on
Gauss elimination
Bisection Method Flow Diagram
- define tolerance tol
In MATLAB, _____ or _____ seperate elements within a row; _____ separate rows
In MATLAB, spaces or commas seperate elements within a row; semi-colons separate rows
Bisection Method
you should continue until the interval width is _____ or _____
you should continue until the interval width is LESS THAN TWO TIMES ALLOWABLE ERROR or SIXTEEN ITERATIONS
