INDUMAT Finals Review Flashcards
In a truth table, what is the mathematical approach in evaluating conjunction (p ʌ q)?
min (p,q)
In a truth table, what is the mathematical approach in evaluating disjunction (p v q)?
max (p,q)
In a truth table, what is the mathematical approach in evaluating conditional (p → q)?
True if and only if the val (p) is less than or equal to val (q)
In a truth table, how do you evaluate a biconditional (p <=> q)?
True if both statements have the same truth value. (Both p and q are true or both q and p are false). Otherwise, it is false.
In a truth table, if all the outputs of a column are true, then it is a _________
Tautology
In a truth table, if all the outputs of a column are false, then it is a _________
Contradiction
In a truth table, if the outputs have at least one true and one false, then it is a _________
Contingent
A matrix where elements below the main diagonal are all zeroes
Upper Triangular Matrix (Right Triangular Matrix)
A matrix where the elements above the main diagonal are all zeroes
Lower Triangular Matrix (Left Triangular Matrix)
Matrix where all elements are zeroes
Null Matrix
True or False. A matrix is symmetrical if A = A^T.
True
Type of matrix that has a determinant value of zero and does not have an inverse.
Singular Matrix
Type of matrix that has a determinant value and has an inverse.
Non-Singular Matrix (Standard Matrix)
True or False. Identity matrices are nonsingular.
True
If a matrix undergoing an iterative method is not diagonally dominant, then _________.If a matrix undergoing an iterative method is not diagonally dominant, then _________.
You must interchange the rows such that the diagonal consists of the highest coefficients of the matrix.
Steps for LU Decomposition
- Setup matrices as AX=B
- Get the upper triangular matrix based on A
- Put the multipliers in the lower triangular matrix (Make sure to negate or make “+” into “-“ and vice versa)
- Get y values from LY = B
- Get x values from UX = Y
Steps for Inverse Method
- Setup the matrices as AX = B
- Find A^-1
- X = A^-1 B
Steps for Gaussian Elimination
- Setup augmented matrix
- Use Elementary Row Operations until you create an upper triangular matrix
- Make sure the main diagonal values are equal to ‘1’.
- Convert back into equation form
- Back substitute
Steps for Gauss Jordan Method
- Setup augmented matrix
- Use Elementary Row Operations until you create an identity matrix
- Convert back into equation form
Steps for Gauss Jacobi
- Check for diagonal dominance (rearrange rows if found otherwise)
- Isolate the variables per row based on the diagonal
- Initialize/ Get k=0 iteration wherein variables are all equal to zero
- Substitute values into the equations of the variables using values computed from previous iterations
- Solve for error values (error = absolute value of old-new)
- Repeat the process until the calculated answer has an error value below the tolerable error.
Steps for Gauss Seidel
- Check for diagonal dominance (rearrange rows if found otherwise)
- Isolate the variables per row based on the diagonal
- Initialize/ Get k=0 iteration wherein variables are all equal to zero
- Substitute values into the equations of the variables using the most recent values
- Solve for error values (error = absolute value of old-new)
- Repeat the process until the calculated answer has an error value below the tolerable error.
Necessary and Sufficient Conditions for Local Minima (Theorem 1)
- Equate first derivative to zero
- Get the extreme points
- Plug in the extreme points to the second derivative
- If the value is greater than 0, it is a minima.
Necessary and Sufficient Conditions for Local Maxima (Theorem 2)
- Equate first derivative to zero
- Get the extreme points
- Plug in the extreme points to the second derivative
- If the value is less than 0, it is a maxima.
Convex Graph
U
Concave Graph
∩
Both Concave and Convex
\ or / (Linear Line)
Formula and Procedure for Secant Method
- Assume x0 and x1.
- If absolute value of f (x0) < f(x1), then swap x0 and x1; otherwise keep it as it is.
- Solve for x2
- Set x0 = x1 and x1=x2
5.Solve for the new x2 - Continue until less than tolerable error
Formula: x2 = x1-f(x1) [(x1-x0) / f(x1) - f(x0)]
Procedure for Bisection Method
- Make columns (k, a , f(a), b, f(b), m, f(m), and error)
- Get the value of f(m) wherein m = (a+b) / 2
- If f(m) is equal to 0, then m is a root.
- If f(m) is less than 0, set a = m. If f(m) is greater than 0, set b = m.
For Secant Method, if the given is a trigonometric function, then calculator must be set to ________ .
Radians
