Ch 5 Comp Methods: Bracketing Methods
According to fundamental principles, the parameters of Kirchoff's Laws are electrical properties of a system such as:
- capacitance - inductance - resistance
Disadvantages of the graphical method
- graphical methods cannot be employed on all types of functions - graphical techniques are of limited practical value bc they are not precise
Advantages of the graphical method used to estimate the root of an equation
- the estimates obtained by the graphical method can be employed as starting guesses for numerical methods - graphical interpretations are important tools for understanding the properties of functions - graphical methods help predict the pitfalls of numerical methods
What is the minimum number of initial guess required to obtain the root of an equation using a bracketing method?
2
Which method exploits the fact that a function typically changes sign in the vicinity of a root?
bisection method
Which types of functions are not suitable for using graphical methods to estimate the root of a function: a. continuous function b. functions that are parallel to the y-axis on the xy-plane c. Discontinuous functions d. functions that are tangential to the x-axis on the xy-plane
c. d.
One potential problem that arises in bracketing methods is the possible existence of multiple roots. A partial remedy for such cases is to compute the first derivative of the function f(x) at the beginning and the end of each interval. If the derivative ___________, it suggest that a minimum or maximum may have occurred and that the interval should be examined more closely for the existence of a possible root
changes sign
What is the parameter of mass balance?
chemical behavior of material, mass transfer coefficients, and geometry of system
What bracketing method is used to obtain rough estimates of roots and is useful for understanding the properties of the functions?
graphical method
What is the method that finds a root by locating an interval of x in which the function changes sign?
incremental search method
A potential problem with an incremental search is the choice of the increment ______________
length
In the bisection method, if a function changes its sign over an interval [a,b], then the function is evaluated at the ___________________ to estimate the location of its root
midpoint
what is the parameter of force balance?
strength of material, structural properties, and geometry of system
What is the parameter of heat balance?
thermal properties of material and geometry of sysem
What is the parameter of energy balance?
thermal properties, mass of material, and system geometry
Which technique consists of guessing a value of x and evaluating whether a function f(x) is equal to zero to determine a root of that function?
trial and error method
