South Dakota School of Mines and Technology
Department of Mathematics and Computer Sciences
Math 373
HQ 2A
March 30, 2011
Closed notes, books, and calculators
Turn in ONLY the printed sheets with your solutions in space provided. If a question seems to co
function [x_root,func_val,error_approx,num_iterations] = IQI(func,.
x_guess_one,x_guess_two,x_guess_three,error_desired,max_iterations)
% Name:
% Date: 02/17/17
% Function Description:
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The Inverse Quadratic Interpolation is a root finding me
function [root, func_val, error_approx,num_iterations] = bisection(func,.
x_min ,x_max, error_desired, max_iterations )
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% Name:
% Date: 01/31/17
% Function Description:
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HAS SOME MINOR ERRORS
%
% In the Bisection Method, we are starting with a closed i
function [x_root,func_val,error_approx,num_iterations] = secant(func,.
x_guess_one,x_guess_two,error_desired,max_iterations)
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% Name:
% Date: 02/06/17
% Function Description:
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The Secant Method is a root finding algorithm that uses a success
function [root, func_val, error_approx,num_iterations] = false_position.
(func, x_min ,x_max, error_desired, max_iterations)
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% Name:
% Date: 01/31/17
% Function Description:
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HAS SOME MINOR ERRORS
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% The False Position Method identifies the roots of a
South Dakota School of Mines and Technology
Department of Mathematics and Computer Sciences
Math 373
HQ 2A
Nov 10, 2010
Closed notes, books, and calculators
Turn in ONLY the printed sheets with your solutions in space provided. If a question seems to cont
Taylor Series and the Mean Value Theorem
Hour Exam 2001F
4. Indicate on the sketch below where the value of
of Derivatives.
lies that satisfies the Mean Value Theorem
f(x)
x
x+h
The value of x where the slope is
f ( x + h) f ( x )
x
Final 2002F
2. Mark th
Deriving Differential Equations
Hour Exam 2001F
1. Derive the Heat Equation for a one-dimensional, cylindrical coordinate, unsteady
state heat conduction problem (i.e. 1D USS HT Cyl).
As with all differential equation derivations, this one follows the sam
Elementary PDQs
Oct 15, 1999
1. a) Write the Heat Equation in incremental form and
b) solve it for the new temperature.
2
2
T + T = T
x 2 y 2 t
2. Sketch a spreadsheet solution to determine temperature profiles in a one-dimensional system
as a function
ODEs
Final Exam 1999S
3. The rate of change of z with t is given below. At t=1 , z = 3. Find z when t= 2 by any order RungeKutta method. Use a step size of 1.
dz
= (1+t)- 0.05z2
dt
Final Exam 2001F
4. The rate of change of y with t is given below and that
Intermediate PDQs
Hour Exam Oct 15, 1999
4. Describe the Dufort-Frankel Method of solving a 1D USS HT transfer problem.
Final Exam 1999S
6. Describe the Saulyev Method of solving a 1D USS HT problem. Label the sketch for reference.
Hour Exam 1998F
6. Desc
Root Finding
Final Exam 1999S
1. Use Newton's method to find a root of the following equation. Start at x=2.
x3 - 70= 0
7. Solve the following set of linear equations using Gauss-Seidel
-x+2y+4z
x+3y+2z
2x+ y
= 10
= 11
=5
Hour Exam 2000S
2) Use Newton's M
Interpolation
Final 2002F
1. Using the data in Table 1 answer the following questions:
a) What order polynomial do the data appear to observe?
b) Approximate f(2.33) using a third order approximation. (Perform no arithmetic.)
Table 1. Difference Table for
Numerical Integration
Final Exam 1999S
2. Find the value of
x
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.6
0
f ( x)dx by any two methods. Clearly identify the methods by name.
f(x)
2.00000
1.91984
1.67808
1.27352
0.70976
0.00000
-0.82816
-1.72792
-2.62
Optimization
Hour Exam 2000S
1) Describe in mathematical detail how to find the best values of A, B, C, D, E, and F for the
following set of data. The following relationships must be satisfied: A=B+C and C+D=E.+F
A
200
201
204
198
197
201
B
80
81
79
88
74
function [x_root,func_val,error_approx,num_iterations] = secant_modified.
(func,x_guess,delta,error_desired,max_iterations)
% Name:
% Date: 02/06/17
% Function Description:
%
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The Modified Secant Method is an alternative method to the Secant Meth