Assignments Requirement:
For the computing projects - type both the questions and your answers into a
document named as CS350_assignment#_firstname_lastname.doc. Highlight
your final answers with yellow colors. For programming
projects - proper comments and format for the code and its detailed I/O examples; BOTH of the code and the I/O document copied to a document
. Email the document as attachment to the instructor
(usvwccs@gmail.com)*. The email subject
is the same as the file name. A hard copy of the document should be
handed-in on the due date.
Assignment
1 (Due: Mon. 2/1) (i) Show the equation, x cos x - 2x^{2} + 3x - 1 = 0, has at least one solution in [1.1, 1.4]. (ii)
Test an equation if it has a solution or not, in given intervals. The given equation is:
(x-2)^{2} - lnx = 0; the intervals are [2, 4].
(iii) Let f(x) = x^{3}+ x. find the second Taylor polynomial P_{2}(x) about
x_{0} =
0.
Assignment
2 (Due:
Mon. 2/8)(i) Write a Java program to assign 3.1416 to p* and
actual value of π (MATH.PI) to p,
and then display the absolute error (AE) and relative error (RE) in approximations
of p by p^{*}. The rest questions are
no-programming ones; just type the questions and answers that are
highlighted. (ii) Using 3-digit chopping arithmetic for 133+0.921,
compute the AE and RE. (iii) Using 4-digit chopping arithmetic to find
the most accurate approximations of the solutions (roots) with appropriate formula
(1.1) - (1.3) in p.23-p.24, for the equation 1.002x^{2}-11.01x+0.01265 = 0.
Hint:since b<0 and |b|~sqrt(b^{2}-4ac), use (1.1a) to
calculate x1, and (1.3) to calculate x2. (iv)
Using 4-digit chopping arithmetic to evaluate f(2.279) for f(x)
= 1.013x^{5}-5.262x^{3}-0.01732x^{2}+0.8389x -
1.912 by first calculating the power terms using 4-digit chopping
arithmetic. (v) Find the rates of convergence. Exercise Set 1.4, #10(d),
#11(d).
Assignment 3 (Due:
Mon. 2/15) (i) Evaluate textbook P.24 Example 1 function, f(x) = x^{3}
-6.1x^{2} + 3.2x +1.5 at x=4.71 using 4-digitchopping.
(ii) Write a Java program to use the Secant Method to find the solution accurate to within
10^{-4} (TOL) for the following equation: x^{3} -
2x^{2} -5 = 0, on [1, 4]. (iii) Use Bisection method to find p_{3} for f (x)= 3(x+1)(x-1/2)(x-1) on [-2, 1.5].
(iv) Use the Newton's Method to find the solution accurate to within
10^{-4} for the following equation: x^{3} - 2x^{2} -5 = 0, on [1,
4].
Assignment 4 (Due:
Mon. 2/22) For the function f(x) = (x-1)^{1/2}, let x_{1}=1,
x_{2}=1.6, x_{3}=1.9. (i) Construct the Lagrange
interpolating polynomial of degree 2, P_{2, }and
simply to a general form. (ii) find the approximation of f(1.45) with
P_{2}.
Assignment 5 (Due:
Mon. 3/07) (a)P.81, #1a. For degree 2, use the first three data. (b) Show the
details of the Midpoint, Trapezoidal, and Simpson's rules applied to the
integration of x^{4} over [0.5, 1].
Assignment
6 (Due: Wed. 4/06) take-home projects that will be posted on
Blackboard (Content) after Test 1B.
Assignment
7 (Due: Wed. 4/13) Numerical differentiation, P.170 Exercise Set 4.9, #1b,
#2b (compute absolute errors and relative errors), #3b,
#4b (compute absolute errors and relative errors). Show the solving processes.
Assignment
8 (Due: Wed. 4/20) i) Solve IVP with the Euler's method. P.
182 Exercise Set 5.2, #1 c. Show the solving processes. ii) re-do the
last question with the Modified Euler Method - P.189 Set 5.3 #1 c. iii)
re-do the Midpoint method. Compare all the results to the actual values
(P.189, y = t*lnt +2t).
Assignment
9 (Due: Mon. 4/25) Write a Java program to implement the RK4 and solve the
same question in Assignment 8. To compare the result, display the exact
solution also.
* The email (usvwccs@gmail.com) is just for
collecting the assignments/tests; for the purpose of communications, please
use the VWC email (zwang@vwc.edu)
Topics
covered
1/25:
Syllabus, and class policy. Review of Java (Click
here to download the note).
1/27:
intermediate value theorem (IVT), Taylor polynomials.
3/14
Online review with worksheet. NO classroom meeting, but do the worksheet
on Blackboard (Content) during the class time.
3/16
Test 1B (covering class materials taught until 2/29, including
interpolation methods and basic quadrature rules), 2:30pm-3:45pm,
online
test ONLY, NO classroom meeting, but do the test on Blackboard (Content)
during
the class time. You may use books, notes, and online materials. But you cannot talk to others during the test.
(3/21-3/25
Spring
break).
3/28
Easter Monday (school close).
3/30 Take-home
projects for assignment 6. NO
classroom meeting, but use the class time to do the projects on
Blackboard (Content) that would be due April 6.
4/04
On test 1B and project.
4/06 Assignment 6 due at 1pm. Numerical methods on derivative.
4/11 IVP
- Euler's method (click here
for notes) and its Java implementation (click here).