Class meets: MTWH 10:45am - 11:35am
Where: JTB 130
Textbook: Burden and Faires, Numerical Analysis, Thomson Brooks/Cole, ninth edition.
Prerequisites: Multivariate calculus (e.g. Math 2210 Calculus
III), basic linear algebra (e.g. Math 2250 or Math 2270) and basic
programming.
Instructor: Fernando Guevara Vasquez
Office: LCB 212
Office hours: MTW 9:30am-10:30am or by appointment
Phone number: +1 801-581-7467
Email: fguevara(AT)math.utah.edu
(replace (AT) by @)
Homeworks 40%, Project 15%, Midterm 15%, Final 30%. Expect between 6 and 8 homeworks during the semester. Projects will be announced in class.
Letter grade Final exam grade
A :***** 110:***
A-:***** 100:******
B+:*** 90:***
B :**** 80:
B-:*** 70:***
C+:* 60:*
C :* 50:*
40:**
30:**
30: * 40: ** 50: * 60: ** 70: ********* 80: ******** 90: * 100: 110: *
50: ** 60: **** 70: ****** 80: **** 90: ******* 100: 110: *
sign
to write the quadratic formula (as is done in the equation immediately above Algorithm 2.8 in your book, which I call from now on Eq. (A)). The problem with sign
is that it has a meaning for complex numbers. What you can do is evaluate the denominator of Eq. (A) with both a plus and a minus sign and determine which sign gives the largest one (Step 4 in Algorithm 2.8). The new guess of the root will be the solution with the largest denominator of Eq. (A) (Step 5 in Algorithm 2.8).newtondd.m
is assumed to be a vector with the coefficients of the Newton interpolation polynomial. To test your code you may use the code from help newtondd
, which is:x = linspace(0,5); xd = [1 2 3 4]; yd = [-1 2 -2 5]; d = newtondd(xd,yd); y = newtonev(xd,d,x); plot(x,y,xd,yd,'r+')
The plot you should get looks like this one:
abs(f(x)) <= TOL
, as your code may terminate early (in the sample problem the initial guess does actually satisfy this stopping criterion). Please use the stopping criterion abs(x-xnew) <= TOL
.x^6 + 6*x^5 + 9*x^4 + ...
(the first term is x^2
in the book, which does not give a multiple root)Announcements, assignments and other class information will be posted here.