Mathematics 147, alias Computer Science 102, aka Engineering 101
Numerical Methods (or is it New Miracle Methods?)
Spring 2010
MWF 10:10-11:05 a.m. (216 McEwen Hall)
Instructor: Dr. Raymond Greenwell
Office: 100C Adams Hall, 463-5573
E-mail: matrng@hofstra.edu
Home: (516) 705-6575; fax: (516) 463-6596
Web page: http://people.hofstra.edu/rgreenwell
Office Hours: MF 11:15-11:45, MWF 12:50-1:45
or by appointment or whenever you can catch me.
Text: Numerical Methods (3rd ed), by Faires and Burden

The purpose of this course is to study methods for finding approximate solutions to mathematical problems when an exact solution is difficult or impossible to obtain. Sometimes the approximation is caused, not by the method, but by the roundoff when the method is implemented on a computer, so the effect of roundoff will be an important topic in the course. The goals of the course are to learn to implement the methods manually with a calculator, as well as by programming a computer, and to analyze the methods for a deeper understanding of how and why they work.

Your grade will be based on three tests (each worth 100 points), roughly 4 programming assignments (worth a total of about 140 points), and a final exam (worth about 175 points). Grades of Incomplete will not be given except for extraordinary circumstances.

Below is the tentative daily homework assignment; stay tuned for additions and deletions. You should do as many additional problems as you have time for. The more you do, the more you learn. Turn in the homework two class days after it is assigned. To be counted, the homework must be done correctly and turned in on time with all the work showing. Late homework will not be accepted unless illness prevents you from attending class. Your homework will be graded by one of your classmates. Each of you will grade homework at least one day. Your homework grade will be averaged with your lowest test grade, assuming that improves your grade.

Programming assignments will be done using Maple, a computer algebra system. The disk that comes with the book has all the algorithms in the languages C, FORTRAN, Maple, Mathematica, Matlab, and Pascal. I have put these files in the Greenwell folder in a directory entitled "numerical methods". This folder is in the S drive (HU 20) if you are on a DOS/Windows machine on the campus network, or in the HU20 or HU21 SHARED area on a Macintosh.

All computer programs must be your own work. Although there is great value in working on large programs in a group, you will learn the most by doing the programs assigned in this class by yourself. Further, a student who only does half the work should not receive the same credit as one who does all the work. It is permissible to exchange ideas, but not to copy code. If more than one person submits the identical program, the total credit will be divided between them.

Since you are responsible for everything said in class, be sure to get the notes from someone else if you are absent. This syllabus is subject to change; stay tuned for the latest update.

Prerequisite: Math 72 and CSC 15 or Engg 10 or equivalent programming experience.

All students are expected to abide by the University's Policy on Academic Honesty (p. 52 of the Hofstra University Undergraduate Bulletin 2009-2010).

Date	Sec.	page	assignment	topic
M 1-25	1.2	14	7,9,13	Review of Calculus
W 1-27	1.3	20	1ac,3ach,5ach,9,10(ans: a. -1.81, b. .00709)	Round-off error, computer arithmetic
F 1-29	1.3		(continued)
M 2-1	1.4	27	3(correct ans:b: -.09),7,8(ans: a. 2000 b. 20,000,000,000),11,12	Errors in scientific computation
W 2-3	2.2	38	3,5,9,11,13	Bisection Method
F 2-5	2.3	43	3ac,5ac,7	Secant Method
M 2-8	2.4	50	3ac,5,13	Newton's Method
W 2-10	3.2	75	1a,2a(ans: .03375,.003966),3a,8(ans: .7314, 2.7*10^(-8)),13,16(ans: 169,649,000, 191,767,000, 171,351,000)	Lagrange polynomials
F 2-12	3.2		(continued)
W 2-17	3.3	84	4,6(ans: a. 169,649,000 b. 171,351,000)	Divided differences
F 2-19	3.3		(continued)
M 2-22			Review
W 2-24			Test 1
F 2-26	3.6	104	3ac	Parametric curves
M 3-1	4.2	118	1bc,2b(ans: 3.961*10^(-4), 4.859*10^(-4))c(ans: .0179285, .0198486),3bc,4b(ans: 7.943*10^(-4), 9.718*10^(-4))c(ans: .0358147, .0396972),5bc,6b(ans: 7.14*10*(-7), 9.92*10^(-7))c(ans: 1.406*10*(-5), 2.170*10^(-5)),9,11,13	Basic quadrature
W 3-3	4.2		(continued)
F 3-5	4.3	127	1ac,2ac(ans: .6363098,.7853980),7ab(don't compute the approximation)	Composite quadrature
M 3-8	4.6	148	1abc,2a(change 10^(-3) to 5*10^(-7); ans .19225930)	Adaptive quadrature
W 3-10	4.6		(continued)
F 3-12	4.9	174	1a,2a,3a,4a,12	Numerical differentiation
M 3-15	6.2	249	2a(ans: 1.0,-.98,2.9),3ac,5	Gaussian elimination
W 3-17	6.2		(continued)
F 3-19	6.3	259	5ad(correct ans: same as 7d),7ad,8a(ans: 10.0,1.00)d(.993,.500,-1.00)	Pivoting strategies
M 3-22			Review
W 3-24			Test 2
F 3-26	6.5	277	1a,2a	Matrix factorization
W 4-7	6.5		(continued)
F 4-9	6.6	286	5d	Techniques for special matrices
M 4-12	7.4	311	1ab,2a(ans: .1111111,-.2222222,.6190476)b(ans: .979,.9495,.7899)	Jacobi and Gauss-Seidel Methods
W 4-14	3.5	99	3cd,4c(ans: .1774144, 1.574209)d(ans: -.1315912, 2.908242),5cd,6c(ans: .174519, 1.668000)d(ans: -.1327722, 2.907063)	Spline interpolation
F 4-16	3.5		(continued)
M 4-19	5.2	190	1ac,2ac	Taylor methods
W 4-21	5.3	199	1ac,3ac,10ac,13	Runge-Kutta methods
F 4-23	5.3		(continued)
M 4-26	5.4	207	1a(two-step only),4a(two-step only)(ans: 3.330956)	Predictor-corrector methods
W 4-28			(continued)
F 4-30			Review
M 5-3			Test 3
W 5-5			Review

Friday, May 14, 8:00-10:00 a.m.: The Final Exam!