Course 3043 - Numerical Analysis I - Fall 2011

Official Information
Course Number:Mathematics 3043.001
Course Title:Numerical Analysis I
Times:TR 11:40-1:20 (lectures) and W 9:00-10:50 (lab)
Places:WCHMAN 447 (lectures) and TTLMAN 9 (lab)
Instructor: Benjamin Seibold
Instructor Office:518 Wachman Hall
Instructor Email: seibold(at) 
Instructor Office Hours:T 2:00-4:00
TA:Stephen Shank
TA Office:521 Wachman Hall
TA Email: sshank(at) 
TA Office Hours:R 2:00-4:00
Course Textbook: Brian Bradie, A Friendly Introduction to Numerical Analysis, Pearson Prentice Hall, 2006.
Prerequisites:see Math Course Listing
Topics Covered:Computer arithmetic, pitfalls of computation, iterative methods for the solution of a single nonlinear equation, solution of linear systems by direct and iterative methods, eigenvalue problems, polynomial interpolation, cubic spline interpolation, elementary least squares, numerical differentiation, numerical integration.
Course Goals:Provide a sound working base in numerical methods, increase ability to apply proper mathematical tools to specific situations, introduce computing technology using MATLAB and apply it to problem solving, increase ability to work independently and formulate problem solving approaches, provide a set of experiences that can be utilized in other courses and beyond the classroom.
Attendance Policy:Attendance is required.
Course Grading:A(100-92), A-(91-90), B+(89-88), B(87-82), B-(81-80), C+(79-78), C(77-72), C-(71-70), D+(69-68), D(67-62), D-(61-60), F(below 60).
Grading:Homework/quizzes/lab 33%, exams 67%; two midterm exams and one final exam.
Exam Dates:Midterm exams on 10/04/2011 and 11/16/2011; final exam Tuesday 12/13/2011 from 10:30-12:30.
Homework:No late submits. No make-ups. Naked numbers are not acceptable. Solutions must include a short write-up describing the problem, your solution technique, and procedural details. To include a computer printout use the cut and paste method for placement of materials in your work. All things must be clearly labeled.
Computational Devices: You must ensure to have access to a computer, the internet, and the software package MATLAB to work on certain homework problems. MATLAB is available at various places on campus, for instance at the Tech Center.
Other Formalities: Any student who has a need for accommodation based on the impact of a disability should contact the instructor privately to discuss the specific situation as soon as possible. Contact the Disability Resources and Services Office at 215.204.1280 in 100 Ritter Annex to coordinate reasonable accommodations, if needed.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Re- sponsibilities (Policy # 03.70.02) which can be accessed at
Students will be charged for a course unless a withdrawal form is processed by a registration Office of the University by the Drop/Add deadline date given below. For this semester, the crucial dates are as follows:
The first day of classes is Monday, August 29.
The last day to drop/add (tuition refund available) is Tuesday, September 13.
The last day to withdraw (no refund) is Monday, November 1.
The last day of classes is Wednesday, December 8.
During the first two weeks of the fall or spring semester or summer sessions, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.
The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the used in case the I grade is not resolved within 12 months.
Course Schedule
08/30/2011   Lec 1 Getting Started: Overview and fundamental challenges (1.0)
08/31/2011   Lab 1 Introduction to Matlab
09/01/2011   Lec 2 Rate and order of convergence (1.2)
09/06/2011   Lec 3 Taylor's theroem (1.2), floating point number systems (1.3)
09/07/2011   Lab 2 Algorithms (1.1)
09/08/2011   Lec 4 Round-off errors (1.3), floating point arithmetic (1.4)
09/13/2011   Lec 5 Accumulation of round-off errors (1.4), ill-conditioned problems (1.3)
09/14/2011   Lab 3 Accumulation of round-off errors (1.4)
09/15/2011   Lec 6 Rootfinding: Overview (2.0)
09/20/2011   Lec 7 Bisection method (2.1), method of false position (2.2)
09/21/2011   Lab 4 Bisection method (2.1)
09/22/2011   Lec 8 Fixed point iteration schemes (2.3)
09/27/2011   Lec 9 Newton's method (2.4)
09/28/2011   Lab 5 Newton's method (2.4), secant method (2.5)
09/29/2011   Lec 10 Secant method (2.5), accelerating convergence (2.6)
10/04/2011   Exam 1 Mitterm 1
10/05/2011   Lab 6 Accelerating convergence (2.6), roots of polynomials (2.7)
10/06/2011   Lec 11 Systems of Equations: Gaussian elimination (3.1), pivoting (3.2)
10/11/2011   Lec 12 Error Estimates and Condition Number (3.4)
10/12/2011   Lab 7 Elimination (3.1+3.2)
10/13/2011   Lec 13 LU decomposition (3.5)
10/18/2011   Lec 14 Special matrices (3.7)
10/19/2011   Lab 8 Debugging, examples for special matrices
10/20/2011   Lec 15 Iterative methods for linear systems (3.8)
10/25/2011   Lec 16 Conjugate gradient method (3.9), nonlinear systems (3.10)
10/26/2011   Lab 9 Linear systems in the forward heat equation and Newton iteration
10/27/2011   Lec 17 Eigenvalues and Eigenvectors: Power method (4.1), inverse power method (4.2)
11/01/2011   Lec 18 Rayleigh quotient iteration, deflation (4.3)
11/02/2011   Lab 10 (Inverse) power method, Rayleigh quotient iteration
11/03/2011   Lec 19 QR Method (4.5)
11/08/2011   Lec 20 Interpolation: Vandermonde matrix, Lagrange form (5.1)
11/09/2011   Lab 11 QR Method (4.5), polynomial interpolation (5.1)
11/10/2011   Lec 21 Neville's algorithm (5.2)
11/15/2011   Lec 22 Newton form (5.3), optimal interpolation points (5.4), piecewise linear interpolation (5.5)
11/16/2011   Exam 2 Midterm 2
11/17/2011   Lec 23 Cubic spline interpolation (5.6), Hermite cubic interpolation (5.7)
11/22/2011   Lec 24 Regression (5.8)
11/29/2011   Lec 25 Differentiation and Integration: Numerical differentiation (6.1+6.2)
11/30/2011   Lab 12 Polynomial and spline interpolation, numerical differentiation
12/01/2011   Lec 26 Richardson extrapolation (6.3), Newton-Cotes quadrature (6.4)
12/05/2011   Lec 27 Composite Newton-Cotes quadrature (6.5), Gaussian quadrature (6.6)
12/06/2011   Lab 13  Quadrature, review
12/13/2011 Final Exam
Matlab Programs
  • A concise implementation of the bisection algorithm: bisection_short.m
  • A flexible implementation of bisection, including the visualization of the problem: bisection_visual.m
  • A second order accurate solver for the time-dependent heat equation; serves as a wrapper to test linear solvers: temple3043_heateqn.m
  • Draws the Gerschgorin circles corresponding to the rows and columns of a given matrix: gerschgorin.m
  • Plots the total error in derivative approximation as a function of the step size: derivative_error.m
Additional Course Materials
Homework Problem Sets