Class meetings: TuesThurs, 11am12:15pm, in CIWW 317.
Last day of class: Thursday, April 29.
Final exam: Thursday, May 6, 1011:50am, in CIWW 317.
Two review sessions (to answer questions), in CIWW 317.
May 4 and May 5, 11:00am12:15pm.
This class will cover several topics, including: onedimensional nonlinear equations; understanding and dealing with sources of error; linear equations and linear leastsquares; data fitting; and ordinary differential equations. As much as possible, numerical methods will be presented in the context of realworld applications.
A set of approximately 50 questions (containing all possible final
exam questions) will be passed out in class on April 22 ,2010,
two weeks before the final exam. At the time of the final exam,
each student will receive a list of (approximately) 6 of these
questions that he/she is to answer during the exam period.
Each student will receive a
different subset of questions to be answered.
During the final examination, students must use only their knowledge and a pencil/pen. Written or electronic answers prepared in advance must not be consulted in physical or electronic form during the exam, nor are students allowed to use laptops, cell phones, or any other communication device during the exam.
Revised projects must be submitted by 12:15pm on Tuesday May 4.
January 19  Course overview. 
January 21  Onedimensional
nonlinear equations (1). Chapter 3 of textbook (Ascher and Greif). Handout 1. 
January 26  Onedimensional nonlinear equations (2). First homework assignment, due February 2. 
January 28  Onedimensional nonlinear equations (3). 
February 2  Errors (1). Chapters 1 and 2 of textbook (Ascher and Greif). Second homework assignment, due February 11. 
February 4  Errors (2). Floatingpoint systems. 
February 9  IEEE arithmetic (1). Handout 2. 
February 11  IEEE arithmetic (2). Second homework assignment, due February 12 (postponed one day by weather). Third homework assignment, due February 23. 
February 16  Linear algebra review.
Direct methods for nonsingular linear systems (1). Chapters 4 and 5 of Ascher and Greif. 
February 23  Direct methods for nonsingular
linear systems (2). 
February 25 
Direct methods for nonsingular linear systems (3). Fourth homework assignment, due March 11. 
March 2  LU factorization.
The need for pivoting in Gaussian elimination. List of possible projects handed out. 
March 4 
Pivoting strategies in Gaussian elimination. Stability analysis of Gaussian elimination with partial pivoting. 
March 9  NO CLASS.

March 11  Disadvantages of calculating the inverse. Symmetric linear systems. Positive definite symmetric systems. Fourth homework assignment due. 
March 1520  SPRING BREAK. 
March 23 
Positive definite symmetric systems.
Symmetric indefinite systems. Householder transformations and triangularization. Chapter 6 of Ascher and Greif. 
March 25  Householder transformations and triangularization. Data fitting; linear leastsquares. Normal equations. QR factorization. Chapter 6 of Ascher and Greif. 
March 30 
Normal equations. QR factorization. 
April 1 
Numerical rank estimation. SVD. Rankrevealing QR. 
April 6 
Start interpolation and approximation. Polynomial interpolation. Chapters 10, 11, 12 of Ascher and Greif. 
April 8 
Polynomial interpolation. Representations of the interpolating polynomial. Polynomial interpolation at many equally spaced points. 
April 13 
Piecewise polynomial interpolation. Splines. 
April 15 
Piecewise polynomial interpolation. Piecewise cubic Hermite interpolation. Smoothing splines. 
April 20 
Numerical integration (quadrature). Chapter 15 of Ascher and Greif. 
April 22 
Numerical integration (continued). Composite quadrature rules. Romberg integration 
April 27 
Initial value problems in ordinary differential equations. Chapter 16, Ascher and Greif. 
April 29 
Initial value problems in ordinary differential equations. Short summary of course content. 
May 4, 5 
Review sessions (11:00am12:15pm). 