Syllabus for APMA 5070

Numerical Methods

University of Virginia

Spring 2014

Instructor: Kathy Gerber, kathy@virginia.edu

Office hours: TBD

Class meets Mondays and Wednesdays, 3:30-4:45 p.m. in Olsson Hall, Room 011

Required Text: Classical and Modern Numerical Analysis, by Azmy S. Ackleh, Edward James Allen, Ralph Baker Kearfott, Padmanabhan Seshaiyer, CRC Press.

We will cover the following core topics:

 1. Computer Arithmetic (Chapter 1)

 2. Floating-point Representation (Chapter 1)

 3. Locating Roots of Equations (Chapter 2)

 4. Systems of Linear Equations (Chapter 3)

 5. Polynomial Approximation (Chapter 4)

 6. Approximation by Spline Functions (Chapter 4)

 7. Numerical Differentiation (Chapter 6)

 8. Numerical Integration (Chapter 6)

 9. Initial Value Problems for ODEs (Chapter 7)

10. Systems of Ordinary Differential Equations (Chapter 7)

11. Boundary Value Problems (Chapter 10)

12. Partial Differential Equations

13. Monte Carlo Methods

Class attendance is required.  Some exam questions may come directly from examples discussed in class.

Homework:  Homework will be assigned most Wednesdays and will be due the following Wednesday at the beginning of class. You are encouraged to work together, but write up solutions yourself, in your own words. Programming problems will be submitted to the course collab site drop box.

Midterm exam: Wednesday, March 5, in class.

Project:  A collaborative (small group) project in the broad area of numerical optimization will be due April 7.

Final exam: Tuesday, May 6, 2-5 pm in Olsson, Room 005 unless we are given an alternate room.

Your course grade will be determined by 25% homework, 20% midterm exam, 25% project and 30% final exam.