Spring 2004 (MTWF 8:35-9:25, JWB 333)Mathematics 5620 Introduction to Numerical Analysis II Spring 2004 (MTWF 8:35-9:25, JWB 333) Instructor: Grady Wright Phone: 581-8649 Office: JWB 126 E-mail: [email protected] Office Hours: MTWF 9:35-10:35, or by appointment Text: • Atkinson, An Introduction to Numerical Analysis, 2nd ed., John Wiley and Sons, 1987 We will use this text for studying numerical linear algebra (Ch. 7, 8, and 9). • Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996. Website: http://www.math.utah.edu/~wright/courses/5620 Course Description: This is the second half of a yearlong introductory course on numerical analysis at the 5000 level. The topics covered this semester include numerical linear algebra (solving systems of linear equations and solving eigenvalue problems), numerical methods for solving ordinary differential equations (ODEs) (both initial-value and boundary-value problems), and numerical methods for solving partial differential equations (PDEs) (primarily finite difference methods, but, if time permits, we may also study spectral and finite element methods). Prerequisites: No previous experience in numerical analysis is necessary. However, knowledge of the following topics is required: • Single and multivariable calculus • Linear algebra • Computer programming Homework: There are weekly homework assignments consisting of three to four problems. Homework is handed out in class (and posted on the class website) on Wednesday and due the following Wednesday in class. The problems involve a mix of theory and computing. Regarding the latter, please read the text below the Programming heading. Your submitted homework should show all necessary work you used to solve the problems; mathematical statements should be complete (or nearly complete) sentences; and the reasoning and logic underlying all arguments should be clearly spelled out. Please see the document “How to Present your Work” on the course web page for tips on meeting these requirements. Failure to adhere to the above requirements may result in a loss of points. Teamwork: Teamwork is part of the real world and therefore permitted (and encouraged) for all homework assignments (but not exams). Keep in mind that the purpose of teamwork is to enhance the learning effect, not to decrease the workload. It is up to each team member to prevent abuse. Please observe the following rules: • No teams with more than three members! • If you work in a team then clearly state so and hand in just one set of answers. If you collaborate on some problems but not on others then clearly state so on your turned-in solution. 1• In general, you can consult literature and people, but you have to acknowledge all help so obtained (except for the textbook or myself). Homework solutions (taken from selected students solutions) are posted on the course website once the grading has concluded. Grading Policy: The final grade for the course is on based homework assignments, a midterm exam, and a final project. The breakdown for the course grade is as follows: • Homework: 60% • Midterm exam (probably at the beginning of March): 20% • Final Project: 20% Your lowest homework score is discarded. Note that unlike last semester, no portion of your midterm score can be discarded. As mentioned above, homework assignments are due on Wednesday in class. Late homework assignments are accepted up to three days beyond their due date. However, a 10% penalty is applied for each day they are late. This means that if an assignment is turned in on Saturday, then 30% is automatically deducted. Late homework assignments need to be put into my box (located JWB 228) or, if you have the means, e-mailed to me. Please indicate the date and time you put the homework in my box. Programming: All programming assignments involving numerical computations are to be done in MATLAB. An important part of numerical analysis today is the use of commercial or public domain software packages for solving particular problems. In order to gain exposure to this side of numerical analysis, students need to practice using such packages. MATLAB offers the perfect opportunity for such practice; it is one of the most dominant commercial computing environments. If you have not used MATLAB previously, help resources are available on the course website and from the instructor. MATLAB is available in the Undergraduate and Graduate student mathematics computing labs (as well as various other locations on campus). For more information on these labs, including hours of operation and location, go to http://www.math.utah.edu/ugrad/lab/. Problems involving symbolic computations can be done using Maple or Mathematica. The former is available in the Undergraduate and Graduate student mathematics computing labs. Final Project: Instead of a final exam, you will prepare and present a final project to the class. The purpose of the final project is to investigate a problem in numerical analysis that interests you. For example, if you are a mathematician, you may be interested in comparing (in detail) the accuracy, stability and convergence of some different numerical methods we discuss, or perhaps developing your own technique. If you are a computer scientist, you may choose to implement (optimally of course) a software package for some complicated algorithm we discuss. If you are an engineer (or applied mathematician), you may be interested in applying some numerical method we discuss to some physical problem (for example, solving some ordinary or partial differential equations). The focus of your investigation should be primarily on numerical methods we discuss this semester, although exceptions can be made if a persuasive argument is made. You must work in groups of two or three on the project. 2The final project will consist of a proposal for the investigation you wish to undertake (due April 5), a final typewritten report (5 to 30 pages), and a final presentation (15 to 20 minutes). More information about the project will be given as the semester proceeds. This does not mean that you should procrastinate until then; start thinking about a possible project now! Important Dates: • Jan. 19 – Martin Luther King Jr. day, i.e. No Class • Jan. 21 – Last day to drop term and first session classes (and get your money back) • Jan. 26