Numerical Analysis Fall 2014, Math 165 (http://www.math.hmc.edu/math165) MW 2:45-4:00 pm, Shanahan Center for Teaching and Learning 2454 Prof. Darryl Yong (dyong@hmc.edu), SHAN 2410, x72844 Office Hours: MW 1-2:30pm, Th 1-3pm, and by appointment Graders: Ki Wan Gkoo, Yukun Lin

Course description

Math 165 is designed to introduce students to the analysis and implementation of basic numerical techniques. It is intended for anyone who will ever have to solve a mathematical problem with a computer. In this course, you will learn about fundamental issues that arise when obtaining numerical solutions to problems and whether you should trust your answers.

By the end of this course, I hope that you will be able to

• analyze the accuracy, stability, and efficiency of numerical algorithms, and
• use that information to help you select an appropriate numerical technique for a given problem.

Topics covered: root-finding, interpolation and polynomial approximation, numerical differentiation and integration, initial value problems and ordinary differential equations, direct and iterative methods for solving linear systems of equations, partial differential equations.

Notes, handouts and suggested texts

• Burden and Faires, Numerical Analysis, Thomson/Brooks Cole (8th ed ISBN 0534392008, 9th ed ISBN 0538733519)
• Gerald and Wheatley, Applied Numerical Analysis, 7th ed, Addison Wesley (ISBN 0321133048)
• Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, free online text at http://people.maths.ox.ac.uk/trefethen/pdetext.html.
  For convenience, here's the entire book as one PDF file.

Computing resources

• http://www.math.hmc.edu/computing -- everything you need to know about computing in the math dept
• http://www.math.hmc.edu/computing/support/tex/ -- lots of help on LaTeX
• LaTeX for PC try MiKTeX, LaTeX for Mac try MacTeX
• Wikibook on LaTeX

Assignments and grading

Most of your learning will occur while completing your homework assignments, so take them seriously, and complete them thoroughly. Your homework should show clearly your solution processes. All code should be properly commented, graphs should be annotated. I encourage you to describe your solution process in words. Poor presentation may result in loss of credit.

All homeworks should be written up using LaTeX and should be submitted electronically through our Sakai site. Please use sensible file names for your files, and make sure your file names start with your last name.

No late homeworks will be accepted except for family or medical emergencies. Your lowest homework grade will be dropped.

You are encouraged to work cooperatively on your homework assignments with your classmates. However, every student MUST write up his/her own homework separately. In addition, you must cite any sources of help that you use. If you work with one of your classmates on a problem, be sure to acknowledge that person in your homework write-up; if you use any published source besides our textbook, acknowledge that too. HMC's honor code is in effect for all students in this course.