ES 105
NumericalMethods for Partial Differential Equations


Keith D. Paulsen
136 Cummings (Thayer School), 646-2695
Secretary: Roxanne Campagna, 137 Cummings, 646-3860

Meeting Rooms:

Regular Class: MWF 11:15-12:20, 202 Cummings
X-hour: Tues Noon-12:50, 202 Cummings
The Linux Lab: 218 Cummings

TA: Matthew McGarry

Weekly Schedule

Week 1: on Friday we will meet in the Linux Lab.

After Week 1, we will begin a regular weekly schedule
Mon, Tues, Wed in class.
Wed: Office hrs 12:30-2pm
Fri: HW due and individual meetings: 11am-2pm, 136 Cummings; no formal class

Linux System Administrator (Matt Dailey): 227 MacLean
TSCC Support: 126 MacLean
TSCC Public Help: Mon, Thurs 3:00-4:00, MacLean Atrium

Thayer School Map


Numerical Partial Differential Equations for Environmental Scientists and Engineers -- A First Practical Course, D.R. Lynch -- Springer, 2004.

Weekly readings from the text will be assigned.

Course Web Page

Most Useful Supplementary Texts

The ENGS91 prerequisite:
Burden R.L. and J.D. Faires, Numerical Analysis Brooks Cole; 9th edition (August 9, 2010).
A large body of work is available in Feldberg Library; see the online reference list. There are a few especially relevant and simple volumes re PDE's:
Smith, Numerical Solution of Partial Differential Equations, Oxford Univ. Press, 1st ed. (1965) [3rd ed, 1985 etc. not as good as 1st ed. for learners]. [Roughly equivalent to Morton and Mayers.]

Morton, K.W. and D.F. Mayers. Numerical Solution of Partial Differential Equations. Cambridge University Press, 1994.[Roughly equivalent to Smith.]

Segerlind, Applied Finite Element Analysis, Wiley, latest edition

Lapidus and Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley, latest edition.

Some standard Linear Algebra works are valuable:
Trefethen, L.N. and D. Bau, III: Numerical Linear Algebra.  SIAM, 1997.

Demmel, J. W. , Applied Numerical Linear Algebra.  SIAM, 1997.

The LAPACK Subroutine Library and Users Guide:
E. Anderson et al, LUG -- LAPACK Users' Guide. SIAM, 1999; online LUG; LAPACK source code

The Numerical Recipes is all-around useful and practical:

Press, W.H., B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes: The Art of Scientific Computing. Cambridge Univ. Press, 1986 or latest.


There will be weekly graded problem sets, due in class on Friday afternoons beginning January 13. Each student will be required to solve the problem, post solutions on the www, and present it to Prof. Paulsen individually. These sessions with Prof.Paulsen will be 20 minutes, beginning with 10 minutes for presentation of your work; and the balance for discussion.

The first week (Homework 0) is a warmup/review exercise; it is due on Monday Jan 9. Do not ignore it! The rest of the HW's will use the simple things covered.

Late homework will not be accepted. Each student may have two exceptions to this rule; they must be claimed at least 2 days in advance.

Nearly all homework will require computer programming, graphics, and verbal report generation backed up with www-posted results. Schedule your time accordingly during heavy load periods.


There will be a mid-term and a final exam. Homework will count 60%; Midterm 20%; Final 20%.

Computer Languages: Fortran will be the primary compuational language. It supports the library LAPACK and related software, which we will use. Matlab and TekPlot will be used as the primary graphical packages. Homeworks will be submitted electronically as .html documents as described above. All of these languages are supported within the Dartmouth/Thayer Linux system. Each student has a special directory which is web-served; use it responsibly!

Honor Principle: applies to all homework and exams. All work is to be attributed to its author(s). Being an author indicates that the student has mastered the content of the homework and that he/she has cited all individuals who have contributed. If you recieve assistance other than routine help from faculty, students, or staff, that should be cited. Copying computer code or files without citation is plagiarism. The work you turn in must be the product of its authors or cited sources.

Special obligations are connected to the web-accessible directories. We will use these for strictly professional, course-related communications among the class. Abuses of this privilege will be considered Honor Code violations.


Dartmouth will ensure that every student has meaningful and physical access to all activities of the College. Students requiring disability-related accommodations must register with the Student Accessibility Services office. Once SAS has authorized accommodations, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their professor. As a first step, if you have questions about whether you qualify to receive accommodations, contact the SAS office. All inquiries and discussions about accommodations will remain confidential.

Laptop Policy in Class Meetings

No laptops, phones, ipods, or other electronic devices in class, unless otherwise stated.