Math 116

General Information

Instructor Information
Anne Gelb	Office: 207 Kemeny	Office Hours: M 10-11 (in person) Th 9-10 (zoom); By appointment.	Anne.E.Gelb@Dartmouth.edu

Recommended References: Some books are better than others for various topics and I will try to let you know which book I am referencing.
A First Course in Numerical Methods by Ascher and Grief. This is a SIAM e-book available through the Dartmouth library: This is a nice accessible book. It also has some simple to follow MATLAB codes. It is not rigorous. Numerical Mathematics, 2nd edition, by Quarteroni, Sacco, and Saleri. This is a classical rigorous textbook . Elementary Numerical Analysis, An Algorithmic Approach, by Conte and de Boor. This is a SIAM e-book available through the Dartmouth library. The topics are classical, and I have not looked through this version. I expect it is more rigorous than AG but more accessible than QSS. Numerical Analysis, 9th edition, by Burden and Faires. This book is not as difficult as QSS, and more rigorous than AG. The explanations are clear. It does not provide any MATLAB code. The pseudocode is useful for understanding. Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems by Randall Leveque (ISBN: 978-0-898716-29-0). This is a SIAM book and is available to Dartmouth students at http://epubs.siam.org.dartmouth.idm.oclc.org/doi/book/10.1137/1.9780898717839. This is a very nice book that will also be useful for future reference. Finite Volume Methods for Hyperbolic Problems by Randall Leveque (ISBN: 978-0-521-00924-9). See above. Finite Difference Schemes and Partial Differential Equations Second Edition by John Strikwerda (ISBN: 0-89871-567-9) This is a SIAM book and is available to Dartmouth students at http://epubs.siam.org.dartmouth.idm.oclc.org/doi/book/10.1137/1.9780898717938. This book is nicely organized. It is very classical and spends more time explaining the properties underlying PDEs.

Recommended References: Some books are better than others for various topics and I will try to let you know which book I am referencing.

A First Course in Numerical Methods by Ascher and Grief. This is a SIAM e-book available through the Dartmouth library: This is a nice accessible book. It also has some simple to follow MATLAB codes. It is not rigorous.
Numerical Mathematics, 2nd edition, by Quarteroni, Sacco, and Saleri. This is a classical rigorous textbook .
Elementary Numerical Analysis, An Algorithmic Approach, by Conte and de Boor. This is a SIAM e-book available through the Dartmouth library. The topics are classical, and I have not looked through this version. I expect it is more rigorous than AG but more accessible than QSS.
Numerical Analysis, 9th edition, by Burden and Faires. This book is not as difficult as QSS, and more rigorous than AG. The explanations are clear. It does not provide any MATLAB code. The pseudocode is useful for understanding.
Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems by Randall Leveque (ISBN: 978-0-898716-29-0). This is a SIAM book and is available to Dartmouth students at http://epubs.siam.org.dartmouth.idm.oclc.org/doi/book/10.1137/1.9780898717839. This is a very nice book that will also be useful for future reference.
Finite Volume Methods for Hyperbolic Problems by Randall Leveque (ISBN: 978-0-521-00924-9). See above.
Finite Difference Schemes and Partial Differential Equations Second Edition by John Strikwerda (ISBN: 0-89871-567-9) This is a SIAM book and is available to Dartmouth students at http://epubs.siam.org.dartmouth.idm.oclc.org/doi/book/10.1137/1.9780898717938. This book is nicely organized. It is very classical and spends more time explaining the properties underlying PDEs.

Exams
Exam 1 February 4 2022 (take home);
Exam 2 TBD.

Homework Policy

Written homework will be posted on the canvas website approximately one week before it is to be turned in. Homework must be submitted by hardcopy.
Late homework will be penalized 10% for each day it is late.
You may collaborate on your homework and help each other with difficult problems. However, everyone is responsible for turning in his/her own homework and writing his/her own numerical code. Consult the honor principle (below) as it applies to this course.
Your solutions must be clearly written and you must form coherent arguments to discuss your results. Please make sure your writing is legible.
Posted homework solutions will be compiled from student solutions. It will be helpful, therefore, if you use LaTex to write up your homework solutions.

Student Project

If you took Math 116 in Fall 2019, you will not have to do homework or take exams. There are two other options: (i) You can read approved texts on numerical PDEs" or (ii) you can do a long term project. I am happy to suggest topics and articles that are interesting and assessible. Students can either provide a written or oral report (during an X hour) by the end of term. A good report will include an overview of the problem, a discussion of the numerical method, and numerical simulations that either reproduce the experiments or demonstrate the advantages of the proposed algorithm.

Grades
The course grade will be based upon the scores on the exams, homework, and the project as follows:
Two take home exams	25 points (each)
Five homework assignments	10 points (each). Note that the complexity of homework will vary. Nevertheless, they will all be worth the same amount.
Total	100 points

The Honor Principle

On Homework:	Collaboration is permitted and encouraged, but no copying , and to be clear, this means no copying even from a board or scrap of paper on which a solution was hashed out collaboratively. What a student turns in as a homework solution is to be his or her own understanding of how to do the problems. Students must state what sources they have consulted, with whom they have collaborated, and from whom they have received help. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Academic Honor Code. Moreover, if in working with someone they have provided you with an important idea or approach, they should be explicitly given credit in your writeup. Hints given in office hours need not be cited. Note: It is not sufficient to annotate your paper with a phrase like ``I worked with Joe on all the problems.'' Individual ideas are to be credited at each instance; they represent intellectual property.
On Exams:	Students may not receive assistance of any kind from any source (living, published, electronic, etc), except for what is approved prior to the exam, and may not give assistance to anyone. Matters of clarification are to be left to the professor. If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me, and I will be glad to help clarify things. It is always easier to ask beforehand.

On Homework:

Collaboration is permitted and encouraged, but no copying , and to be clear, this means no copying even from a board or scrap of paper on which a solution was hashed out collaboratively. What a student turns in as a homework solution is to be his or her own understanding of how to do the problems. Students must state what sources they have consulted, with whom they have collaborated, and from whom they have received help. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Academic Honor Code.

Moreover, if in working with someone they have provided you with an important idea or approach, they should be explicitly given credit in your writeup. Hints given in office hours need not be cited. Note: It is not sufficient to annotate your paper with a phrase like ``I worked with Joe on all the problems.'' Individual ideas are to be credited at each instance; they represent intellectual property.

On Exams:

Students may not receive assistance of any kind from any source (living, published, electronic, etc), except for what is approved prior to the exam, and may not give assistance to anyone. Matters of clarification are to be left to the professor.

If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me, and I will be glad to help clarify things. It is always easier to ask beforehand.

Disabilities, Religious Observances, etc.
Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see their instructor privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (205 Collis Student Center, 646-9900, Student.Accessibility.Services@Dartmouth.edu). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their instructor. As a first step, if you have questions about whether you qualify to receive academic adjustments and services, you should contact the SAS office. All inquiries and discussions will remain confidential.

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.

Anne Gelb
Last updated January 30, 2022

Math 116

Numerical methods for approximation, ordinary and partial differential equations

General Information