MATH 174 MATH 274 - Numericl Methods/Physcl Modlng - Briones [FA24]
Math 174/274: Numerical Methods for Physical Modeling
General information
- Title: Numerical Methods for Physical Modeling
- Credit Hours: 4 (Students may not receive credit for both MATH 174 and PHYS 105, AMES 153 or 154. Students may not receive credit for MATH 174 if MATH 170A, B, or C has already been taken.)
- Prerequisite: Math 20D or MATH 21D, and either Math 18 or MATH 20F or MATH 31AH, or consent of instructor.
- Catalog Description: Floating point arithmetic, direct and iterative solution of linear equations, iterative solution of nonlinear equations, optimization, approximation theory, interpolation, quadrature, numerical methods for initial and boundary value problems in ordinary differential equations. Graduate students will do an extra assignment/exam.
Instructional Staff
Name |
Role | Office/Tutor/One-on-one hours | |
Jor-el Briones | Instructor | jbriones@ucsd.edu |
(Actual Office in AP&M 1131) AP&M 1218 (Wednesdays, 2 - 4PM) |
Qihao Ye | Instructional Assistant | q8ye@ucsd.edu | AP&M 5720 (Thursday 1 - 3 PM) |
Piazza: Accessible Through Canvas
Discord (Not formal/technically official): https://discord.gg/yYA5h6tSqV
Lecture Schedule (subject to change throughout the quarter, without notice)
Lecture | Date | Topics | Textbook Sections |
1 | 9/27/24 | Course Overview, Intro, Floating Point Numbers, Numerical Error | |
2 | 9/30/24 | Solving Equations: Bisection Method | |
3 | 10/2/24 | Solving Equations: Fixed Point Method | |
4 | 10/4/24 | Solving Equations: Newton's Method | |
5 | 10/7/24 | Solving Systems of Linear Equations: Gaussian Elimination | |
6 | 10/9/24 | Solving Systems of Linear Equations: LU Factorization and PA+LU Factorization | |
7 | 10/11/24 | Sources of Error for Systems of Linear Equations | |
8 | 10/14/24 | Iterative Methods: Jacobi | |
9 | 10/16/24 | Iterative Methods: Gauss-Sidel | |
10 | 10/18/24 | Iterative Methods for SPD Matrices: Conjugate Gradient Method | |
11 | 10/21/24 | Midterm 1 | Up to (...) |
12 | 10/23/24 | Solving Systems of Nonlinear Equations | |
13 | 10/25/24 | Interpolation: Data and Interpolating Functions | |
14 | 10/28/24 | Interpolation Error | |
15 | 10/30/24 | Interpolation: Chebyshev | |
16 | 11/1/24 | Interpolation: Cubic Splines (piecewise functions) | |
17 | 11/4/24 | Least Squares | |
18 | 11/6/24 | Numerical Differentiation | |
19 | 11/8/24 | Numerical Integration: Newton-Cotes Method | |
20 | 11/11/24 | Veterans Day (No Lecture) | n/a |
21 | 11/13/24 | Numerical Integration: Romberg Integration | |
22 | 11/15/24 | Numerical Integration: Gaussian Quadrature | |
23 | 11/18/24 | Initial Value Problems Intro | |
24 | 11/20/24 | Initial Value Problems: Analysis of IVP Solvers | |
25 | 11/22/24 | Systems of Differential Equations | |
26 | 11/25/24 | Midterm 2 | Up to (...) |
27 | 11/27/24 | Runge-Kutta Methods and Applications | |
28 | 11/29/24 | Thanksgiving Holiday (No Lecture) | n/a |
29 | 12/2/24 | Implicit Methods and Stiff Equations | |
30 | 12/4/24 | Shooting method | |
31 | 12/6/24 | Finite Difference Method | |
n/a | 12/9/24 | FINAL EXAM (11:30-2:30PM) | All |
Book
The textbook for the course is
T. Sauer, Numerical Analysis, Third Edition.
In an effort to ease financial burden, homework will be drawn from the book, BUT the problems themselves will be compiled into a separate document (so that you need not purchase the textbook to know the homework problems).
We will try to include all necessary information within the lecture and the homework problems. If you do need examples and practice problems, I do recommend you buy some edition of the textbook (it need not be Third Edition, though I will be referring to sections that go off the Third Edition numbering)
Assignments
You can access homework assignments through the Modules Tab on Canvas. Assignments will be submitted through GRADESCOPE. A selection of problems will be graded for correctness, while the rest of the problems will be graded by fair effort/completion. Some homework assignments will require MATLAB (or a coding language of your choice), and we expect you to submit the code for those portions of the assignment as well (you can copy the code onto your doc; please make sure it is formatted to be easily read).
Exam Information
We will have two IN PERSON midterms and one IN PERSON final.
- Midterm 1: Monday, October 21, 2024 (Beginning of Week 4) - During Lecture - Covers (...) (In lecture room)
- Midterm 2: Monday, November 25, 2024 (Beginning of Week 9) - During Lecture - Covers (...) (In lecture room)
- Final exam. Monday, December 9, 2024 – 11:30AM-2:30PM – Covers all the topics that are covered in the course. (Location TBA)
Note: It is standard Math Department practice to utilize different versions of exams, both within each lecture's exam, and between lectures whose exams are at different times
A few general policies for the exams:
-
NO CALCULATORS OF ANY KIND WILL BE ALLOWED ON EXAMS
- You may NOT use the internet, notes, or your textbook during exams, and assistance from other people is not allowed during the exams.
-
To be clear, YOU WILL NOT BE ALLOWED A CHEAT SHEET ON ANY EXAMS
- A sheet of formulas may be provided on the exam (what may be included on that sheet is pending)
Grade
FOR STUDENTS TAKING MATH 174:
Weighted Score. Your weighted score is the best of the following grading schemes:
- HW assignments (9%) + Midterm 1 (20%) + Midterm 2 (20%) + Final Exam (50%) + Professionalism (1%)
- HW assignments (9%) + Highest Midterm (25%) + Lowest Midterm (5%) + Final Exam (60%) + Professionalism (1%)
FOR STUDENTS TAKING MATH 274:
Weighted Score. Your weighted score is the best of the following grading schemes:
- HW assignments (9%) + Midterm 1 (20%) + Midterm 2 (20%) + Final Exam (40%) + Final Project (10%) + Professionalism (1%)
- HW assignments (9%) + Highest Midterm (25%) + Lowest Midterm (5%) + Final Exam (50%) + Final Project (10%) + Professionalism (1%)
Possible Bonus. Because your feedback is very important for us, there may be some bonus, if enough students fill out the SETS questionnaire at the end of the quarter. Details to be determined at a later date.
Homework. The HW assignments are due on Sundays at 11:59pm, including on week 1 (no homework is due on week 0). Up until week 9, homework that is assigned will only go up to topics that are fully covered by the Wednesday of that week. Any problems based on sections that have not yet been covered would be moved to the following week. You are expected to follow along for which problems would be moved, as announcements for this may be limited. The lowest homework assignment will be dropped.
Late submission: Late submissions are NOT accepted automatically. You may request homework extensions, within reason for any assignment, prior to grades being published. You are NOT guaranteed to be granted a homework extension for any assignment.
Professionalism Score. This will usually be a free 1% of your grade, as my course tends to be pretty chill. You will automatically receive this professionalism grade in full, UNLESS you are egregiously unprofessional in this course. Some examples of this include:
- Bullying and/or harassment of other students or instructional staff
- Having a loud, unrelated meeting during office hours, in the office hours room
- Declining to leave the room when asked to do so by a member of the instructional staff
- Violating Academic Integrity
- Leaving an exam room and re-entering without having turned in the exam or without permission from a member of the instructional staff
Displaying such poor professionalism will cost this 1%. More egregious offenses, like violating academic integrity, will be met with other consequences as well.
Letter grade. Your letter grade is determined based on your weighted score using the best of the following methods:
A |
A- |
B+ |
B |
B- |
C+ |
C |
C- |
F |
93 |
90 |
87 |
83 |
80 |
77 |
73 |
70 |
<70 |
A few general grading notes:
- I do NOT give Ds due to administrative issues involved in advancing in the math department. Since math courses will often require the prerequisites to be passed with a C- or higher, and a D is considered a passing grade, it becomes more difficult to take further courses in the department if you do end up with a D.
- Unlike in other courses, achieving a 97% or higher does NOT guarantee an A+ in the course. The thresholds or requirements for an A+ will likely be different and more strict, and reflective of consistent, exemplary work in the course.
- The following will disqualify you from receiving an A+ in the course, as they all disrupt the process of getting grades out:
- Asking what the cutoff for an A+ is
- Asking for an A+ directly
- Pointing out that your grade, or any part of it, is "high enough" for an A+
- Asking why or pointing out that you did not receive an A+
-
You must pass the final exam to pass the course, even if your weighted average is above a passing threshold.
For this course, the default passing grade for the final exam is 70%. This threshold can be adjusted and is often adjusted, but that is left to the discretion of the instructor. - Exams themselves are generally not curved. This may change in extreme cases–in particular, a curve is more likely (but not guaranteed) if the mean falls below 70%. These extreme cases are separate for the extreme cases of the passing threshold for the final exam.
- No one will know if the course itself is curved at all until after all grades are in. Even if it is determined there would be a curve, it is not guaranteed that such information or the nature of any curve would be given to students. I usually do not tell students how grades are decided.
Regrade. You will be able to see the score of your midterm exam and final exam in Gradescope. After that, there will be a limited window of time during which the regrade request feature will be active. Please notice that the regrade request window will be at least 24 hours for both exams, and you will be given at least 24 hour notice before the regrade window closes. The only exceptions to this rule are regrades for final exams and assignments that may end up graded close to the end of the quarter, for which regrade requests will close at 5pm on the day of grade submission (Tuesday, June 20, 2024).
Make sure that you make the regrade request during the allowed time if you want to make such a request. Please understand that while we will correct errors in the grading, we will not modify the grading rubric after graded papers are returned to students.
General advice
Here are a few general comments that hopefully help you have a more successful education here in UCSD.
- I personally, throughout lectures and on announcements, tell you a lot about what I expect on exams. Please pay attention to those statements and announcements.
- Pay attention to Canvas Announcements in General, as they will frequently if not always contain important information.
- Take advantage of office hours of your instructors and your TAs. You are in one of the best colleges, so why not take advantage of all the good things this institution can offer you!
- The Math Science Tutorial Program (MSTP) has workshops, which you can attend for academic support. You can sign up for the workshops here.
- Any institution can only provide help and the right environment for growth, but it is YOU who have to do the work! Before every lecture go over the assigned reading and after every lecture do the assigned practice. More importantly make sure to do weekly homework assignments. Questions in the exams will be similar, if not identical, to the ones in your HW assignments.
- One of the important points of being in a good institution is having excellent colleagues who help you grow! So find friends and study together: share your frustrations and work on your HW assignments. But at the end write your own solution: your own wording.
- Academic Integrity. Be fair to your friends! According to the UCSD Policy on Integrity of Scholarship, "no student shall engage in an activity that undermines academic integrity or facilitates academic integrity violations by others". According to the policy, you are not allowed to:
- Complete, in part or in total, any assignment for another person.
- Have any of your course work be completed, in part or in total, by someone else.
- Plagiarize or copy even part of the work of another person or source and submit it as your own work.
- Employ aids excluded by the instructor in completing any assignment, eg AI tools like chatGPT.
- Alter graded class assignments, then resubmit them for re-grading;
- Submit substantially the same material in more than one course without prior authorization; and misrepresent, to your instructor, any aspect of your academic work.
- Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university.
- Electronic computing devices. Graphing calculators and computer programs (or online computing websites such as Wolfram-Alpha Links to an external site.) can be very helpful when working through your homework. However, a calculator/computer should be used as an aid in learning concepts, not just as a means of computation. You can use these devices when working on math problems, but always keep in mind that any answers you give must be accompanied by accurate justification.
- Name and Gender Pronouns. UC San Diego is committed to supporting its students' name and gender preferences. Class rosters provided to your instructor and TAs have students' legal names, but we will strive to honor your request to be addressed using a preferred name or gender pronoun. Please let your instructor and TA know your preferences so that we can make changes to our records. (Certain university records may be beyond our ability to change, however.)
- Equity, Inclusion, and Respect. We are committed to the UC San Diego Principles of Community . "To foster the best possible working and learning environment, UC San Diego strives to maintain a climate of fairness, cooperation, and professionalism. These principles of community are vital to the success of the University and the well being of its constituents." The principles of community include (but are not limited to): "We affirm each individual's right to dignity and strive to maintain a climate of justice marked by mutual respect for each other." "We reject acts of discrimination based on race, ethnicity, sex, gender identity, age, disability, sexual orientation, religion, and political beliefs, and, we will confront and appropriately respond to such acts." "We promote open expression of our individuality and our diversity within the bounds of courtesy, sensitivity, confidentiality, and respect." "We are committed to promoting and supporting a community where all people can work and learn together in an atmosphere free of abusive or demeaning treatment." Visit the Office for Equity, Diversity, and Inclusion for more information.
- Accomodations. The Office for Students with Disabilities is another resource on campus. Students who are requesting accommodations due to a disability can get a current Authorization for Accomodation (AFA) letter from this office. Students are required to discuss accommodation arrangements with instructors and OSD liaisons in the department in advance of any exams or assignments.
Course Summary:
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