MATH 374M: Mathematical Modeling in Science and Engineering Spring 2025 (Section 54490)
Description
This course is for students interested in mathematical modeling and analysis. The goals are to develop tools for studying differential equation models that arise in applications, and to illustrate how the analysis of models can be used to gain insight and make predictions about physical systems. Emphasis will be placed on examples, and a broad range of applications from the engineering and physical sciences will be considered. Topics include dimensional analysis, scaling, dynamical systems, stability and bifurcation, perturbation methods, and calculus of variations. This course carries the quantitative reasoning (QR) flag.
Prerequisites
The prerequisites are a grade of at least C- in Mathematics 427J or 427K (differential equations), and in Mathematics 340L or 341 (linear algebra) . It is also expected that students will have some familiarity with software tools for graphing (such as Matlab, Mathematica, or Desmos), and a capacity for independent study.
Meetings
Class meetings: Class meetings will be held simultaneously in-person and on-line at the regularly scheduled times. The in-person meetings will be in the scheduled room, and the on-line meetings will be conducted live via Zoom from this room. Links to join the on-line meetings will be available in Canvas. Any student may attend on-line as desired.
On-line disclaimer: On-line meetings require properly functioning equipment that satisfy University security requirements, and cannot be guaranteed. Some on-line meetings may be partially or entirely cut-off . In cases of equipment issues, the in- person meetings will have priority. Students attending on-line do so at their own risk.
Notes and videos: Notes and recorded videos from class meetings will be posted on Canvas for later viewing as desired.
Policies
Homeworks: Homework sets will be assigned and collected weekly via Canvas. To submit an assignment, students will need to save a scan/image of their work into a single file and upload it into the Canvas system. Please ensure that your name and EID are visible within the work. Students may help each other with the homeworks; however, each student must write up and submit their own work.
Exams: There will be two take-home midterm exams and a take-home final exam. The exams will be distributed and collected via Canvas in the same way as the homeworks. Students are not allowed to discuss, share information, receive help, or provide help in any way with the exams. The tentative dates are:
Exam 1 (Feb 19-21), Exam 2 (Mar 26-28), Final (Apr 30 - May 2) .
Course grade: Your course grade will be a weighted sum of your homework average and exam grades. The weights will be:
Homework average (30%), Exam 1 (20%), Exam 2 (20%), Final (30%) .
Grade notes: One homework grade will be dropped. Homeworks and exams will usually be graded within about a week.
Written solution keys to homeworks and exams will unfortunately not be available.
Grade scale: Homeworks and exams will be assigned grades based on a 100-point scale. The weighted sum of your
homework average and exam grades will determine your course letter grade as follows:
A (100-92), A- (91-90), B+ (89-86), B (85-82), B- (81-80), C+ (79-76), C (75-72), C- (71-70),
D+ (69-66), D (65-62), D- (61-60), F (59-0) .
Video recordings: Class video recordings are for educational purposes and are reserved for students in this class only. The recordings are protected under FERPA and should not be shared outside the class in any form.
Documents and files: Class documents and files provided by the instructor, such as notes, videos, assignments, and exams, are reserved for students in this class only. The documents and files should not be shared outside the class unless you have my explicit, written permission.
Honor code: As a student at UT-Austin you are expected to abide by the core values of the University and uphold academic integrity. Any suspected violations of the honor code will be investigated and reported to the University for further action.
Students with disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the office of Disability and Access (D&A) .
Drop dates: The last day to drop the course without permission is January 29, 2025. The last day to drop the course for academic reasons is April 16, 2025. After this date, students may go to the Dean's Office to request a drop for urgent non- academic reasons.