University at Buffalo · Department of Mathematics
MTH 537: Numerical Analysis I
Fall 2026 · Homework and Tentative Weekly Schedule
Meetings: MWF, 11:00–11:50 a.m., Math 205
Instructor: Sergey A. Dyachenko
Office hours: W, 3:00–4:00 p.m., Math 312, and by appointment
Email: sergeydy@buffalo.edu
Syllabus: Course information and policies
Recommended text: Timothy Sauer, Numerical Analysis, 2nd ed., Pearson.
Purchase of the textbook is not required.
Grading and Examination Schedule
Homework: 20% · Midterm examination: 40% · Cumulative final examination: 40%.
Midterm: Date to be announced.
Final / qualifying examination: Wednesday, December 9, 2026, 11:45 a.m.–2:45 p.m., Math 205.
Tentative Weekly Schedule
Homework links and due dates will be added as the semester progresses. Topics, their order, and the amount of time devoted to each topic may change.
| Week | Material | Assignment | Due date |
|---|---|---|---|
| 1 | Introduction to MATLAB or GNU Octave; floating-point arithmetic | Notes | |
| 2 | Numerical errors, conditioning, stability, and computational cost | To be announced | TBA |
| 3–4 | Nonlinear equations; bisection, fixed-point iteration, Newton's method, and related methods | To be announced | TBA |
| 5–6 | Linear systems; Gaussian elimination, pivoting, and matrix factorizations | To be announced | TBA |
| 7 | Least-squares problems and QR factorization | To be announced | TBA |
| 8 | Midterm examination; introduction to eigenvalue problems | Midterm date TBA | TBA |
| 9 | Eigenvalue problems and basic iterative methods | To be announced | TBA |
| 10–11 | Polynomial interpolation, Chebyshev nodes, piecewise interpolation, and splines | To be announced | TBA |
| 12 | Numerical differentiation and integration | To be announced | TBA |
| 13–14 | Ordinary differential equations; Euler and Runge–Kutta methods | To be announced | TBA |
| 15 | Introduction to finite-difference methods; cumulative review | Review materials TBA | TBA |
Homework Expectations
Submit clear mathematical reasoning together with any requested code, numerical output, plots, and interpretation. Collaboration in discussing problems is allowed, but all submitted work must be prepared independently. One lowest homework score will be dropped.
Guidelines for the Use of Artificial Intelligence
AI tools may be used to clarify course material, explore examples, and assist with programming. However, students must develop their own solutions to assigned problems and must be able to explain all submitted reasoning and code. AI may not be used to generate mathematical solutions that are submitted as the student's own work.