MATH 6610-001 — Analysis of Numerical Methods I


Fall 2025


Instructor: Akil Narayan
Email: akil(-at-)sci.utah.edu
Office phone: +1 801-581-8984
Office location: WEB 4666, LCB 116
Office hours: Tuesdays 4-5pm, Fridays 3-4pm, WEB 4666


Class meeting time: Monday, Wednesday, Friday 11:50am - 12:40pm
Class meeting location: JWB 208


Mathematical analysis of numerical methods in linear algebra, interpolation, integration, differentiation, approximation (including least squares, Fourier analysis, and wavelets), initial- and boundary-value problems of ordinary and partial differential equations.

The course syllabus is here: PDF



There is a weekly problem session run by the TA for this course. This is held Mondays at 9:30-10:30 in LCB 218

The content of this course is split across this website and Canvas. The material available on this website is:
  • Course syllabus
  • Homework assignments
  • Lecture slides and notes
  • Miscellaneous handouts and resources
The material available on Canvas is:
  • Course syllabus
  • Homework assignments and submission portal
  • Grades

Graded assignments


Individual grades for each assignment will be posted to Canvas. (uNID login required.) Note that the letter grades appearing on Canvas are not representative of predicted final letter grades for the course. Final letter grades will be computed according to the rubric and policies on the syllabus.



Homework assignments


Homework will be collected through Gradescope on Canvas, with a due date of Wednesday. See Canvas for details of each assignment. Late work will not be accepted without advance approval from the instructor.

Problem set description Due date Homework
1 : Linear Algebra August 27, 2025 PDF
2 : Unitary and projection matrices September 3, 2025 PDF
3 : Eigenvalues September 10, 2025 PDF
4 : Singular Values, I September 17, 2025 PDF
5 : Singular Values, II September 24, 2025 PDF



Miscellaneous handouts


The following are slides from class.

Description Posting date Download Marked document
D00: Introduction and hello August 01, 2025 PDF
D01: Linear algebra preliminaries August 01, 2025 PDF PDF
D02: Unitary, projection matrices August 22, 2025 PDF PDF
D03: Eigenvalues and eigenvectors August 25, 2025 PDF PDF
D04: The SVD September 7, 2025 PDF PDF
D05: Floating-point arithmetic, conditioning, and stability September 14, 2025 PDF PDF
D06: The LU and Cholesky decompositions September 19, 2025 PDF