Numerical Methods for Physical Modeling
Math 174/274 --- Winter 2021

Lecture site: Remote. Videos are made available on Canvas.
Discussion sessions B01 36145: Thursday 9:00am-9:50am, remote with Bingni Guo
B02 36148: Thursday 10:00am-10:50am, remote with Bingni Guo
Meeting ID:
Final Exam
time and place
Remote March 17th, 2021, 8:00am - 10:59pm.
Instructor Martin Licht
Email: mlicht AT ucsd DOT edu
Office Hours: Monday, Wednesday, Friday, 9am-10am.
Meeting ID: 990 0333 4314
Teaching Assistant Bingni Guo
Email: b8guo AT ucsd DOT edu
Office Hours: Tu 10am-11:59am
Meeting ID:
Section(s) 36145, 36148
Credit Hours: 4 units
Course content 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.
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.) Graduate students will complete an additional assignment/exam.
Formal prerequesite MATH 20D or 21D, and either MATH 20F or MATH 31AH, or consent of instructor.
Homework information Homework is due Sunday 11:59pm and submitted to Gradescope.
Homework 0 is ungraded.
Midterms and Exams Midterm 1: January 29
Midterm 2: February 26
Exams: March 17
The first midterm, the second midterm, and the final exam can be started and completed within a time window of at least 24 hours. You will have 50 minutes for each of the midterms, and you have 3h for the final exam.
Academic Integrity Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. See for UCSD Policy on Integrity of Scholarship.
Resources The textbook for this lecture is:
  • Germund Dahlquist and Åke Björk, Numerical Methods.
    ISBN 10: 0486428079, ISBN 13: 9780486428079
The following textbooks are recommended to supplement the lectures: Some information about floating point arithmetics:
  • D. Goldberg, What every computer scientist should know about Floating-Point arithmetics. [Link]
  • Information about Floating-Point numbers. [Link]
  • E. Wallace Floating-Point Toy. [Link]
Your experience in numerical linear algebra will greatly benefit from a solid background in linear algebra. Your instructor recommends the following textbook as a helpful reference: Assorted links to additional material:
  • Lloyd N. Trefethen, The Definition of Numerical Analysis. [Link]
  • J. R. Shewchuk, The Conjugate Gradient Method without the Agonizing Pain. [Link]
Helpful links Important academic dates for this academic year


From now on, important announcements will be made on this section of the course website / syllabus.

Grading Information

The final grade will be composed by the best of the following two options: (a) 20% homework, 20% first midterm, 20% second midterm, and 40% final exam. (b) 20% homework, 20% best midterm, and 60% final exam. You must pass the final exam to pass the class.

Your course grade will be determined by your cumulative average at the end of the quarter, based on the following scale:

A+ A A- B+ B B- C+ C C-
100 - 96.66 96.65 - 93.33 93.32 - 90.00 89.99 - 86.66 86.65 - 83.33 83.32 - 80.00 79.99 - 76.66 76.65 - 73.33 73.32 - 70

The above scale is guaranteed: for example, if your cumulative average is at least 73, then your final grade will be at least B. However, your instructor may adjust the above scale to be more generous.

Course Calendar

The dates of the exams, holidays, and an outline of topics to be discussed in each week. This calendar is preliminary and may be subject to change as the quarter progresses.
Week Topics
1 Vectors and Matrices on Computer, Floating-point numbers, Linear Systems of Equations
Videos 1, 2, 3
2 Floating-point numbers, Triangular Systems of Equations, LU decomposition
Videos 4, 5, 6
18.01.2021. Martin Luther King, Jr. Holiday
3 Cholesky Decomposition
Video 7
4 Gradient Descent
Videos 8, 9
29.01.2021: Deadline to change grading option, change units, and drop classes without "W" grade on transcript.
5 Nonlinear Systems of Equations: bisection method and Newton method
Videos 10, 11
6 Interpolation
Videos 12, 13, 14
12.02.2021: Deadline to drop with "W" grade on transcript.
15.02.2021. Presidents' Day Holiday
7 Quadrature
Videos 15, 16
8 Introduction to Ordinary Differential Equations, Theory of ODE
Videos 17, 18, 19, 20
9 Theory of ODE
Videos 21, 22, 23
10 Numerical solution of initial value problems
QR decomposition
Videos 24, 25, 26
Final Exam. Details to be announced.


Lecture 01 (Vectors and Matrices)
Lecture 02 (Floating-point numbers)
Lecture 03 (Linear Systems of Equations)

Lecture 04 (Floating-point numbers and rounding errors)
Lecture 05 (Triangular Matrices)
Lecture 06 (Gaussian elimination and LU decomposition)

Lecture 07 (Symmetric Positive-Definite Matrices and LU Decomposition)

Lecture 08 (Gradient Descent)
Lecture 09 (Convergence of Gradient Descent)

Lecture 10 (Bisection Method)
Lecture 11 (Newton's Method)

Lecture 12 (Taylor Polynomials)
Lecture 13 (Lagrange Interpolation)
Lecture 14 (Hermite Interpolation)

Lecture 15 (Numerical Integration)
Lecture 16 (Advanced Numerical Integration)


Homework 0 (ungraded, formally, due 17/01/2021)
Homework 1 (due 17/01/2021)
Homework 2 (due 24/01/2021)
Homework 3 (due 31/01/2021)
Homework 4 (due 07/02/2021)
Homework 5 (due 14/02/2021)
Homework 6 (due 21/02/2021)
Homework 7 (due 28/03/2021)
Homework 8 (due 07/03/2021)
Homework 9 (due 12/03/2021)