Introduction to Numerical Analysis:
Approximation and Nonlinear Equations
Math 170B --- Spring 2020

Lecture site: HSS 1330
Lecture times: Monday, Wednesday, Friday. 4:00pm-4:50pm.
Discussion sessions C01 973183: Monday 5:00p-5:50p, HSS 2150 with David Lenz
C02 973184: Monday 6:00p-6:50p, HSS 2150 with Gunjan Patil
C03 973185: Monday 7:00p-7:50p, AP&M 7421 with Fangyao Su
C03 973186: Monday 8:00p-8:50p, AP&M 7421 with Fangyao Su
Final Exam
time and place
March 16th, 2020, 8:00am - 11am. Place to be announced.
Instructor Martin Licht
Email: mlicht AT ucsd DOT edu
Office: AP&M 5880E
Hours: Wednesday, 1-2pm.
Teaching Assistant David Lenz
Email: dlenz AT ucsd DOT edu
Office Hours: T 1pm-2pm W 10am-11am, AP&M 5760
Teaching Assistant Gunjan, Patil
Email: ggpatil AT ucsd DOT edu
Office Hours: Th 5pm-6pm, MHA 5722
Teaching Assistant Fangyao Su
Email: f2su AT ucsd DOT edu
Office Hours: M 9:30am-12:00pm, F 1pm-2:30pm, AP&M 6452
Section(s) 973183, 973184, 973185, 973186
Credit Hours: 4 units
Course content Rounding and discretization errors. Calculation of roots of polynomials and nonlinear equations. Interpolation. Approximation of functions. Knowledge of programming recommended.
Formal prerequesite Math 170A.
Homework information Homework will announced on Fridays after lecture. Homework can be submitted to the mailboxes (AP&M basement) on Fridays before 3:30pm. All submissions must be in handed-in in handwritten form.
Academic Integrity Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. See http://www-senate.ucsd.edu/manual/Appendices/app2.htm for UCSD Policy on Integrity of Scholarship.
Resources The textbook for this lecture is:
  • Kincaid & Cheney, Numerical Analysis: Mathematics of Scientific Computing. 3rd edition.
The following textbooks are recommended to supplement the lectures: 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: Even though sparse direct methods will not be in the focus of this course, your instructor recommends you the following two references: Assorted links to additional material:
  • E. Wallace Floating-Point Toy. [Link]
  • Lloyd N. Trefethen, The Definition of Numerical Analysis. [Link]
  • D. Goldberg, What every computer scientist should know about Floating-Point arithmetics. [Link]
  • J. R. Shewchuk, The Conjugate Gradient Method without the Agonizing Pain. [Link]
Helpful links

Grading Information

The final grade will be composed by the best of the following two options: (a) 20% homework, 20% midterm, and 60% final exam. (b) 20% homework, 80% final exam.

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

Lecture Content
# 1, 1M
06.01.2020.
Administrativa. Examples and Motivation.
Limits, continuity, differentiability. Fundamental theorem of calculus. Mean value theorem.
# 2, 1W
08.01.2020.
Taylor theorem. Remainder formulas. Error estimates.
# 3, 1F
10.01.2020.
Multivariate functions. Multivariate Taylor formula. Error estimates.
# 4, 2M
13.01.2020.
Nonlinear approximation algorithms: bisection method, error estimate.
# 5, 2W
15.01.2020.
Nonlinear approximation algorithms: newton method, error estimate.
# 6, 2F
17.01.2020.
Nonlinear approximation algorithms: multivariate newton method, error estimate.
Homework 1 & 2 announced.
# 7, 3M
20.01.2020.
Martin Luther King, Jr. Holiday
# 8, 3W
22.01.2020.
Nonlinear approximation algorithms: secant method, error estimate.
# 9, 3F
24.01.2020.
Review of nonlinear approximation methods. Applications in optimization.
#10, 4M
27.01.2020.
Lagrange interpolation: problem setting. monomial basis. vandermonde matrix.
#11, 4W
29.01.2020.
Lagrange interpolation: newton basis. triangular vandermonde matrix.
#12, 4F
31.01.2020.
Midterm
Homework 1 & 2 collected. Homework 3 & 4 announced.
01.02.2020: Deadline to change grading option, change units, and drop classes without "W" grade on transcript.
#13, 5M
03.02.2020.
Lagrange interpolation: lagrange basis. diagonal vandermonde matrix. Review of different interpolation bases.
#14, 5W
0502.2020.
Lagrange interpolation: classical error estimates.
#15, 5F
07.02.2020.
Lagrange interpolation: Newton-Cotes formulas.
#16, 6M
10.02.2020.
Midterm.
#17, 6W
12.02.2020.
Hermite interpolation: problem setting. relation to Taylor and Lagrange interpolation.
#18, 6F
14.02.2020.
Monomial basis. Newton basis. Lagrange basis.
Homework 3 & 4 collected. Homework 5 & 6 announced.
15.02.2020: Deadline to drop with "W" grade on transcript.
#19, 7M
17.02.2020.
Presidents' Day Holiday
#20, 7W
19.02.2020.
Divided differences.
#21, 7F
21.02.2020.
Numerical integration: problem setting.
#22, 8M
24.02.2020.
Numerical integration based on Interpolation.
#23, 8W
26.02.2020.
Numerical integration based on Interpolation.
#24, 8F
28.02.2020.
Numerical differentiation.
Homework 5 & 6 collected. Homework 7 & 8 announced.
#25, 9M
02.03.2020.
Numerical differentiation.
#26, 9W
04.03.2020.
Numerical differentiation.
#27, 9F
06.03.2020.
Numerical Integration: Gauss quadrature.
Homework 7 & 8 collected. Practice Material for Final available..
#28,10M
09.03.2020.
TBA
#29,10W
11.03.2020.
TBA
#30,10F
13.03.2020.
Review.
FI
16.03.2020.
Final Exam. 8am - 11am. Place to be announced.