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

Lecture site: CENTR 212
Lecture times: Monday, Wednesday, Friday. 3:00pm-3:50pm.
Discussion sessions B01 994385: Thursday 5:00p-5:50p, CENTR 217B with Jinjie Zhang
B02 994386: Thursday 6:00p-6:50p, CENTR 217B with Jinjie Zhang
B03 994387: Thursday 7:00p-7:50p, CENTR 217B with Bingni Guo
B03 994388: Thursday 8:00p-8:50p, CENTR 217B with Bingni Guo
Final Exam
time and place
March 18th, 2020, 3:00pm - 6pm. Place to be announced.
Instructor Martin Licht
Email: mlicht AT ucsd DOT edu
Office: AP&M 6442
Hours: Wednesday, 2-3pm AP&M 6303
Teaching Assistant Jinjie Zhang
Email: jiz003 AT ucsd DOT edu
Office Hours: M W 1pm-3pm AP&M 5412
Teaching Assistant Bingni Guo
Email: b8guo AT ucsd DOT edu
Office Hours: Tuesday 3pm-5pm Wednesday 1pm-3pm AP&M 1220
Section(s) 994385, 994386, 994387, 994388
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 will be submitted through Gradescope.
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, 20% midterm, and 40% final exam.
(b) 20% homework, 20% best midterm, 60% final exam.
You must pass the final exam in order to pass the course.
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.
Preliminaries: basic geometry, sequences, limits.
# 2, 1W
08.01.2020.
Preliminaries: continuity. Intermediate value theorem.
# 3, 1F
10.01.2020.
Preliminaries: mean value theorem.
Homework 1 announced.
# 4, 2M
13.01.2020.
Preliminaries: intermediate and mean value theorem.
# 5, 2W
15.01.2020.
Preliminaries: Taylor theorem, remainder formulas
# 6, 2F
17.01.2020.
Preliminaries: Multivariate Taylor formula
Homework 1 collected. Homework 2 announced.
# 7, 3M
20.01.2020.
Martin Luther King, Jr. Holiday
# 8, 3W
22.01.2020.
Preliminaries: Orders of convergence
# 9, 3F
24.01.2020.
Nonlinear approximation algorithms: bisection method
Homework 2 collected. Homework 3 announced.
#10, 4M
27.01.2020.
Nonlinear approximation algorithms: convergence analysis of bisection method.
#11, 4W
29.01.2020.
Nonlinear approximation algorithms: newton method
#12, 4F
31.01.2020.
Midterm
Homework 3 collected. Homework 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.
Nonlinear approximation algorithms: multivariate newton method Nonlinear approximation algorithms: error estimate.
#14, 5W
0502.2020.
Nonlinear approximation algorithms: secant method, error estimate.
#15, 5F
07.02.2020.
Nonlinear approximation algorithms: optimization, gradient descent, secant method.
Homework 4 collected. Homework 5 announced.
#16, 6M
10.02.2020.
Lagrange interpolation: problem setting. monomial basis. vandermonde matrix.
Lagrange interpolation: newton basis. triangular vandermonde matrix.
Lagrange interpolation: lagrange basis. diagonal vandermonde matrix.
#17, 6W
12.02.2020.
Polynomial interpolation: classical error estimates.
Polynomial interpolation: Newton-Cotes formulas.
#18, 6F
14.02.2020.
Midterm.
Homework 5 collected. Homework 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.
Hermite interpolation: problem setting, relation to Taylor and Lagrange interpolation.
Review of different interpolation bases.
#21, 7F
21.02.2020.
Hermite interpolation: divided differences.
Numerical integration: problem setting.
Homework 6 collected. Homework 7 announced.
#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 7 collected. Homework 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 8 collected. Review Exercises announced.
#28,10M
09.03.2020.
Numerical Integration: Gauss quadrature.
#29,10W
11.03.2020.
Numerical Integration: Gauss quadrature.
#30,10F
13.03.2020.
Review.
FI
18.03.2020.
Final Exam. 3pm - 6pm. Place to be announced.