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

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.
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.
#13, 5M
03.02.2020.
Nonlinear approximation algorithms: multivariate newton method, 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 matrix problem.
#17, 6W
12.02.2020.
Lagrange interpolation: lagrange basis. diagonal matrix.
Polynomial interpolation: classical error estimates.
#18, 6F
14.02.2020.
Midterm.
Homework 5 collected. Homework 6 announced.
#19, 7M
17.02.2020.
Presidents' Day Holiday
#20, 7W
19.02.2020.
Review of different interpolation bases.
#21, 7F
21.02.2020.
Divided Differences
Homework 6 collected. Homework 7 announced.
#22, 8M
24.02.2020.
Divided Differences
#23, 8W
26.02.2020.
Hermite interpolation
#24, 8F
28.02.2020.
Hermite Interpolation
Homework 7 collected. Homework 8 announced.
#25, 9M
02.03.2020.
Numerical integration based on Interpolation.
#26, 9W
04.03.2020.
Numerical integration based on Interpolation.
#27, 9F
06.03.2020.