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

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.
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.
#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.
#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.