Paul J. Atzberger

Welcome to the class website for Introduction to Numerical Analysis . Computational approaches play an important role in many fields including basic scientific research, engineering, finance, and recent machine learning and data science approaches. This class will discuss both the mathematical foundations and the practical implementation of modern numerical methods. Examples also will be discussed from related applications areas.

Please be sure to read the prerequisites and grading policies for the class.

Selection of Topics Covered in 104 Series:

Floating Point Number Representation
Round-off Error
Algorithms and Convergence
Catastrophes Caused by Errors in Numerical Algorithms
Finding Zeros of Equations (Bisection, Newton's Method)
Interpolation Methods
Numerical Differentiation
Numerical Integration
Adaptive Quadratures
Initial Value Problems for ODE's
Euler's Method
Higher-Order Methods (Explicit / Implicit)
Multistep Methods
Stability
Stiff Differential Equations
Numerical Linear Algebra
Power Method for Eigenvalues and Eigenvectors
Iterative Methods for Solving Ax = b
Preconditioners
Multigrid Methods
Application Areas
- Statistical Inference and Machine Learning
- Approaches in Data Science
- Computer Graphics and Visualization
- Financial Modeling and Economics
- Engineering and the Sciences

Prerequisites:

Calculus, Linear Algebra, Differential Equations, and some experience programming.

Grading:

The grade for the class will be based on the homework assignments (see policy below), midterm exam, and final exam as follows:

Homework / Quizzes 30%
Midterm Exam 30%
Final Exam/Project 40%

Policies:

To help give feedback throughout the quarter there will be unannounced pop quizzes at the beginning of some lectures. The two lowest quiz scores will be dropped. Homework and other assignments will be given in class and posted on the course website. Prompt submission of homeworks will be required. While no late homework will be accepted, one missed homework will be allowed without penalty. While it is permissible and encouraged for you to discuss materials with classmates, the submitted homework must be your own work.

Class Announcements:

Midterm Outline [PDF].

Supplemental Materials:

Python General Tutorial
Python tutorial at Codecademy
Python 3.7 documentation
Numpy Python Package Tutorial
Enthought Canopy integrated analysis environment.
Jupyter Notebooks: Python Interface
Example Python Code:
- Neville's Method: [PDF] [Python Code] [Jupyter Notebook]

Exams:

A midterm exam will be given in the class on Thursday, May 9.

Midterm Outline [PDF].

Homework Assignments:

Turn all homeworks into the TA's mailbox (Ben Gross) in South Hall 6th Floor by 3pm on the due date. Graded homeworks will be returned in class.

Ben Gross's TA Office Hours in South Hall (SH): Tuesdays, 4:00pm-5:00pm in SH 6431S and also available in (MathLab) SH 1607 on Tuesdays 5:00-7:00pm.

Example python code : Neville's Method [PDF] [Python Code] [Jupyter Notebook]

All problems below are from Numerical Analysis by Burden and Faires (10th edition) unless otherwise noted.

Midterm Outline [PDF].

HW1: (Due Thursday, April 11) 4.1: 1ab, 3, 5ad, 7ad, 10, 12, 20, 22, 26, 29; 4.3: 1adfh, 3.
HW2: (Due Monday, April 22) 4.3: 5, 9, 15ad, 19; 4.4: 1acd, 3, 5, 11, 18; 4.7: 1ad, 3, 7.
HW3: (Due Tuesday, April 30) 5.1: 2acd, 3, 5, 6ad, 7, 10; 5.2: 2bc, 4bc, 5cd, 7, 9, 12, 17. 5.3: 1abd, 3, 6bc, 8, 10, 12.
HW4: (Due Thursday, May 2) 5.4: 1bcd, 4cd, 8, 12, 16, 18, 27, 28. 5.6: 1acd, 3acd, 5, 7, 11, 14, 16, 19. 5.9: 1bc, 4bc, 5, 7;
HW5: (Due Tuesday, May 14) 5.10: 1, 2, 5, 7, 8; 5.11: 1cd, 3, 5, 7, 10, 12.
HW6: (Due Tuesday, May 28) 6.1: 1ad, 3, 5, 7ad, 9, 12; 6.2: 1ad, 3, 7, 9ad, 13; 6.3: 4ad, 6ad, 8. 6.4: 1, 5, 9. 6.5: 1, 5, 9.
HW7: (Due Tuesday, June 4) 7.1: 1ad, 3ad, 7ad; 7.2: 1af, 3, 5; 7.3: 1ad, 3, 5, 7, 9, 14, 16.