Professor Paul J. Atzberger : Atzberger Group Intranet Pages

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: [documentation python 3.7] [general tutorial] [Codecademy]
Numpy python package: [tutorial]
Integrated development environments: [PyCharm] [Enthought Canopy]
Jupyter Notebooks: [python interface]
Python environment manager: [Anaconda]
LaTeX typesetting [documentation] [summary sheet]
Linux Operating System: [Ubuntu] [Summary Sheet] [Tutorial]
Example Python Code:
- Neville's Method: [PDF] [Python Code] [Jupyter Notebook]

Exams:

A midterm exam will be given in the class on Thursday, November 14.

Homework Assignments:

Turn all homeworks into the TA's mailbox Nicolas Gonzalez or Alan Raydan in South Hall 6th Floor by 3pm on the due date. Graded homeworks will be returned in class.

TAs Office Hours in South Hall (SH):

Nicolas Gonzalez: Wednesday 4:00pm - 5:00pm in SH 6431S, Tuesday 5:00pm - 7:00pm in MathLab in SH 1607.
Alan Raydan: Wednesday 10:30am - 11:30am in SH 6431S, Wednesday 5:00pm - 7:00pm in MathLab in SH 1607.

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 Tuesday, October 8) 1.1: 2abc, 3ac, 8, 9abcd, 11, 14, 15, 25; 1.2: 1cd, 2ab, 5ab, 10, 11ab, 15ab, 16, 17, 25. Since many did not yet have textbook, you can find a copy of the problems here [PDF]. You can also purchase a print copy or electronic version online at [amazon link].
HW2: (Due Tuesday, October 15) 1.3: 1b, 2acd, 4, 6, 8ab, 9, 10, 11, 12, 13, 15ab.
HW3: (Due Friday, October 25) 2.1: 1, 4, 6bc, 11bd, 15; 2.2: 1bd, 3ad, 4cd, 5ab, 7, 23; 2.3: 1, 3, 5, 29.
HW4: (Due Tuesday, November 5) 2.4: 1ad, 5, 6, 8; 3.1: 1ad, 2ab, 3, 4, 11, 18, 23; 3.2: 1ab, 3, 6, 12;
HW5: (Due Tuesday, November 12) 3.3: 1ab, 3ab, 4ab, 7, 10, 12, 18; 3.4: 1ac, 3ac, 10, 11;
HW6: (Due Thursday, November 21) 3.5: 1, 3ad, 5ad, 14; 3.6 1ad, 3cd, 5;
HW7: (Due Thursday, December 5) 4.1 1ab, 3, 5ad, 7, 22, 29; 4.3: 1adg, 3dg, 5ad, 15ad;