Paul J. Atzberger

Welcome to the class website for Introduction to Numerical Analysis . Numerical approaches play an important role in many fields including in scientific research, engineering, finance, machine learning, and data analysis. 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
Application Areas
- Engineering and the Sciences
- Statistical Inference, Machine Learning, Data Science
- Computer Graphics and Visualization
- Financial Modeling and Economics

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 30%
Midterm 30%
Final Project 40%

Policies:

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 on Tuesday, October 26.
Midterm Outline [PDF].
Careers in mathematics and related fields [PDF].

Supplemental Materials:

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

Homework Assignments:

Please be sure to turn in all homeworks by 11pm PST on the due date following the instructions on the Gauchospace page. These will be graded by the TA Charles Kulick.

TAs Office Hours are:
Wednesdays 3pm - 5pm, Charles Kulick, SH 6431L

- Example python code : Neville's Method [PDF] [Python Code] [Jupyter Notebook]
- Midterm Outline [PDF]
- Careers in mathematics and related fields [PDF].

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

HW1: (Due Thursday, September 30) 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 12) 1.3: 1b, 2ac, 4, 8ab, 9, 11, 15ab. 2.1: 1, 4, 6bc, 11bd, 15; 2.2: 1bd, 3ad, 4cd, 5ab, 7, 23;
HW3: (Due Thursday, October 21) 2.3: 1, 3, 5, 29; 2.4: 1ad, 5, 6, 8; 3.1: 1ad, 2ab, 3, 4, 11, 18, 23;
HW4: (Due Thursday, November 4) 3.2: 1ab, 3, 6, 12; 3.3: 1ab, 3ab, 4ab, 7, 10, 12, 18; 3.4: 1ac, 3ac, 10, 11;
HW5: (Due Friday, November 12) 3.5: 1, 3ad, 5ad, 14; 3.6 1ad, 3cd, 5;
HW6: (Due Thursday, November 18) 4.1 1ab, 3, 5ad, 7, 22, 29; 4.3: 1adg, 3dg, 5ad, 15ad;

Additional Information

Gauchospace Website