Paul J. Atzberger

Welcome to the class website for Introduction to Numerical Analysis . Computational approaches play an important role in many fields ranging from basic scientific research to engineering to finance to machine learning and data analytics. 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
- Statistical Inference and Machine Learning
- Approaches in Data Science
- Computer Graphics and Visualization
- Financial Modeling and Economics
- Simulation in 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 Assignments 30%
Midterm Exam 30%
Final Exam/Project 40%

Homework Policy:

Assignments will be announced in lecture and posted on the class website. Prompt submission of the homework assignments is required. While no late homework submissions will be accepted, one missed assignment will be allowed without penalty. While you are encouraged to discuss materials with classmates, your 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 Tuesday, February 12th.

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, January 17) 1.1: 2bcd, 3bc, 8, 9abcd, 11, 14, 15, 25; 1.2: 1acd, 2ab, 5ab, 10, 11ab, 15ab, 16, 17, 25. Since the printed textbook seems to be on back-order at the bookstore, 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 Friday, January 25) 1.3: 1b, 2bcd, 4, 6, 8ab, 9, 10, 11, 12, 13, 15ab.
HW3: (Due Friday, February 1) 2.1: 1, 3, 4, 6bc, 11bd, 15; 2.2: 1bd, 3ad, 4cd, 5abcd, 7, 10, 11, 23, 25;
HW4: (Due, Tuesday, February 5) 2.3: 1, 3, 5, 23, 29; 2.6: 1bcd, 9;
HW5: (Due Friday, February 15) 3.1: 1bc, 2ab, 3, 4, 11, 18, 23; 3.2: 1bc, 3, 6, 12;
HW6: (Due Friday, February 22) 3.3: 1ab, 3ab, 4ab, 7, 10, 12, 18; 3.4: 1ad, 3ad, 10, 11;
HW7: (bonus) (Due Friday, March 15) 3.5: 1, 3ad, 6cd, 14; 3.6 1ad, 3cd, 5; 4.3: 1bc, 3, 5bc; 4.7 1ab, 8ab, 13.