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:
Supplemental Materials:
- Python tutorial at Codecademy.
- Python 2.7 documentation.
- Enthought Canopy integrated analysis environment.
- Example Python Code : Neville's Method.
- Numpy Tutorial
Exams:
A midterm exam will be given in the class on Tuesday, February 13th.
Midterm Outline [PDF].
Midterm Sample Exam [PDF].
Homework Assignments:
Turn all homeworks into the TA's mailbox (Sarah Wells) in South Hall 6th Floor by 3pm on the due date. Graded homeworks will be returned in class. Sarah Well's TA Office Hours: Mondays, 2:00pm-3:00pm in SH 6432X and also available in (MathLab) SH 1607 on Wednesdays 5-7pm.
Example python code : Neville's Method.
All problems below are from Numerical Analysis by Burden and Faires (10th edition) unless otherwise noted.
HW1: (Due Thursday, January 25th) 1.1: 2abd, 3ad, 8, 9abcd, 11, 14, 15, 25; 1.2: 1bcd, 2ab, 5ac, 10, 11ab, 15ac, 16, 17, 25.
HW2: (Due Thursday, February 1st) 1.3: 1b, 2bcd, 4, 6, 8ab, 9, 10, 11, 12, 13, 15ab.
HW3: (Due Friday, February 9th) 2.1: 1, 3, 4, 6bc, 11bd, 15; 2.2: 1bd, 3ad, 4cd, 5abcd, 7, 10, 11, 23, 25;
HW4: (Due, Friday, February 16th) 2.3: 1, 3, 5, 10, 12, 19, 23, 25, 29,; 2.6: 1bcd, 5, 9, 10;
HW5: (Due Friday, February 23rd) 3.1: 1bc, 2ab, 3, 4, 11, 18, 23; 3.2: 1bc, 3, 6, 12;
HW6: (Due Friday, March 2nd) 3.3: 1ab, 3ab, 4ab, 7, 10, 12, 18; 3.4: 1ad, 3ad, 10, 11; 3.5: 1, 3ad, 6cd, 11, 14, 15, 21, 26; 3.6 1ad, 3cd, 5;
HW7: (Due Friday, March 9th) 4.1 1bc, 3, 5bc; 4.3: 1bc, 3, 5bc, 15ad; 4.7: 1ad, 4ad, 5, 9.