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 economics and finance. This class will discuss both the mathematical foundations and the practical implementation of modern numerical methods. Examples will also be discussed from applications areas.
Please be sure to read the prerequisites and grading policies for the class.
Selection of Topics Covered:
- 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
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 Study Outline [PDF].
Supplemental Materials:
- Python 2.7 documentation.
- Python tutorial at Code-Academy.
- Enthought Canopy integrated analysis environment.
- Example Python Code : Neville's Method.
- Numpy Tutorial
Exams:
A midterm exam will be given in the class on Thursday, October 27th. Midterm Study Outline [PDF].
Homework Assignments:
Turn all homeworks into the TA's mailbox in South Hall 6th Floor by 5pm on the due date. Graded homeworks will be returned in class. Victoria Kala's TA Office Hours: Tuesday, 5-7pm in SH 1607 (MathLab) and Wednesday, 12-1pm in SH 6432G.
Some solutions may be provided below by the TA.
Example python code : Neville's Method.
Final Project Proposal: (Due Thursday, Nov. 3rd).
Final Project Slides: (Due Wednesday, Nov. 30th).
Final Project Report: (Due Wednesday, Dec. 7th).
HW1: (Due Tuesday, Oct. 4th) 1.1: 2abd, 3ad, 8, 9abcd, 11, 14, 15, 25; 1.2: 1bcd, 2ab, 5aceh, 10, 11abd, 15ac, 16, 17, 25.
HW2: (Due Thursday, Oct. 6th) 1.3: 1b, 2bcd, 4, 6, 8ab, 9, 10, 11, 12, 13, 15bc, 16, 17, 18.
HW3: (Due Friday, Oct. 14th) 2.1: 1, 3, 4, 6, 11, 12, 19; 2.2: 1, 3, 4, 5, 7, 10, 11;
HW4: (Due, Monday, Oct. 24th) 2.3: 1, 3, 5, 10, 12, 19, 24, 26, 34; 2.6: 1, 5, 9, 11, 12;
HW5: (Due Thursday. Nov. 3rd) 3.1: 1bc, 2ab, 3, 4, 11, 18, 23; 3.2: 1bc, 3, 6, 12; 3.3: 1ab, 3ab, 4ab, 7, 10, 12, 18;
HW6: (Due Thursday, Nov. 10th) 3.4: 1ad, 3ad, 4cd, 10, 12; 3.5: 1, 3ad, 6cd, 11, 14, 15, 29, 32; 3.6 1ad, 3cd, 5;
HW7: (Due Thursday, Nov. 17th) 4.3: 1bc, 3bc, 5bc, 15; 4.7: 1ad, 4ad, 5, 8.
HW8: (Due Wednesday, Nov. 23th) 4.1: 1ab, 3ab, 5, 7, 10, 18, 27, 29.