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 the design of financial products. 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:
- No office hours Tuesday, November 4th. Campus Committee Meeting is now scheduled this week at this time.
Supplemental Materials:
- Python 2.7 documentation.
- Python tutorial at Code-Academy.
- Enthought Canopy integrated analysis environment.
- Example Python Code : Neville's Method Δ.
Exams:
A midterm exam will be given in the class on Tuesday, October 28th.
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.
Jon Lo Kim Lin's TA Office Hours: TR 9-10:30 am in SH 6431H. Solutions are provided below by the TA.
Example python code : Neville's Method Δ.
HW1: (Due Tuesday, Oct. 14th) 1.1: 1abcd, 3ad, 8, 9abcd, 10, 15, 25; 1.2: 1adf, 2ac, 5afch, 10, 11abcd, 15ad, 16, 17, 25. [solutions] Δ
HW2: (Due Tuesday, Oct. 21st) 1.3: 1ab, 2acd, 5, 6, 8ab, 11, 12, 13, 15ab, 16. [solutions] Δ
HW3: (Due Thursday, Oct. 30th) 2.1: 1, 6, 12, 19; 2.2: 1, 3, 7, 11; 2.3: 1, 5, 19, 24, 26, 34. [solutions] Δ [python codes] Δ.
HW4: (Due Thursday, Nov. 6th) 2.4: 1ad, 6, 7, 8, 9, 11; 3.1: 1ad, 5acd, 13abd. [solutions] Δ
HW5: (Due Thursday, Nov. 13th) 3.1: 1b, 6ad, 12, 23; 3.2: 1acd, 3, 6, 10. [solutions] Δ
HW6: (Due Tuesday, Nov. 25th) 3.3: 1ab, 3ab, 4ab, 7, 10, 12, 18; 3.4: 1ad, 3bc, 4cd, 10, 12.
HW7: (Due Thursday, Dec. 4th) 3.4: 1bc, 3d, 5ab; 3.5: 1, 3ad, 6cd, 11, 14, 15, 29, 32; 3.6 1ad, 3cd, 5.
Final Project Proposal: (Due Thursday, Nov. 13th).
Final Project Report: (Due Friday, Dec. 12th).