Welcome to the class website for Introduction to Numerical Analysis . Computational approaches play an important role in a variety of fields, ranging from basic scientific research to engineering applications 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 the above applications areas. For more details see the syllabus and the topics listed below.
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 with Matlab/Octave preferred.
Grading:
The grade for the class will be based on the homework assignments (see policy above), midterm exam, and final project as follows:
Homework Assignments 30%
Midterm Exam 30%
Final Project 40%
Homework Policy:
Assignments will be made weekly and posted on the class website. Prompt submission of the homework assignments will be required. While no late homework submissions will be accepted, two missed assignments will be allowed without penalty. While it is permissible to discuss the problems with classmates, the submitted homework must be your own work. The assignments will consist of a combination of analytic problems and numerical simulations. Some basic programming in Matlab/Octave may be required.
Exams:
A midterm exam will be given in the class on Tuesday, July 14th.
Final Project:
A final project will be assigned in which the numerical methods covered in the class will be studied in the context of a specific problem coming from finance, engineering, or basic science. The project will consist of a combination of analysis and implementation of a numerical method. The grade of the project will be based on each individuals written report addressing specific mathematical and experimental questions concerning the methods. The final project is an integral part of the class and will be required to pass.
Final projects description can be found here [PDF] Δ (Due: Friday, August 7th).
TA Office Hours:
No TA assigned at this time.
Office Hours:
WR 11:00am - 12:30pm.
Supplemental Class Notes:
Ch 1. (Sections for HW1) Please order copy of the book on-line soon. Δ
Midterm Solution Key Δ
Matlab Primer Δ
Software and Web Resources:
Companion Website for the Book: Numerical Analysis by Faires and Burden
GNU Octave Software and Documentation
Octave Software (Binaries from SourceForge.net)
GNU Octave Tutorial
GNU Octave Links (Tutorials and other Information)
Matlab Software and Documentation
Explosion of the Ariane 5 Rocket (Consequence of Faulty Numerics)
The Sinking of the Sleipner A Offshore Platform (Consequence of Faulty Numerics)
Quantitative Finance Skills and the Job Market
Article on Computational Finance
QuantFinanceJobs.com
Heard on the Street: Quantitative Questions from Wall Street Job Interviews by Timothy Falcon Crack.
Options, Futures, and Other Derivatives by John Hull.
Class Annoucements:
- The grader for the homework is Briana Tippets and can be contacted at briana_tippets__at__umail.ucsb.edu.
- The midterm will cover all topics discussed in the lecture up to Hermite Polynomial Interpolation.
- Final projects description can be found here [PDF] Δ (Due: Friday, August 7th).
Midterm Solution Key Δ
Homework Assignments:
HW1: (Due Thursday, June 25th) 1.1: 1ad, 8; 1.2: 1adf, 2ac, 5ac, 10.
HW2: (Due Tuesday, June 30th) 1.3: 2acd, 5, 16; 2.1: 5ad, 14, 19.
HW3: (Due Tuesday, July 7th) 2.4: 1ad, 10, 14; 3.1: 1abd, 6abc, 8, 10abc, 18, 20a, 30.
HW4: (Due Tuesday, July 14th) 3.2: 1ad, 3a, 6b, 11, 20.
HW5: (Due Thursday, July 23rd) 3.3: 1bc, 4ac, 6, 10, 11; 3.4: 1, 4bd, 5c, 26, 30.
HW6: (Due Monday, July 27th) 4.1: 1, 5a, 7, 24, 26; 4.3: 1agh, 5, 9, 15, 4.4 1ac, 7, 24; 4.6: 1bh, 3a, 6.
HW7: (Due Wednesday, July 29th) 5.1: 1acd, 9; 5.2: 1abd, 12; 5.4: 1ab, 2a; 5.6: 1cd, 3ac, 5, 14.
HW8: (Due Friday, July 31st) 5.11: 1cd, 3, 5, 7, 10, 11, 12.