Introduction to Numerical Analysis
Professor: Paul J. Atzberger
104A Winter 2016, Meeting in GIRV 2128
TR 9:30am - 10:45am




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Supplemental Class Notes

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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:

Supplemental Materials:

Exams:

A midterm exam will be given in the class on Thursday, February 11th.

Midterm Outline [PDF].

Practice Problems [PDF].

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.

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. Note the TA's mailbox is located on the right-hand side wall of the mail room with last name "Lo Kim Lin."

Jon Lo Kim Lin's TA Office Hours: Mondays 10:00-11:00AM in SH 6431H. Additional MathLab office hours now on Thursdays 5:00pm - 7:00pm.

Some solutions may be provided below by the TA.

I will hold special office hours for any questions before the midterm on Wednesday, Feb 10th, 1:00pm - 3:00pm, South Hall 6635.

Example python code : Neville's Method.

HW1: (Due Tuesday, Jan. 12th) 1.1: 2bcd, 3bc, 8, 9abcd, 11, 14, 15, 25; 1.2: 1acf, 2ab, 5dech, 10, 11bcd, 15ad, 16, 17, 25.
HW2: (Due Tuesday, Jan 19th) 1.3: 1ab, 2abd, 4, 5, 7, 8ab, 10, 11, 12, 13, 15ab, 16, 18.
HW3: (Due Friday, Jan. 29th) 2.1: 1, 6, 12, 19; 2.2: 1, 3, 7, 11; 2.3: 1, 5, 19, 24, 26, 34.
HW4: (Due Friday, Feb. 5th) 2.4: 1ad, 6, 7, 8, 9, 11; 2.6: 1bcd, 5, 10, 11, 12; 3.1: 1ad, 2cd, 5acd, 13abd.
HW5: (Due Tuesday, Feb. 9th) 3.1: 1bc, 2ab, 3, 4, 11, 18, 23; 3.2: 1bc, 3, 6, 12.
HW6: (Due Friday, Feb. 19th) 3.3: 1ab, 3ab, 4ab, 7, 10, 12, 18; 3.4: 1bc, 3ad, 4ab, 10, 12.
HW7: (Due Friday, March 4th) 3.4: 5ab, 11, 12; 3.5: 1, 3ac, 6ab, 11, 14, 15, 29, 32; 3.6 1ac, 3ab, 5.


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