Introduction to Numerical Analysis
Professor: Paul J. Atzberger
104C Spring 2015, Meeting in GIRV 1115
TR 11:00am - 12:15pm




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Syllabus

Homework

Annoucements

Supplemental Materials

Grading

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Atzberger Homepage


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.

Topics:

  • Boundary Value Problems for Ordinary Differential Equations (ODEs)
    • Linear Problems
    • Iterative Methods
    • Non-linear Problems
    • Steepest Descent
    • Newton Methods for Systems
    • Shooting Methods
    • Rayleigh-Ritz Method

  • Eigenvalue Approaches
    • Linear Algebra Background
    • Standard Forms
    • Geršgorin Theorem
    • Power Method
    • Householder’s Method
    • QR Decomposition and Algorithm
    • Singular Value Decomposition (SVD)

  • Solving Partial Differential Equations (PDEs)
    • Parabolic PDEs
    • Elliptic PDEs
    • Hyperbolic PDEs
    • Finite Difference Methods
    • Crank-Nicolson Method
    • Lax-Wendroff Method
    • Consistency, Accuracy, Stability of Methods
    • Courant–Friedrichs–Lewy (CFL) Condition
    • Lax–Richtmyer Theorem
    • Finite Element Methods
    • Lagrange and Hermite Elements
    • Lax–Milgram Theorem

Prerequisites:

Calculus, Linear Algebra, Differential Equations, and experience programming.

Grading:

The grade for the class will be based on the homework assignments (see policy below), midterm exam, and final exam/project 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:

  • For HW2, error found in the book Burden & Faires. On pg. 702, the term Q[4][i] has wrong expression with the scaling term h in the numerator but should be in the denominator.

Supplemental Materials:

Exams:

A midterm exam will be given in the class on Tuesday, April 21st.

Midterm Outline [PDF].

Homework Assignments:

Turn all homeworks into the TA's mailbox John Kaminsky in South Hall 6th Floor by 5pm on the due date. Graded homeworks will be returned in class.

John Kaminsky's TA Office Hours: Tuesdays, 4pm-5pm in South Hall 6432T (graduate tower) and Mondays 5pm-7pm in South Hall Mathlab (ground floor).

Example python code : Neville's Method.

HW1: (Due Tuesday, April 7th) 11.1: 1, 3, 4abd, 7, 9; 11.2: 1, 3abd, 4ac, 5, 6.
HW2: (Due Thursday, April 16th) 11.3: 2ab, 4bcd, 5, 8; 11.4: 2, 6; 11.5: 1, 3abc.
HW3: (Due Thursday, April 23rd) 9.1: 1abcd, 3bcd, 5, 7, 10, 17; 9.2: 1ad, 3c, 7ad, 18; 9.3: 1bd, 5ad, 7, 11, 17, 18.
HW4: (Due Thursday, April 30th) 9.4: 1abc, 2cd, 3b; 9.5: 1ade, 2bd, 4ad, 6, 7, 14, 15.
HW5: (Due Thursday, May 7th) 9.6: 1acd, 2cd, 4, 5, 8, 11, 14, 15, 17, 18.
HW6: (Due Thursday, May 14th) 12.2: 5ab, 6ab, 9, 10, 13, 14, 18.
HW7: (Due Thursday, May 28th) Problem Set [PDF].


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