Introduction to Numerical Analysis
Professor: Paul J. Atzberger
104B Winter 2017, Meeting in North Hall 1105
TR 8:00am - 9:15am




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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 engineering to finance to machine learning and data analytics. 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:

  • Initial-Value Problems for Ordinary Differential Equations
    • Well-posedness of initial-value problems.
    • Euler’s Method of Approximation.
    • Taylor Methods for Higher-order Approximation.
    • Runge-Kutta Methods.
    • Multistep Methods.
    • Convergence Analysis.
    • Order of Accuracy and Stability.
    • Stiff Differential Equations.

  • Solving Linear Systems and Matrix Algebra
    • Linear Equations.
    • Linear Algebra Review.
    • Eigenvalues and Eigenvectors.
    • Direct Methods.
    • Gaussian Elimination.
    • Role of Round-off Errors.
    • Pivoting Methods.
    • Matrix Inversion.
    • LU Factorization.
    • Iterative Methods.
    • Jacobi, Gauss-Siedel, SOR.
    • Conjugate Gradient.

  • Application Areas
    • Statistical Inference and Machine Learning
    • Approaches in Data Science
    • Computer Graphics and Visualization
    • Financial Modeling and Economics
    • Simulation in Engineering and the Sciences

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 16th.

Midterm Outline [PDF].

Homework Assignments:

Turn all homeworks into the TA's mailbox (Yao Xuan) in South Hall 6th Floor by 5pm on the due date. Graded homeworks will be returned in class. Yao Xuan's TA Office Hours: Wednesday, 5-7pm in SH 1607 (MathLab) and Monday, 2-3pm in SH 6432X.

Example python code : Neville's Method.

HW1: (Due Tuesday, Jan. 17th) 5.1: 1acd, 2bc, 3ad, 5ab, 9; 5.2: 1bcd, 4acd, 5bc, 7bc, 9, 12, 15, 16, 17.
HW2: (Due Thursday, Jan. 26th) 5.4: 1cd, 3ab, 4ad, 5, 7, 9, 11, 13, 15, 17, 25, 27, 28, 32.
HW3: (Due Thursday, Feb. 2nd) 5.6: 1acd, 2ad, 3ab, 4, 5, 7, 9, 11, 14, 15, 16.
HW4: (Due Thursday, Feb. 9th) 5.9: 1bcd, 3bcd, 8ab, 9; 5.10: 2ab, 4, 5; 5.11: 1bc, 3bc, 7bc, 9, 11.
HW5: (Due Thursday, Feb. 23rd) 6.1: 5cd, 6ad, 9, 11, 12, 15, 19, 20; 6.2: 2ad, 3, 7, 9c, 13, 19, 29.
HW6: (Due Thursday, March 16th) 6.5: 5ad, 7bc, 9a, 11; 6,6: 1, 3ad, 5, 11ad, 27, 30; 7.1: 1cd, 5ad, 6bc; 7.2: 1af, 5, 9, 17; 7.3: 1ad, 3, 7.


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