Introduction to Numerical Analysis
Professor: Paul J. Atzberger
104B Spring 2019, Meeting in PHELP 1425
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 including basic scientific research, engineering, finance, and recent machine learning and data science approaches. This class will discuss both the mathematical foundations and the practical implementation of modern numerical methods. Examples also will be discussed from related applications areas.

Please be sure to read the prerequisites and grading policies for the class.

Selection of Topics Covered in 104 Series:

  • 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
  • Numerical Linear Algebra
  • Power Method for Eigenvalues and Eigenvectors
  • Iterative Methods for Solving Ax = b
  • Preconditioners
  • Multigrid Methods
  • Application Areas
    • Statistical Inference and Machine Learning
    • Approaches in Data Science
    • Computer Graphics and Visualization
    • Financial Modeling and Economics
    • 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 / Quizzes 30%
Midterm Exam 30%
Final Exam/Project 40%

Policies:

To help give feedback throughout the quarter there will be unannounced pop quizzes at the beginning of some lectures. The two lowest quiz scores will be dropped. Homework and other assignments will be given in class and posted on the course website. Prompt submission of homeworks will be required. While no late homework will be accepted, one missed homework will be allowed without penalty. While it is permissible and encouraged for you to discuss materials with classmates, the submitted homework must be your own work.

Class Announcements:

Supplemental Materials:

Exams:

A midterm exam will be given in the class on Thursday, May 9.

Midterm Outline [PDF].

Homework Assignments:

Turn all homeworks into the TA's mailbox (Ben Gross) in South Hall 6th Floor by 3pm on the due date. Graded homeworks will be returned in class.

Ben Gross's TA Office Hours in South Hall (SH): Tuesdays, 4:00pm-5:00pm in SH 6431S and also available in (MathLab) SH 1607 on Tuesdays 5:00-7:00pm.

Example python code : Neville's Method [PDF] [Python Code] [Jupyter Notebook]

All problems below are from Numerical Analysis by Burden and Faires (10th edition) unless otherwise noted.

HW1: (Due Thursday, April 11) 4.1: 1ab, 3, 5ad, 7ad, 10, 12, 20, 22, 26, 29; 4.3: 1adfh, 3.
HW2: (Due Monday, April 22) 4.3: 5, 9, 15ad, 19; 4.4: 1acd, 3, 5, 11, 18; 4.7: 1ad, 3, 7.
HW3: (Due Tuesday, April 30) 5.1: 2acd, 3, 5, 6ad, 7, 10; 5.2: 2bc, 4bc, 5cd, 7, 9, 12, 17. 5.3: 1abd, 3, 6bc, 8, 10, 12.
HW4: (Due Thursday, May 2) 5.4: 1bcd, 4cd, 8, 12, 16, 18, 27, 28. 5.6: 1acd, 3acd, 5, 7, 11, 14, 16, 19. 5.9: 1bc, 4bc, 5, 7;
HW5: (Due Tuesday, May 14) 5.10: 1, 2, 5, 7, 8; 5.11: 1cd, 3, 5, 7, 10, 12.
HW6: (Due Tuesday, May 28) 6.1: 1ad, 3, 5, 7ad, 9, 12; 6.2: 1ad, 3, 7, 9ad, 13; 6.3: 4ad, 6ad, 8. 6.4: 1, 5, 9. 6.5: 1, 5, 9.
HW7: (Due Tuesday, June 4) 7.1: 1ad, 3ad, 7ad; 7.2: 1af, 3, 5; 7.3: 1ad, 3, 5, 7, 9, 14, 16.

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