Welcome to the class website for Introduction to Numerical Analysis . Numerical approaches play an important role in many fields including in scientific research, engineering, finance, machine learning, and data analysis. 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
• Application Areas
  • Engineering and the Sciences
  • Statistical Inference, Machine Learning, Data Science
  • Computer Graphics and Visualization
  • Financial Modeling and Economics

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 30%
Midterm 30%
Final Project 40%

Policies:

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:

• Careers in mathematics and related fields
  • Profiles of people and jobs I [PDF].
  • Profiles of people and jobs II [PDF].
  • Video: Career Advice from Mathematical Scientists in Industry
  • 
• Midterm Outline [PDF].

Supplemental Materials:

• Python: [documentation python 3.7] [general tutorial] [Codecademy]
• Numpy python package: [tutorial]
• Integrated development environments: [PyCharm]
• Jupyter Notebooks: [python interface]
• Python environment manager: [Anaconda]
• LaTeX typesetting [tutorial] [documentation] [summary sheet]
• Python Debugging with PDB: [Tutorial]
• Linux Operating System: [Ubuntu] [Summary Sheet] [Tutorial]
• Example Python Code:
  • Neville's Method: [PDF] [Python Code] [Jupyter Notebook]
  • LaTeX Table Writer: [PDF] [Python Code] [Jupyter Notebook]
  • CSV Table Writer: [PDF] [Python Code] [Jupyter Notebook]

Homework Assignments:

Please be sure to turn in all homeworks by 11pm PST on the due date following the instructions on the Canvas page. These will be graded by the TA Andre Martins Rodrigues .

Teaching Assistant Info: Andre Martins Rodrigues, South Hall 6432K, Office Hours:
- Tuesdays: 10:00am-11:30am (for the first two weeks via Zoom, see Canvas), then in-person in South Hall 6432K.
- Mondays, 5:00pm-7:00pm, in-person Mathlab South Hall 1607.

This would be a good opportunity for additional help with the course materials.  

- Example python code : Neville's Method [PDF] [Python Code] [Jupyter Notebook]
- Midterm Outline [PDF]
- Careers in mathematics and related fields
-- profiles of people and jobs I [PDF]
-- profiles of people and jobs II [PDF]

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

HW1: (Due Wednesday, January 18) 1.1: 2abc, 3ac, 8, 9abcd, 11, 14, 15, 25; 1.2: 1cd, 2ab, 5ab, 10, 11ab, 15ab, 16, 17, 25. Since many did not yet have textbook, you can find a copy of the problems here [PDF]. You can also purchase a print copy or electronic version online at [amazon link].
HW2: (Due Wednesday, January 25) 1.3: 1b, 2ac, 4, 8ab, 9, 11, 15ab. 2.1: 1, 4, 6bc, 11bd, 15; 2.2: 1bd, 3ad, 4cd, 5ab, 7, 23;
HW3: (Due Wednesday, February 1) 2.3: 1, 3, 5, 29; 2.4: 1ad, 5, 6, 8; 3.1: 1ab, 2ab, 3, 4, 11, 18, 23;
HW4: (Due Wednesday, February 8) 3.2: 1ab, 3, 6; 3.3: 1ab, 3ab, 4ab, 7, 10;
HW5: (Due Wednesday, February 15) 3.4: 1ac, 3ac, 10; 3.5: 1, 3ad, 5ad, 14; 3.6 1ad, 3cd, 5;
HW6: (Due Wednesday, March 1) 4.1: 1ab, 3, 5ad, 22, 29; 4.3: 1ag, 3ag, 5ag, 15;

Additional Information

• Canvas Website

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