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
• Numerical Linear Algebra
• Power Method for Eigenvalues and Eigenvectors
• Iterative Methods for Solving Ax = b
• Preconditioners
• Multigrid Methods
• 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/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. One 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:

• Midterm on Wednesday, May 17.
• 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
  • 

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]
  • Generate Markdown within Notebook: [PDF] Δ [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 Blaine Quackenbush.

• Blaine Quackenbush TA Office Hours:
  • Tues 10-11am in SH 6432V,
  • Mon 5-7pm in MathLab in SH 1607.
• Additional general help also available: Mon, Tues, Wed, Thurs, 5-7pm in MathLab in SH 1607.

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

• Midterm Outline [PDF].

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

HW1: (Due Wednesday, April 12) 4.1 2ab, 4, 6bc, 8, 23, 29; 4.3: 1bce, 3bc, 5bc, 15bc;
HW2: (Due Wednesday, April 19) 5.1: 1acd, 3, 5, 6cd, 7, 10; 5.2: 2ab, 4ab, 5cd, 7, 10, 12, 16; 5.3: 1bd, 3, 6bc, 8, 10.
HW3: (Due Wednesday, April 26) 5.4: 2bcd, 3ab, 7, 15; 5.6: 2bcd, 4bcd, 6, 17, 19. 5.9: 1ab, 4ab, 6, 7.
HW4: (Due Friday, May 5) 5.10: 1, 2, 4, 6, 7; 5.11: 2bc, 4, 6, 8, 11, 13.
HW5: (Due Friday, May 12) 6.1: 1bd, 3ab, 5bd; 6.2: 1bc, 3, 7, 10b, 12; 6.3: 3bc, 5bc, 9;
HW6: (Due Monday, May 22) 6.4: 2, 6; 6.5: 3, 11; 6.6: 1, 4; 7.1: 2cd, 4cd, 9.
HW7: (Due Monday, May 29) 7.2: 2af, 4, 6; 7.3: 1b, 2cd, 4, 6, 8, 10, 18; 7.5: 1cd, 3cd.

Additional Information

• Canvas Website

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