Notes
AMSC/CMSC 460 - Spring 2018

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Principle Texts

We will primarily use the following texts for the course. Both texts are free and will contain most of the required readings for the course.

• Numerical Computing with MATLAB by Cleve Moler required
  This is the "recommended" text for the course. It is available for free online. We will roughly cover Chapters 1-7.
• Introduction to Numerical Analysis by Doron Levy required
  These excellent note will also be used frequently for the course.

Additional Notes

Here are a collection of notes and reading material for the course. They are from various sources and authors. I will also add personal notes for the class as the course progresses.

Required readings are marked with Required, while suggest readings marked with Suggested. Information about when to read these can be found in the course schedule page.

• Introduction, Errors, Machine Arithmetic
  1. Errors and where they come from Required
     Tobias vonPetersdorf
  2. Error Propagation and Roundoff Error Required
     Tobias vonPetersdorf
  3. Machine Numbers and Machine Arithmetic Required
     Tobias vonPetersdorf
  4. Errors and Arithmetic Suggested
     Dianne P. O'Leary
  5. Floating Point Representation and the IEEE Standard Suggested
     Michael L. Overton
• Solving Non-Linear Equations
  1. Non-linear Equations Suggested
     Tobias vonPetersdorf
• Numerical Linear Algebra
  1. Linear Systems Required
     Tobias vonPetersdorf
  2. Example for Gaussian Elimination with Pivoting Required
     Tobias vonPetersdorf
  3. Errors for Linear Systems Required
     Tobias vonPetersdorf
  4. Intro to Numerical Linear Algebra: Lecture 1 Suggested
     Jacob Bedrossian
  5. Intro to Numerical Linear Algebra: Lecture 2 (LU) Suggested
     Jacob Bedrossian
  6. Intro to Numerical Linear Algebra: Lecture 3 (LU w/ Pivoting) Suggested
     Jacob Bedrossian
  7. Intro to Numerical Linear Algebra: Lecture 4 (Cholesky) Required
     Jacob Bedrossian
• Interpolation
  1. Interpolation (Sections 3.5, 3.6) Required
     Tobias vonPetersdorf
  2. Splines Required
     Sam Punshon-Smith
  3. Splines Suggested
     Tobias vonPetersdorf
• Approximation of Functions: Least Squares
  1. The Linear Least Squares Problem Required
     Tobias vonPetersdorf
  2. Approximation of functions Suggested
     Jacob Bedrossian
• Numerical Differentiation
  1. Numerical Differentiation Suggested
     Jacob Bedrossian
• Numerical Integration
  1. Numerical Integration Suggested
     Tobias vonPetersdorf
  2. Numerical Integration Suggested
     Jacob Bedrossian
• Numerical Ordinary Differential Equations
  1. Ordinary Differential Equations Required
     Tobias vonPetersdorf
  2. Numerical Differential Equations Required
     Jacob Bedrossian
  3. Runge Kutta Required
     Jacob Bedrossian