Note

I have passed this course and will not keep updating this repository. Feel free to contribute missing solutions.

Notes, anki cards, and exercise solutions for Numerical Analysis

second edition, Timothy Sauer

This repository contains my attempts to solve the exercises given in the aforementioned book, during my enrolment in the Numerical Analysis course (FMNF05) at Lunds Tekniska Högskola (LTH) @ Lund University : Lund, Sweden - as part of my computer science program.

It also includes my notes, and you can find my anki cards here.

Feel free to submit an issue, or contact me, if you discover any errors or have intellectual property rights concerns.

This repository is part of a wider project of mine, to document my notes and exercises throughout my university degree. You can find more here :)

Running locally

If using this repository I strongly recommend installing MATLAB locally, and opening the repository in Visual Studio Code. Using the following command, after opening a terminal in Visual Studio Code, you can run MATLAB inside of Visual Studio Code:

matlab -nodesktop -nojvm -nosplash

Tip

Add the above command as some alias in Linux, by adding alias matlab-console = "matlab -nodesktop -nosplash" to your ~/.bashrc (or applicable for your shell) and then running source ~/.bashrc.

Additionally, using the recommended extensions, you can open relevant .pdf files and split your view for efficiency.

To run any function, start your MATLAB terminal, then cd into the directory and simply write the name of the file without the .m extension.

Chapters completed

• Chapter 0: Fundamentals (partial)
  • 0.1 Evaluating polynomials
    • Notes
    • Anki cards
    • Exercises
    • Computer problems
  • 0.2 Binary numbers
    • Notes
    • Anki cards
    • Exercises
  • 0.3 Floating Point Representation of Real Numbers
    • Notes
    • Anki cards
    • Exercises
  • 0.4 Loss of significance
    • Notes
    • Anki cards
    • Exercises (skipped)
    • Computer problems (skipped)
  • 0.5 Review of calculus
    • Notes
    • Anki cards
    • Exercises (skipped)

From this point on, I stopped doing the computer problems.

• Chapter 1: Solving equations
  • 1.1 The bisection method
    • Notes
    • Anki cards
    • Exercises
    • Computer problems
  • 1.2 Fixed-point iteration
    • Notes
    • Anki cards
    • Exercises
  • 1.3 Limits of accuracy
    • Notes
    • Anki cards
    • Exercises
  • 1.4 Newton's method
    • Notes
    • Anki cards
    • Exercises
  • 1.5 Root-finding without derivatives
    • Notes
    • Anki cards
    • Exercises

From this point on, I also stopped writing anki cards.

• Chapter 2. Systems of equations

  • 2.1
    • Notes
    • Exercises
  • 2.2
    • Notes
    • Exercises
  • 2.3
    • Notes
    • Exercises
  • 2.4
    • Notes
    • Exercises
  • 2.5
    • Notes
    • Exercises
  • 2.6
    • Notes
    • Exercises (just one)
  • 2.7
    • Notes (partial)
    • Anki cards
    • Exercises (just one)

• Chapter 3. Interpolation (partial)

  • 3.1
    • Notes
    • Exercises (partial)
  • 3.2
    • Notes
    • Exercises (partial)
  • 3.3
    • Notes
    • Exercises (partial)
  • 3.4
    • Notes
    • Exercises (partial)
  • 3.5 (skipped)
    • Notes (skipped)
    • Exercises (skipped)

• Chapter 4. Least squares (partial)

  • 4.1
    • Notes
    • Exercises (partial)
  • 4.2
    • Notes
    • Exercises (partial)
  • 4.3
    • Notes
    • Exercises (partial)
  • 4.4 (skipped)
    • Notes (skipped)
    • Exercises (skipped)
  • 4.5 (skipped)
    • Notes (skipped)
    • Exercises (skipped)

• Chapter 5. Numerical Differentiation and Integration (partial)

  • 5.1
    • Notes
    • Exercises (partial)
  • 5.2
    • Notes
    • Exercises (partial)
  • 5.3
    • Notes (partial)
    • Exercises (skipped) 5.4 and 5.5 are not part of my course

Chapters 6 through 9 are not part of my course

Chapter 10 coming soon (decided to skip, as it wasn't common on the exam)

Chapter 11 is not part of my course

• Chapter 12. Eigenvalues and Singular Values (partial)

  • 12.1
    • Notes
    • Exercises (partial)
  • 12.2
    • Notes
    • Exercises (partial)
  • 12.3
    • Notes
    • Exercises
  • 12.4
    • Notes

  Chapter 13 is not part of my course