**Instructor:** Dr. Gantumur Tsogtgerel

**Prerequisite:** MATH 325 (Honours ODE) or MATH 315 (ODE), COMP 202 or permission of instructor.

**Corequisite:** MATH 255 (Honours Analysis 2) or MATH 243 (Analysis 2).

**Restriction:** Intended primarily for Honours students.

**Calendar description:**
Error analysis.
Numerical solutions of equations by iteration.
Interpolation.
Numerical differentiation and integration.
Introduction to numerical solutions of differential equations.

**Topics to be covered:**

- Absolute and relative precision. Evaluation of Taylor series.
- Root finding. Bisection. Fixed point iterations. Newton-Raphson method.
- General theory of error analysis and concept of stability.
- LU and QR factorizations.
- Newton's method. Steepest descent. Simple iterative methods.
- Interpolation. Newton's divided differences. Lagrange and Hermite polynomials.
- Least squares and uniform approximations.
- Numerical differentiation. Quadrature.
- Eigenvalue solvers and SVD (if time permits).
- Computation with polynomials. Fast Fourier transform (if time permits).
- Introduction to ODE integrators (if time permits).

**Homework:** We will have 3–4 homework assignments. Each assignment will consist of theoretical and programming components.

**Exams:** A midterm exam and a final exam. The midterm will most probably be a take-home exam,
and the final will consist of a theory exam in class,
and a programming ("lab") exam to be done at home.

**Grading:** Homework 30%, Midterm 20%, Final 50%.

- E. Süli.
*An introduction to numerical analysis*. Cambridge University Press 2003 - G. Dahlquist and A. Bjorck.
*Numerical methods*. Dover 2003 - L.R. Scott.
*Numerical analysis*. Princeton University Press 2011

- Anaconda
- Introduction to Python at DataCamp
- Getting started with SciPy
- Applied Numerical Computing by Prof. Lieven Vandenberghe (UCLA)
- Significant figures. Suggestions to Authors of the Reports of the United States Geological Survey
- David Goldberg. About floating-point arithmetic [pdf] [published version]
- Notes, Presentations, Simulations in Maple, Mathcad, Matlab, Mathematica, and Self-Assessment Tests at Holistic Numerical Methods Institute
- Lecture Notes and other resources by Professor Kendall Atkinson (University of Iowa)
- Homepage of Lloyd N. Trefethen
- Endre Suli's homepage (scroll down to see the "Lecture notes" section)

- WF 11:35–12:55, Burnside Hall 1205
*Note*: This schedule is subject to revision during the term.

Date |
Topics |

W 1/10 | ... |

F 1/12 | ... |

... | ... |

3/5–3/9 | Reading week |

... | ... |

F 3/30 | Good Friday |

W 4/4 | ... |

F 4/6 | ... |

W 4/11 | ... |

F 4/13 | ... |