- The lab final exam is due Sunday April 22, 18:00 EST.
- The final exam is scheduled on Thursday April 19, starting at 9am, in Burnside Hall 1B23.
- It is a closed book, closed note exam. No calculators will be allowed or needed.
- There will be 5–6 questions, with each question comparable in difficulty to an "easier" question from the assignments.
- Please review the past assignments and the midterm exam.
- Here are some practice problems.

- In each of the categories (assignments, midterm, and final exam), the theory and lab parts will be equally weighted.

- Lab assignment 3 due Friday April 13, 18:00 EST
- Practice problems for the final exam
- Assignment 4 [tex] due Wednesday April 11 in class
- Midterm exam [tex] due Saturday March 17, 18:00 EST
- Assignment 3 [tex] due Wednesday March 14 in class
- Lab assignment 2 due Sunday March 4, 18:00 EST
- Assignment 2 [tex] due Friday February 23 in class
- Lab assignment 1 due Friday February 16, 18:00 EST
- Assignment 1 [tex] due Wednesday February 7 in class
- Instructor's office hours are T 11:00–12:00, WF 13:00–13:05, Burnside Hall 1123

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

Date |
Topics |

W 1/10 | Floating point numbers. Axiom 0. |

F 1/12 | Floating point arithmetic. Axiom 1. |

W 1/17 | Propagation of error. Roundoff error analysis of summation methods. |

F 1/19 | Products. Condition number of a function. Elementary analytic functions. |

W 1/24 | Roundoff error analysis of power series. Babylonian method. |

F 1/26 | Fixed point iterations. Newton-Raphson method. |

W 1/31 | Modified Newton. Reciprocal iteration. Complexity of division. Bisection. |

F 2/2 | Secant method. Regula falsi. Gaussian elimination. |

W 2/7 | LU decomposition. GEPP. Condition number of a matrix. |

F 2/9 | Gram-Schmidt orthogonalization. QR decomposition. |

W 2/14 | Householder's elimination. |

F 2/16 | Backward error analysis. |

W 2/21 | Backward stability of Housholder's elimination. |

F 2/23 | Some examples. Cholesky factorization. |

W 2/28 | Lagrange interpolation. Vandermonde matrices. |

F 3/2 | Newton's divided differences. Lebesgue's lemma. |

3/5–3/9 | Reading week |

W 3/14 | Peano kernel theorem. Weierstrass approximation theorem. |

F 3/16 | Bézier curves. Existence of minimax polynomials. |

W 3/21 | Oscillation theorems of de la Vallée-Poussin and Chebyshev. Chebyshev polynomials. |

F 3/23 | Least squares approximation. Legendre polynomials. |

W 3/28 | Dirichlet kernel. Chebyshev kernel. Lebesgue constants for Chebyshev truncation. |

F 3/30 | Good Friday |

W 4/4 | Newton-Cotes quadrature. Romberg integration. |

F 4/6 | Gauss quadrature. |

W 4/11 | Euler-Maclaurin formula. Bernoulli numbers. |

F 4/13 | Fourier series. Jackson's inequality. |

R 4/19 | Final exam (9am, in department) |

- Principles of Scientific Computing book draft by David Bindel (Cornell) and Jonathan Goodman (NYU)
- 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)

- Anaconda
- Python
- Introductory course and tutorials at DataCamp
- Python Wiki
- Getting started with SciPy

- 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

**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 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% + MAX { Midterm 20% + Final 50% , Final 70% }.