Textbook: «Numerical Analysis» by T. Sauer, 3rd edition — Homework assignments and computer problems are from this book!!!
Programming requirements: familiarity with Matlab or Octave is REQUIRED to complete the computer problem assignments
Assignments: 20 homework problems and 20 computer problems from the book, listed on Blackboard
Assignment submission: online via Blackboard
Assignments due: next Friday after the week the topic is covered. Two exceptions: the Thanksgiving week, in which case the homework is deferred until Monday, and the last week, in which case the homework is due on the last day of classes (the deadline for each problem is also specified on Blackboard).
Assignment grading: Each problem will be weighted equally (or, in other words, will be worth the same amount of points).
Late assignments: two points will be subtracted from the score (which roughly corresponds to minus one letter grade).
Exams: Two midterm exams (both in-class) and the final exam.
Exam dates:
| First midterm – | Friday October 4 |
| Second midterm – | Friday November 1 |
| Final exam – | Friday December 13, 10:30 am – 12:30 pm |
Missed exams: no make-ups, unless I decide that there was a compelling reason.
Final grade calculation:
| Homework problems | 20% |
| Computer problems | 20% |
| First midterm exam | 15% |
| Second midterm exam | 15% |
| Final exam | 30% |
| Total | 100% |
Tentative cut-offs for final grades:
| A: | ≥85% |
| B: | ≥70% |
| C: | ≥60% |
| D: | ≥50% |
Syllabus and assignments: (HW – homework problems, CP – computer problems)
| Class date | Topics (book section and title) | HW | CP | Due date |
|---|---|---|---|---|
| Week 1 | ||||
| August 26 | Introduction, course policy, Octave discussion | |||
| August 28 | 3.1: Lagrange interpolation polynomial | 3.1-1 | September 6 | |
| August 30 | 3.1: Newton's divided differences | 3.1-2 | 3.1-1 | September 6 |
| Week 2 | ||||
| September 2 | Labor day – no classes | |||
| September 4 | 3.2: The error of interpolation | 3.2-2 | 3.2-1 | September 13 |
| September 6 | 3.3: Chebyshev polynomials | 3.3-1 | 3.3-4 | September 13 |
| Week 3 | ||||
| September 9 | 1.1: Bisection | 1.1-6 | 1.1-2 | September 20 |
| September 11 | 1.2: Fixed point iteration | 1.2-8 | September 20 | |
| September 13 | 1.4: Newton's method (quadratic convergence) | |||
| Week 4 | ||||
| September 16 | 1.4: Newton's method (linear convergence) | 1.4-3 | 1.4-2 | September 27 |
| September 18 | 1.5: Secant and false position methods | 1.5-2 | 1.5-1 | September 27 |
| September 20 | 1.5: IQI and Brent's methods | |||
| Week 5 | ||||
| September 23 | 13.1: Golden section search | 13.1-2 | 13.1-1 | October 4 |
| September 25 | 13.1: Successive parabolic interpolation | |||
| September 27 | 2.2: LU-factorization | 2.2-2 | 2.2-1 | October 4 |
| Week 6 | ||||
| September 30 | 2.3: Errors and condition number | 2.3-1 | 2.3-1 | October 11 |
| October 2 | Review before the first midterm exam | |||
| October 4 | First midterm exam, covers 1.1–1.5, 3.1–3.3, 13.1 | |||
| Week 7 | ||||
| October 7 | 2.5: Jacobi and Gauss-Seidel methods | 2.5-1 | 2.5-1 | October 18 |
| October 9 | 2.5: Convergence of iterative methods | |||
| October 11 | 4.1: Least squares and normal equations | 4.1-1 | 4.1-1 | October 18 |
| Week 8 | ||||
| October 14 | 4.3: Gram–Schmidt orthogonalization | |||
| October 16 | 4.3: QR-factorization | 4.3-1 | 4.3-1 | October 25 |
| October 18 | 2.7: Newton method | 2.7-4 | October 25 | |
| Week 9 | ||||
| October 21 | 2.7: Broyden method | 2.7-8 | November 1 | |
| October 23 | 13.2: Newton's method | 13.2-2 | November 1 | |
| October 25 | 13.2: Steepest descent | |||
| Week 10 | ||||
| October 28 | 13.2: Conjugate gradient method | |||
| October 30 | Review before the second midterm | |||
| November 1 | Second midterm exam, covers 2.2–2.3, 2.5, 2.7, 4.1, 4.3, 13.2 | |||
| Week 11 | ||||
| November 4 | 5.1: Finite difference formulas | 5.1-1 | November 15 | |
| November 6 | 5.1: Richardson's extrapolation | 5.1-11 | November 15 | |
| November 8 | 5.2: Trapezoid and Simpson's rules | 5.2-3 | 5.2-8 | November 15 |
| Week 12 | ||||
| November 11 | 6.1: Formulation of IVP, Euler's method | 6.1-1 | November 22 | |
| November 13 | 6.2: Local and global truncation error | |||
| November 15 | 6.2: Heun's method; 6.4: The midpoint method | 6.2-1 | November 22 | |
| Week 13 | ||||
| November 18 | 6.4: The RK2 family, Ralston's method | |||
| November 20 | 6.6: Stability, backward Euler method | 6.6-4 | December 2 | |
| November 22 | 8.1: Heat equation, forward and backward difference methods | 8.1-3 | December 2 | |
| Week 14 | ||||
| November 25 | 8.1: Von Neumann's stability analysis | 8.1-4 | December 6 | |
| November 27 | 8.2: Wave equation, finite difference method | 8.2-4 | December 6 | |
| November 29 | Thanksgiving – no classes | |||
| Week 15 | ||||
| December 2 | 8.2: Courant – Friedrichs – Lewy condition | 8.2-2 | December 6 | |
| December 4 | 8.3: Poisson equation, finite difference method | |||
| December 6 | Review before the final exam |
Sample exams:
2011 Midterm 1, 2011 Midterm 2, 2011 Final.
2015 Midterm 1, 2015 Midterm 2, 2015 Final.
Summer 2019 Midterm 1, Summer 2019 Midterm 2, Summer 2019 Final.
Note that I changed the syllabus somewhat for this year, so the past
exams do not necessarily cover the same material.
I will be continuously updating this webpage as the course progresses. Please watch this webpage, although I will try to announce any further changes by e-mail.