43 Schedule
Warning
This schedule is subject to change.
Here is the planned course schedule: Assignments will be made available on Mondays and due the following Wednesday.
(L = Lecture, P = Problem Class, A = Assignment)
| Week # | Date | Topic | Assignments |
|---|---|---|---|
| 1 | Jan 21 | L1: Introduction to Math 5486. Note: no lecture on Jan 19 |
A1: Notebooks & Prerequisites, Due: Jan 28, 23:59 Read: Section 5.1 and 5.2 up to “Error bounds for Euler” of Burden, Faires, and Burden (2015) |
| 2 | Jan 26, 28 | Chapter 1: Numerical Methods for Initial Value Problems L2: Basic theory of IVPs L3: Euler’s Method |
Read: Section 5.2, 5.3 of Burden, Faires, and Burden (2015) |
| 3 | Feb 2, 4 | L4: Higher order methods P1: Exercises |
A2: Systems of IVP, Due: Feb 11, 23:59 Read: Sections 5.4, 5.5 of Burden, Faires, and Burden (2015) |
| 4 | Feb 9, 11 | L5: Runge-Kutta Methods L6: Multistep Methods |
Read: Section 5.6 of Burden, Faires, and Burden (2015), zero stability of Driscoll and Braun (2018) |
| 5 | Feb 16, 18 | L7: Zero Stability Chapter 2: Iterative Methods in Matrix Algebra L8: Reminders on matrix analysis, direct methods, condition numbers, Jacobi & Gauss-Seidel methods |
A3: Absolute Stability Due: Feb 25, 23:59 (catch up on reading) Read 7.1-7.3 Burden, Faires, and Burden (2015) |
| 6 | Feb 23, 25 | P2: Exercises, L9: Krylov subspace methods I |
Read: Sections 7.4, 7.5 Burden, Faires, and Burden (2015) |
| 7 | Mar 2, 4 | L10, L11: Krylov subspace methods II | Read: Section 7.6 Burden, Faires, and Burden (2015) Note: no assignment - revise for midterm instead! |
| . | . | Note: Spring break, no lectures | . |
| 8 | Mar 16, 18 | Revision Session, Midterm Exam |
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| 9 | Mar 23, 25 | Chapter 3: Finite Differences for Boundary Value Problems L12: Reminders and theory L13: BVP I |
A4: Sparse Arrays Due: Apr 1, 23:59 Read: Burden, Faires, and Burden (2015) 11.1, 11.2: Shooting method |
| 10 | Mar 30, Apr 1 | L14, L15: BVP II | Read: Lecture notes on stability (lectures 14 and 15) |
| 11 | Apr 6, 8 | P3: Exercises, L16: Galerkin & Finite Elements |
A5: Fast Fourier Transform Due: Apr 15, 23:59 Read: Driscoll and Braun (2018) Galerkin method |
| 12 | Apr 13, 15 | L17: Convergence of finite elements Chapter 4: Partial Differential Equations L18: PDE I |
Read: Chapter 14.4 of Suli and Mayers (2012): Theorem 14.6 |
| 13 | Apr 20, 22 | L19: Methods for Heat Equation, L20: Methods for Wave Equation |
A6: Transport Equation Due: Apr 29, 23:59 |
| 14 | Apr 27, 29 | Presentations | Read: TBC |
| 15 | May 4 | Revision Session Note: no (official) lecture on May 6 - I’ll be around in the classroom for an extra office hours - feel free to come and work/ask questions/listen to other people’s questions… |
. |
| . | May 11 | Final Exam | . |
43.1 Important dates
Please see Spring 2026 Calendar for important dates.
Burden, Richard L., Douglas J. Faires, and Annette M. Burden. 2015. Numerical Analysis. 10th ed. CENGAGE Learning.
Driscoll, Tobin A, and Richard J Braun. 2018. Fundamentals of Numerical Computation. https://fncbook.com/.
Suli, Endre, and David F Mayers. 2012. An Introduction to Numerical Analysis. Cambridge, England: Cambridge University Press.