Course Schedule
AMSC/CMSC 460 - Spring 2018
Below is a course schedule. It contains an outline of course topics and reading assignments. Most of the readings are from the book by Moler and the Notes by Levy (see the list of principle texts for more information on how to get these). Other notes will be used where Moler and Levy fall short (see notes for a more detailed list).
I will from time to time add other supplementary notes to the notes page.
Note: This schedule is approximate and will evolve as the course progresses. Lectures
may be rearranged and split between days.
| Date | Material | Reading |
|---|---|---|
| Introduction, Errors, Machine Arithmetic | ||
| Th 1/25 | Error, Conditioning, Stability | vonPetersdorf [1], [2] |
| Tu 1/30 | Floating Point Arithmetic, IEEE 754 | Moler §1.7 vonPetersdorf [3] |
| Finding Roots: Solving Nonlinear Equations | ||
| Th 2/1 | Iterative Methods, Bisection |
Moler §4.1
Levy §2.1, 2.3 |
| Tu 2/6 | Newton's Method and Secant Method | Moler §4.2, 4.3
Levy §2.2, 2.4 |
| Th 2/8 | Order of Convergence and Error Analysis | Moler §4.4
Levy §2.5 |
| Numerical Linear Algebra (NLA): Solving Linear Systems | ||
| Tu 2/13 | Gaussian Elimination, $LU$ Decomposition | Moler §2.4, 2.5 vonPetersdorf [1] |
| Th 2/15 | $LU$ Decomposition with Pivoting | Moler §2.6, §2.7 vonPetersdorf [1], [2] |
| Tu 2/20 | Special Structure, SPD, Cholesky Factorization | Moler §2.10 Bedrossian [4] |
| Th 2/22 | Operations, Errors, Condition number | Moler §2.8, §2.9 vonPetersdorf [3] |
| Tu 2/27 | First Midterm Exam | |
| Approximation of Functions: Interpolation | ||
| Th 3/1 | Polynomial Interpolation, Lagrange | Moler §3.1, §3.2 Levy §3.1, §3.2, §3.5 |
| Tu 3/6 | Newton, Divided Differences | Levy §3.3, §3.6 |
| Th 3/8 | Error, Chebyshev Nodes | Levy §3.7, §3.8 vonPetersdorf [1] (only sections 3.5, 3.6) |
| Tu 3/13 | Hermite Interpolation | Moler §3.3 Levy §3.9 |
| Th 3/15 | Spline Interpolation | Moler §3.5 Levy §3.10 Punshon-Smith [1] New Notes |
| Tu 3/20 | Spring Break - No Class | |
| Th 3/22 | Spring Break - No Class | |
| Approximation of Functions: Least Squares | ||
| Tu 3/27 | Linear Least Squares | Levy §4.1, §4.3
vonPetersdorf [1] |
| Th 3/29 | Orthogonal Polynomials, Weighted Least Squares | Levy §4.3 |
| Numerical Differentiation | ||
| Tu 4/3 | Interpolation and Finite Difference | Levy §5.1, §5.2 |
| Th 4/5 | Richardson Extrapolation | Levy §5.3, §5.4 |
| Tu 4/10 | Second Midterm Exam | |
| Numerical Integration | ||
| Th 4/12 | Basic Quadrature and Interpolation | Moler §6.1 Levy §6.1, §6.2 |
| Tu 4/17 | Composite Methods, Undetermined Coefficients | Moler §6.2
Levy §6.3, §6.4, §6.5 |
| Th 4/19 | Weighted Quadrature, Gaussian Methods | Levy §6.6 |
| Tu 4/24 | Romberg Integration, Extrapolation | Levy §6.7 |
| Numerical Ordinary Differential Equations (NODEs) | ||
| Th 4/26 | Euler Methods, Error |
Moler §7.4
vonPetersdorf [1] Bedrossian [1] |
| Tu 5/1 | Implicit Schemes and stability | vonPetersdorf [1] |
| Th 5/3 | Runge-Kutta Methods | Bedrossian [1] Section 1 |
| Tu 5/8 | Extra Topic, Buffer Day, Review | |
| Th 5/10 | Extra Topic, Buffer Day, Review |
- Sam Punshon-Smith 2018