| Official Information |
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| Course Number: | Mathematics 3044.001 |
| Course Title: | Numerical Analysis II |
| Times: | TR 12:30-1:50 |
| Places: | BARTNB 205 |
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| Instructor: |
Benjamin Seibold |
| Instructor Office: | 518 Wachman Hall |
| Instructor Email: |
seibold(at)temple.edu |
| Instructor Office Hours: | T 11:15-12:15, R 2:00-3:00 |
| | |
| TA: | Shimao Fan |
| TA Office: | 515 Wachman Hall |
| TA Email: |
tub00072(at)temple.edu |
| TA Office Hours: | MW 2:00-3:30 |
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| Course Textbook: |
Brian Bradie,
A Friendly Introduction to Numerical Analysis,
Pearson Prentice Hall, 2006.
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| Official: | Course Syllabus |
| Prerequisites: | see Math Course Listing |
| Topics Covered: |
Adaptive quadrature, initial value problems of ordinary differential equations, Runge-Kutta methods, multistep methods, stiff problems, two-point boundary value problems, partial differential equations: Poisson equation, diffusion equation, advection equation. |
| Course Goals: | Provide a sound working base in numerical methods, increase ability to apply proper mathematical tools to specific situations, introduce computing technology using MATLAB and apply it to problem solving, increase ability to work independently and formulate problem solving approaches, provide a set of experiences that can be utilized in other courses and beyond the classroom. |
| Attendance Policy: | Attendance is required. |
| Course Grading: | A(100-92), A-(91-90),
B+(89-88), B(87-82), B-(81-80), C+(79-78), C(77-72), C-(71-70),
D+(69-68), D(67-62), D-(61-60), F(below 60).
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| Grading: | Homework 30%, Course project 30%, exams 40%; one midterm exam and one final exam. |
| Exam Dates: | Midterm exam TBA; final exam Thursday 05/03/2012 from 10:30-12:30. |
| Homework: | No late submits. No make-ups. Naked numbers are not
acceptable. Solutions must include a short write-up describing the problem,
your solution technique, and procedural details. To include a computer
printout use the cut and paste method for placement of materials in your work.
All things must be clearly labeled. |
| Computational Devices: |
You must ensure to have access to a computer, the internet, and the software package MATLAB to work on certain homework problems. MATLAB is available at various places on campus, for instance at the Tech Center. |
| Course Schedule |
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| 01/17/2012 Lec 1 |
Review and Overview |
| 01/19/2011 Lec 2 |
Numerical differentiation and Newton-Cotes quadrature |
| 01/24/2012 Lec 3 |
Adaptive quadrature (6.8) |
| 01/26/2011 Lec 4 |
Initial Value Problems of ODE: ODE theory, examples |
| 01/31/2012 Lec 5 |
Key numerical concepts (7.1), truncation errors, consistency, stability |
| 02/02/2011 Lec 6 |
Euler's method (7.2), Taylor methods (7.3) |
| 02/07/2012 Lec 7 |
Runge-Kutta methods (7.4) |
| 02/09/2011 Lec 8 |
Implicit Runge-Kutta methods, Adams-Bashforth methods (7.5) |
| 02/14/2012 Lec 9 |
Adams-Moulton methods (7.5), BFD methods (7.9), convergence and stability (7.6) |
| 02/16/2011 Lec 10 |
Adaptive step size control (7.7) |
| 02/21/2012 Lec 11 |
Absolute stability and stiff problems (7.9) |
| 02/23/2011 Lec 12 |
Two-Point Boundary Value Problems: Finite difference method (8.1) |
| 02/28/2012 Lec 13 |
Non-Dirichlet boundary conditions (8.2) |
| 03/01/2011 Lec 14 |
Non-linear BVP (8.3), shooting methods (8.4 & 8.5) |
| 03/13/2012 Lec 15 |
Elliptic Partial Differential Equations: Theory |
| 03/15/2011 Lec 16 |
Poisson equation on a rectangle (9.1) |
| 03/20/2012 Exam 1 |
Midterm Exam |
| 03/22/2011 Lec 17 |
Irregular domains (9.5), comments on suitable linear solvers |
| 03/27/2012 Lec 18 |
Parabolic Partial Differential Equations: Theory, method of lines (10.1) |
| 03/29/2011 Lec 19 |
Temporal discretization (10.1) |
| 04/03/2012 Lec 20 |
Large time steps and L-stability |
| 04/05/2011 Lec 21 |
Von-Neumann stability analysis (10.2), more general parabolic PDE (10.3) |
| 04/10/2012 Lec 22 |
Hyperbolic Partial Differential Equations: Examples, linear advection, upwind method (11.1) |
| 04/12/2011 Lec 23 |
Modified equation |
| 04/17/2012 Lec 24 |
Lax-Wendroff, Lax-Friedrichs |
| 04/19/2011 Lec 25 |
Wave equation, staggered grids |
| 04/24/2012 Lec 26 |
Course Project Presentations |
| 04/26/2011 Lec 27 |
Course Project Presentations |
| 05/03/2012 |
Final Exam |
| Matlab Programs |
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- A second order accurate solver for the time-dependent
heat equation; serves as a wrapper to test linear solvers:
temple3043_heateqn.m
- Simulation of an N-body problem in celestial mechanics.
The example contains the sun, earth, jupiter, and the
Voyager 1 probe, performing a swing-by at jupiter:
temple3044_voyager.m
- Perform numerical error analysis for the Poisson equation.
A differentiable but oscillatory right hand side is considered:
mit18336_poisson1d_error.m
- Solves the Poisson equation in 1d, 2d, and 3d, and plots
the sparsity patterns of the respective system matrices:
temple3044_poisson.m
- A finite difference solver for the 1D heat equation with
time-dependent boundary conditions. Can easily modified to
implicit time stepping schemes:
temple3044_heateqn.m
- Finite differences for the one-way wave equation,
additionally plots the von Neumann growth factor:
mit18086_fd_transport_growth.m
- Finite differences for the wave equation, using a leapfrog method:
mit18086_fd_waveeqn.m
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| Additional Course Materials |
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| Homework Problem Sets |
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| Course Projects |
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- Zachary Ankuda: Heat exchange of a modern CPU heat sink
- Matthew Berardi: Numerical methods of triangulating a geometry
- Alexander Gonzalez: Modeling Cymatic waves using Matlab
- Dylan Lexie: Tank wars in space
- Kathryn Lund: Numerical solution of bound-state resonances on a perturbed cylinder
- Elisheva Stern: Impact of driving behavior on fuel consumption
- Zhou Ye: Numerical methods to solve initial value problem of Stochastic Differential Equations (SDE)
The midterm project reports are due 03/15/2012.
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