Official Information 
Course Number:  Mathematics 3044.001 
Course Title:  Numerical Analysis II 
Times:  TR 12:301:50 
Places:  BARTNB 205 
 
Instructor: 
Benjamin Seibold 
Instructor Office:  518 Wachman Hall 
Instructor Email: 
seibold(at)temple.edu 
Instructor Office Hours:  T 11:1512:15, R 2:003:00 
 
TA:  Shimao Fan 
TA Office:  515 Wachman Hall 
TA Email: 
tub00072(at)temple.edu 
TA Office Hours:  MW 2:003:30 
 
Course Textbook: 
Brian Bradie,
A Friendly Introduction to Numerical Analysis,
Pearson Prentice Hall, 2006.

 
Official:  Course Syllabus 
Prerequisites:  see Math Course Listing 
Topics Covered: 
Adaptive quadrature, initial value problems of ordinary differential equations, RungeKutta methods, multistep methods, stiff problems, twopoint 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(10092), A(9190),
B+(8988), B(8782), B(8180), C+(7978), C(7772), C(7170),
D+(6968), D(6762), D(6160), F(below 60).

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 10:3012:30. 
Homework:  No late submits. No makeups. Naked numbers are not
acceptable. Solutions must include a short writeup 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 
01/17/2012 Lec 1 
Review and Overview 
01/19/2011 Lec 2 
Numerical differentiation and NewtonCotes 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 
RungeKutta methods (7.4) 
02/09/2011 Lec 8 
Implicit RungeKutta methods, AdamsBashforth methods (7.5) 
02/14/2012 Lec 9 
AdamsMoulton 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 
TwoPoint Boundary Value Problems: Finite difference method (8.1) 
02/28/2012 Lec 13 
NonDirichlet boundary conditions (8.2) 
03/01/2011 Lec 14 
Nonlinear 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 Lstability 
04/05/2011 Lec 21 
VonNeumann 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 
LaxWendroff, LaxFriedrichs 
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 
 A second order accurate solver for the timedependent
heat equation; serves as a wrapper to test linear solvers:
temple3043_heateqn.m
 Simulation of an Nbody problem in celestial mechanics.
The example contains the sun, earth, jupiter, and the
Voyager 1 probe, performing a swingby 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
timedependent boundary conditions. Can easily modified to
implicit time stepping schemes:
temple3044_heateqn.m
 Finite differences for the oneway 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

Additional Course Materials 

Homework Problem Sets 

Course Projects 
 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 boundstate 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.
