Giulia Spaletta
Italian
version
 Teaching
activity
NUMERICAL ANALYSIS (Laurea Magistrale Quantitative
Finance)
 Students are invited to control this site
regularly.
 Please, note that I will not
answer emails containing questions whose answer is in this
page.
Note also that enrolled students are required to send me emails
from their unibo institutional address
(name.surname@studio.unibo.it); I might not receive/answer
enrolled students' emails not sent from their unibo address.
 Lectures.
1. Wednesday 15/2/2012, 9-12, AULA 2 (Bologna, Piazza Scaravilli 2,
ground floor).
During the first lecture, all information will be given on the
course and on the account-test (how to prepare for it and
when/where it will take place), necessary to use Mathematica
software and resources available at the Ranzani Laboratory.
The account-test will take place at the Lab. Ranzani, at the
beginning of the second or third lecture.
Task 1: send me an email, from your Bologna University
account, containing your Name, Surname, Registration Number, Name
of the Course, Year of Attendance.
Task 2: fill in the form at account.cs.unibo.it, print it on
paper, sign it, take it with you at the next lecture.
Task 3: study the database
of questions, to prepare for the account test. The database is
partially translated into English. It will be updated (with new
translated questions) during these days, so please, keep
re-checking it.
Documents/links used during lecture 1
Numerical
Disasters
A
student's introduction to Mathematica video by Cliff
Hastings
Useful related documentation
The Structure of Mathematica (tutorial)
Notebook Interface (tutorial)
Getting Started (tutorial)
Getting Information from Mathematica (tutorial)
The Mathematica System (tutorial)
2. Monday 20/2/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12. Account-test will start at 10.30.
Documents/links used during lecture 2
Sources of Error by A. Kaw and L. Snyder
(http://numericalmethods.eng.usf.edu)
Measuring Errors by A. Kaw and L. Snyder
(http://numericalmethods.eng.usf.edu)
3. Wednesday 22/2/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12. Students that still need to take the account test, will take
it at the end of the lecture (at 11.45 ish).
Approximation
and Errors by Wen-Chieh Lin
(http://caig.cs.nctu.edu.tw/course/NM/), inspired by M.T. Heath's
slides
(http://www.cse.illinois.edu/heath/scicomp/notes/chap01.pdf)
4. Monday 27/2/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12.
Floating
Point System by M.T. Heath
Useful related documentation
Types of Numbers (tutorial)
Exact and Approximate Results (tutorial)
Numerical Precision (tutorial)
Arbitrary Precision Calculations (tutorial)
Machine Precision Calculations (tutorial)
Arithmetic (tutorial)
Numerical Mathematics in Mathematica (tutorial)
The Uncertainties of Numerical Mathematics (tutorial)
5. Wednesday 29/2/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12. Linux commands:
cd (change directory; by default, it takes us to our home
directory)
cd directoryname (it takes us inside directory
directoryname)
mkdir directoryname (it creates the directory
directoryname)
ls (it list files inside current directory)
ssh -X -l accountname machinename (it allows the user
accountname to connect from the local computer to another
computer machinename, retaining graphic interface
capabilities)
mathematica & (it launches mathematica in the
background)
Lecture
Notebook on Setting up vectors and matrices, visualizing them
via MatrixForm, solving linear systems.
Vectors and Matrices (tutorial)
Vector Operations (tutorial)
Constructing matrices (tutorial)
Basic Matrix Operations (tutorial)
6. Monday 5/3/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12.
Lecture
Notebook (nb format)
Lecture
Notebook (pdf format)
Solving Linear Systems (tutorial). Solving linear equations A
x = b can be performed via: direct, stable, matrix
factorization methods (usually best suited for dense nxn matrices
A; computational cost is of the order of n^3 operations);
iterative, convergent, matrix decomposition methods (usually best
suited for sparse nxn matrices A; computational cost s of the order
of n at each iteration).
Useful related documentation
LinearSolve
(help page)
L U
Decomposition: if A is nxn, the computational cost of LU is of
the order of n^3 operations (2 n^3/3)
LUDecomposition (help page)
Q R
Decomposition: if A is nxn, the computational cost of QR is of
the order of n^3 operations (4 n^3/3)
QRDecomposition (help page)
LeastSquares
(help page)
Eigenvalues and Eigenvectors (tutorial)
7. Wednesday 7/3/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12.
Do Basic
Algebra with Mathematica
Do Basic
Calculus with Mathematica
Finding Limits (tutorial)
Differentiation (tutorial)
D
(help page)
Integration (tutorial)
Integrate
(help page)
Numerical Integration (tutorial)
NIntegrate
(help page)
8. Monday 13/3/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12.
Equations
(tutorial)
Solving Equation (tutorial). Solving non linear equations
requires iterative convergent methods.
Simultaneous Equations (tutorial)
Numerical Equation Solving (tutorial)
Useful related documentation
Solve
(help page)
NSolve
(help page)
FindRoot
(help page)
Inequalities (tutorial)
Minimization and Maximization (tutorial)
Numerical Optimization (tutorial)
9. Wednesday 15/3/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12.
DSolve
(help page)
NDSolve
(help page)
Useful related documentation
Differential Equations (tutorial)
Introduction to Numerical Differential Equations
(tutorial)
Solving Recurrence Equations (tutorial)
10. Monday 19/3/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12.
Course evaluation.
Interpolation
(help page)
InterpolatingPolynomial (help page)
Fit
(help page)
Manipulating Numerical Data (tutorial)
Curve Fitting (tutorial)
Approximate Functions and Interpolation (tutorial)
Useful related documentation
Basic Statistics (tutorial)
Create Plots
using Mathematica
11. Wednesday 21/3/2012, Lab. Ranzani (Bologna, Via Ranzani 14B)
9-12.
Exam simulation.
Results
Tuesday 3/4/2012: exam.
Results
Monday 4/6/2012: exam. It is compulsory to be in the
online Almaesami list.
Documentation.
- Students may find documentation to prepare for the lab activities
at the Wolfram Research sites:
HowTo
Hands-on-Tutorials
- Suggested reading, available at various Department Libraries
of Bologna University:
Hal R. Varian, Computational economics and finance: modeling and
analysis with Mathematica, New York, Springer Telos, 1996.
- 2001-2007. Computer Science: Numerical Analysis
(AN-MZ). Lectures and Lab. activities.
Syllabus
- 1996-2001. Computer Science: Numerical Analysis
(AN). Seminars and Lab. activities.
- 1999-2003 and 2008-current. Computer Science: Computational
Mathematics (MC): symbolic calculus in
Mathematica. Lectures and Lab. activities.
- 1994-1997. Computer Science: Approximation Methods
(MA). Seminars on graphics programming.
- 1992-1994. Computer Science: Approximation Methods
(MA). Lab. activities.
- 1991-2000. Computer Science: Numerical Calculus
(CNum). Seminars and Lab. activities.
- 1991-1994. Computer Science (in Cesena): Optimization Theory
and Methods (TMO). Lab. activities.
- 2006-2009. Industrial Chemistry: Numerical Calculus
(CN). Lectures.
Syllabus
- 2006-2009. Industrial Chemistry: Numerical Computing
Laboratory: (LCN). Lab. activities.
Syllabus
- 2004-2007. Management Sciences (in Pescara): Mathematical
Methods and Development Dynamics (MMDS). Lectures.
- 2010-current. Quantitative Finance: Numerical Analysis
(QFNA). Lectures.
- 1999-current. Medical Studies: Fundamentals of
Informatics (IG). Lectures.
Syllabus
- 2001-current. Medical Studies: Calculus and Programming
Laboratory (LPC). Lab. activities.
Syllabus
- 1997-1998. Pharmacy: Fundamentals of Mathematics
(FM). Lectures. Syllabus
Research
interests
- Numerical Linear Algebra and Parallel Computing: direct methods
for large dimension linear systems with structure; iterative
methods for highly nonlinear systems; regularization for highly ill
conditioned problems; Medical and Astronomical Imaging
- Symbolic and Numerical Calculus in Mathematica: ordinary
differential equations integrators (ODEs); Geometric Integration;
elementary differential Runge - Kutta methods (EDRKs); rounding
error analysis and automatic control
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