| Office | ||
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Eighth Floor Department of Mathematics University of Bologna Piazza di Porta S. Donato, 5 40127 Bologna |
Tel: +39 051 20 94482 Fax: +39 051 20 94490 Email: giulia.spaletta@unibo.it |
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 (tentative schedule for the current academic year).
1. Monday 17/2/2014, Ranzani Laboratory (Bologna, Via Ranzani 14B) 9-12.
During the first lecture,
all information will be given on the course;
each student must have a Computer Studies Department cs.unibo.it account
(further to the Bologna University studio.unibo.it account)
necessary to use Mathematica software
and resources available at the Ranzani Laboratory.
How to launch Mathematica from a Ranzani Lab workstation
Task: send me an email, from your Bologna University account,
containing your Name, Surname, Registration Number, Name of the Course, Year of Attendance.
Lecture notes and useful related documentation
Numerical Disasters
(html link)
Use the Virtual Book (HowTo)
The Structure of Mathematica (Tutorial)
Notebook Interface (Tutorial)
Working With Cells (Tutorial)
Create and Work with Cells (HowTo)
2. Wednesday 19/2/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Why studying Numerical Analysis
(pdf document)
First Calculation in Mathematica
Notebook (in pdf format) related to Mathematica
Menu: Help, Virtual Book, Introduction, Getting Started,
Your First Mathematica Calculation
3. Monday 24/2/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Introduction to Numerical Analysis
(pdf document)
Mathematica Lab and application to Economics
without all 3D figures
(pdf format)
4. Wednesday 26/2/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Finite Arithmetic
(Floating Point System by M.T. Heath)
Mathematica Lab and application to Economics
(nb format)
Lab Exercises on Linear Algebra
(nb format)
Lab Exercises on ODEs, Minimization, Linear Algebra
(nb format)
5. Monday 3/3/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Linear Problems
(taken from M.T. Heath)
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);
L U Factorization:
if A is nxn, the computational cost of LU is of the order of n^3 operations (2 n^3/3)
Q R Factorization:
if A is nxn, the computational cost of QR is of the order of n^3 operations (4 n^3/3)
ITERATIVE, convergent, matrix DECOMPOSITION methods
(usually best suited for sparse nxn matrices A;
computational cost is of the order of n^2 at each iteration and in some cases it can be lowered to n).
Jacobi Method and Gauss-Seidel Method
if A is nxn, the computational cost of each step is of the order of
n^2 operations (if A is nxn sparse, then the cost of each step is of the ordere on n)
6. Wednesday 5/3/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Interpolation
(help page)
InterpolatingPolynomial
(help page)
Fit
(help page)
LeastSquares
(help page)
Polynomial Interpolation
(wiki page)
7. Monday 10/3/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Numerical Differentiation
Differentiation
(tutorial)
Numerical Integration
Trapezoidal Rule
(Newton - Cotes Method)
Simpson Rule
(Newton - Cotes Method)
Newton - Cotes Methods
Integration
(tutorial)
Numerical Integration
(tutorial)
8. Wednesday 12/3/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Solving non linear equations requires iterative convergent methods.
Non Linear Problems
9. Monday 17/3/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Differential Equations
Numerical Methods for
Differential Equations
(by Gonze)
Differential Equations
(tutorial)
Introduction to
Numerical Differential Equations
(tutorial)
Solving Recurrence Equations
(tutorial)
10. Wednesday 19/3/2014, Lab. Ranzani, 9-12.
Lecture notes and useful related documentation
Monte Carlo Method
(from MathWorld)
Monte Carlo Integration
(from MathWorld)
Monte Carlo Method to approximate Pi
(link to the Numerical Analysis Project by J.H Matthews)
Monte Carlo Integration
(link to the Numerical Analysis Project by J.H Matthews)
Numerical Integration
Examples of determinstic or statistical approaches
Calculate Basic Descriptive Statistics
(How To)
Work with Statistical Distributions
(How To)
Perform a Monte Carlo Simulation
(How To)
11. Monday 24/3/2014, Lab. Ranzani, 9-12
12. Wednesday 26/3/2014, Lab. Ranzani, 9-12
Exam: Monday 31/3/2014, Aula + Lab. Ranzani, 9-13
Documentation.
- Students may find documentation to prepare for the lab activities at
the Wolfram Research sites:
Virtual Book
(Tutorial)
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.
Research interests
Related homepages