- Docente: Daniele Ritelli
- Credits: 3
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Financial Markets and Institutions (cod. 0901)
Learning outcomes
Basic Operations on Numbers, Expressions, and Functions
- Numerical Calculations and Built-in Functions
- Expressions and Functions: Elementary Algebra
- Graphing Functions, Expressions, and Equations
- Solving Equations
Course contents
Overview on Computer Algebra
Simplification to a smaller expression or some standard form, simplification with constraints substitution of symbols or numeric values for certain expressions
Change of form of expressions: expanding products and powers, partial and full factorization, rewriting as partial fractions, constraint satisfaction, rewriting trigonometric functions as exponentials.
Partial and total differentiation
Symbolic constrained and unconstrained global optimization
Some indefinite and definite integration (see symbolic integration)
Solution of some differential and difference equations
Series operations such as expansion, summation and products
Matrix operations including products, inverses, etc.
Black Sholes Equation:
Integral transforms
Symbolic validation of the solution using Mathematica
Derivation of Basic Option Prices
Readings/Bibliography
P. Antognini
G.C, Barozzi
Matematica & Mathematica
Zanichelli 1995
D. Malchiodi
FARE MATEMATICA con Mathematica
Pearson 2007
W.T. Shaw
Modelling Financial derivatives with Mathematica
Cambridge University Press 1998
Teaching methods
Direct usage of Scientific Software shared using video beamer
Assessment methods
Elaboration of a notebook to solve problems assigned by the instructor
Teaching tools
Laptop, Tablet, Video Beamer
Links to further information
https://www.wolfram.com/mathematica/trial/
Office hours
See the website of Daniele Ritelli