COURSE PRESENTATION FORM - MATHEMATICAL METHODS FOR PHYSICS - 2009/2010
COURSE NAME: Mathematical Methods for Physics
COURSE CODE: 70131
LECTURER: Leonardo Colletti
TEACHING ASSISTANT: None
TEACHING LANGUAGE: English
CREDIT POINTS: 4
LECTURE HOURS: 24
EXERCISE HOURS: 12
TIMESPAN: 22.02.2010 - 12.06.2010
TIMETABLE: see
Timetable Page
OFFICE HOURS LECTURER: Thursdays when exercise hour is scheduled, 15:00 - 16:00, Faculty of CS, Piazza Domenicani 3, office P2.10
OFFICE HOURS TEACHING ASSISTANT: --
PREREQUISITES
Differentiation and integration of a one-variable function and related practical skills.
The student is supposed to have taken and passed the Analysis exam.
OBJECTIVES
- differentiation and integration of multivariable functions.
- interpreting and solving ordinary differential equations.
- interpreting and solving partial differential equations.
- gaining some qualitative insights in physics and models.
- learning basic numerical approaches to differential equations.
SYLLABUS
Multivariable Calculus
- Many-variable functions.
- Differentiation of many-variable functions.
- Partial derivatives. The differential.
- The gradient. The directional derivative.
- The Hessian.
- Maxima and minima. Saddles. Lagrange multipliers.
- Multiple integrals.
- Flux, line integral, divergence and curl of a vector field.
- The divergence theorem. The Stokes theorem.
- Physical examples: gravitational, electric and magnetic fields.
Differential Equations
- Physics as paradigm for science: the search for description and predictability; quantitative models and equations.
- Differential equations: basic concepts.
- Initial-value and boundary-value problems.
- Ordinary differential equations.
- Basic principles of classical dynamics and electromagnetism.
- Application of first-order differential equations.
- Non linear differential equations.
- Partial differential equations.
- Heat transfer equation. Diffusion equation. Wave equation.
Numerical Analysis
- Zero and extremes of a function.
- Numerical differentiation.
- Numerical integration.
- Random number generators and Monte Carlo integration.
- Numerical methods for solving ordinary differential equations.
- Predictor-corrector methods. The Euler and Picard methods.
- The Runge-Kutta method.
- Numerical metods for solving partial differential equations.
TEACHING FORMAT
Frontal lectures
ASSESSMENT
Final exam only, written (100% of mark)
READING LIST
Textbook:
Reading suggestions:
SOFTWARE USED
None.
LEARNING OUTCOME
Insights into the scientific method, in particular about modellization and computation.
Ability in recognizing and interpreting a certain number of typologies of differential equations; solving skills, both analytical as well as numerical, with application to basic physical models.
COURSE PAGE
http://www.teleacademy.it/