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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:
  • None
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/



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