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B013437 - DIFFERENTIAL EQUATIONS OF MATHEMATICAL PHYSICS (INTRODUCTION)
Main information
Course Content
Suggested readings
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2010-11
Coorte 2010 - Second Cycle Degree in SCIENZE FISICHE E ASTROFISICHE
Course year
First year - Second Semester
Belonging Department
Physics and Astronomy
Course Type
Single education field course
Scientific Area
MAT/07 - MATHEMATICAL PHYSICS
Credits
3
Teaching Hours
24
Teaching Term
01/03/2011 ⇒ 23/06/2011
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Course Content
The use of PDE’s in Physics. First order equations. Classification of second order equations. Hyperbolic equations. Elliptic equations. Parabolic equations.
Suggested readings (Search our library's catalogue)
Inner notes are available
Prerequisites
Courses required: Calculus
Courses recommended: a course on ODE’s
Courses recommended: a course on ODE’s
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...):
75
Hours reserved to private study and other individual formative activities:
Contact hours for: Lectures (hours): 25
75
Hours reserved to private study and other individual formative activities:
Contact hours for: Lectures (hours): 25
Further information
Office hours:
Any time, on request
Any time, on request
Type of Assessment
Exam modality:
Oral examination
Oral examination
Course program
Course Contents (detailed program):
Examples of applications of PDE’s in Physics (Burgers’ equation, KdV equation and solitons, etc.)
First order equations. Shocks propagation. Classification of second order equations. Characteristic lines. Examples of ill posed problems.
Hyperbolic equations, the initial-boundary value problem, d’Alembert’s solution of the waves equation, Fourier’s method and Helmholtz’ equation, Riemann’s method, Goursat’s problem, method of descent.
Elliptic equations (Laplace and Poisson equations, harmonic functions), maximum principles, Green’s and Neumann’s functions, solution of the Dirichlet problem in the sphere and in a semi-infinite domain, representation formulas, relationship between harmonic and holomorphic functions, conformal mappings.
Parabolic equations, the heat equation, maximum principles, self-similar solutions, the fundamental solution, Green’s and Neumann’s functions, thermal potentials, the jump relation, representation formulas of solutions of initial-boundary value problems.
Examples of applications of PDE’s in Physics (Burgers’ equation, KdV equation and solitons, etc.)
First order equations. Shocks propagation. Classification of second order equations. Characteristic lines. Examples of ill posed problems.
Hyperbolic equations, the initial-boundary value problem, d’Alembert’s solution of the waves equation, Fourier’s method and Helmholtz’ equation, Riemann’s method, Goursat’s problem, method of descent.
Elliptic equations (Laplace and Poisson equations, harmonic functions), maximum principles, Green’s and Neumann’s functions, solution of the Dirichlet problem in the sphere and in a semi-infinite domain, representation formulas, relationship between harmonic and holomorphic functions, conformal mappings.
Parabolic equations, the heat equation, maximum principles, self-similar solutions, the fundamental solution, Green’s and Neumann’s functions, thermal potentials, the jump relation, representation formulas of solutions of initial-boundary value problems.