EQUATIONS OF MATHEMATICAL PHYSICS
Academic year and teacher
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- Versione italiana
- Academic year
- 2017/2018
- Teacher
- MARIA CRISTINA PATRIA
- Credits
- 7
- Didactic period
- Primo Semestre
- SSD
- MAT/07
Training objectives
- The aims of the course is to give to the students basic concepts about tensor analysis and continuum mechanics together with the basics on the partial differential equations (PDE). In particular the students know the principal equations of Mathematical Physics: Laplace, Fourier and d'Alembert equations.
The course aims to develop student's ability to address and solve mechanical problems.
At the end the student will know the basic topics of mathematical physics and its PDE and will expose with mathematical language the arguments. Prerequisites
- Good knowledge of differential and integral calculus of real functions in several variables and of ordinary differential equations.
Basic concepts of classical mechanics of a particle and rigid bodies. Course programme
- 56 hours are scheduled: Elements of Tensor Analysis and differential operators (15 hours)- Continuum Thermomechanics. Cauchy's Theorem for the existence of stress. Local forms of force and moment balances. Laws of thermodynamics. Ideal fluids and their properties(18 hours)- Basic concepts about partial differential equations (PDE) and classification of semi-linear PDE of two variables (8 hours)- Principal value-boundary problems for Laplace, Fourier and d'Alembert equations. Harmonic functions (15 hours).
Didactic methods
- Lectures on all the topics previously stated are scheduled. The theoretical discussion is supported by examples and exercises.
Learning assessment procedures
- The aim of the exam consists in verifying the level of knowledge of the formative objectives. The exam is oral; questions are asked on tensorial calculus, on continuum mechanics and on PDE. The resolution of an exercise is required. The student is invited to present a topic on the PDE of Mathematical Physics and to solve some exercises assigned during the lessons.
Each answer contributes to the final vote. Reference texts
- Notes are available at the course Web site.
Specific topics can be further developed on:
R. Gouyon: Calcul Tensoriel. Voibert, Paris, 1963
S. Salsa: Equazioni a derivate parziali: metodi, modelli e applicazioni. Springer Italia, 2004
M. E. Gurtin: Introduction to continuum mechanics. Academic Press, 1981
