


Politecnico di Torino  
Academic Year 2009/10  
15BCGFL Geometry 

1st degree and Bachelorlevel of the Bologna process in Environmental Engineering  Torino 





Objectives of the course
This course gives the students skills for problem analysis (hypothesis, thesis, demonstration). Linear algebra and analytical geometry are studied, connected to Mathematical analysis I and II.

Expected skills
Comprehension of liner algebra and skills in using it in problem solving. Good skills in solving analitical and differential geometry problems, explaining the methods used.

Prerequisites
Real and complex numbers, trigonometric calculus, simple and quadratic equations and inequalities, differential calculus in one variable.

Syllabus
1. Ordinary space vectors and their operations (sum; product).
2. Vectorial spaces in real and complex field. Spaces with a finite dimension. 3. Matrix and their operations. Reduced matrix, reduction method. 4. Linear systems. RouchèCapelli's theorem. Reductionmethod. 5. Linear applications. Linear applications in spaces with finite dimension. 6. Eigenvectors and eigenvalues. Simple endomorphisms. 7. Euclidean spaces and quadratic forms. 8. Plane analytical geometry. Etc. 9. Analytical geometry in space. Lines, planes, spheres, circumferences, curves, space surface, etc. 10. Differential calculus in many variables. Partial and directional derivative, gradient, divergence, rotor, differential, Taylor's formula. Etc. 11. differential geometry of curves and surface. 
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