Cours de mathématiques Tome 4 Equations différentielles by J.Lelong-Ferrand, J.M.Arnaudiès

By J.Lelong-Ferrand, J.M.Arnaudiès

Show description

Read Online or Download Cours de mathématiques Tome 4 Equations différentielles Intégrales multiples PDF

Similar mathematics_1 books

Mathematics, Affect and Learning: Middle School Students' Beliefs and Attitudes About Mathematics Education

This publication examines the ideals, attitudes, values and feelings of scholars in Years five to eight (aged 10 to fourteen years) approximately arithmetic and arithmetic schooling. essentially, this ebook makes a speciality of the advance of affective perspectives and responses in the direction of arithmetic and arithmetic studying. additionally, apparently scholars improve their extra adverse perspectives of arithmetic throughout the center university years (Years five to 8), and so the following we pay attention to scholars during this severe interval.

Additional resources for Cours de mathématiques Tome 4 Equations différentielles Intégrales multiples

Sample text

Basis of a vector space) A linearly independent set B of vectors is said to be a (Hamel) basis of V if every vector of V is a linear combination of the vectors in B. The vector space V is said to be finite dimensional if there exists a Hamel basis B consisting of finitely many vectors. It is not clear at the outset whether a vector space possesses a basis. Using Zorn's lemma, one can demonstrate the existence of a maximal linearly independent system of vectors in any vector space. ) Any maximal set is indeed a basis of the vector space.

Since Xl, X2 E M(X3, X4), it follows that M(xI, X2) = M(X3, X4). Consequently, there is one and only one line containing any two points. Consider now two different two-dimensional subspaces M (Xl, X2) and M(X3, X4) of V(F). The vectors x}, X2, X3 and X4 are linearly dependent as our vector space is only three dimensional. ) Obviously, y is non-zero. Clearly, the point y belongs to both the lines M(XI' X2) and M(X3, X4). This means that there is at least one point common to any two distinct lines.

8 1 n 8 2 = {a}. The following results give some properties of the operation + defined for subspaces. 7 Let 8 1 and 8 2 be two subspaces of a vector space V. Let 8 be the smallest subspace of V containing both 8 1 and 8 2 . Then (1) S = 8 1 + 82, (2) dim(S) = dim(8 1 ) + dim(S2) that 8 1 + 8 2 S dim(Sl n 8 2), PROOF. It is clear 8. Note that 8 1 + 8 2 is a subspace of V containing both 8 1 and 8 2. Consequently, 8 S 8 1 + S2. This establishes (1). • ,X r be a basis for 8 1 n 8 2, where r = dim(SI n 8 2).

Download PDF sample

Rated 4.51 of 5 – based on 33 votes