## layer and the Euler-Bernoulli beam hypothesis is used to ..

Due to the implemented constitutive equations for elastoplas-tic material behaviour the element can be used to evaluate the load carrying capacity of beam structures.

Daniel Bernoulli is sometimes called the "Founder of Mathematical Physics."

Euler may be the most influential mathematicianwho ever lived (though some would make him second to Euclid);he ranks #77 on Michael Hart's famous list ofthe Most Influential Persons in History.

## beam theory of Jakob Bernoulli, ..

Linear Algebra: Vectors in Rn; Vector subspaces of Rn; Basis of vector subspace; Systems of Linear equations; Matrices and Gauss elimination; Determinants and rank of a matrix; Abstract vector spaces, Linear transformations, Matrix of a linear transformation, Change of basis and similarity, Rank-nullity theorem; Inner product spaces, Gram-Schmidt process, Orthonormal bases; Projections and least-squares approximation; Eigenvalues and eigenvectors, Characteristic polynomials, Eigenvalues of special matrices; Multiplicity, Diagonalization, Spectral theorem, Quadratic forms. Differential Equations: Exact equations, Integrating factors and Bernoulli's equation; Orthogonal trajectories; Lipschitz condition, Picard’s theorem; Wronskians; Dimensionality of space of solutions, Abel-Liouville formula; Linear ODE’s with constant coefficients; Cauchy-Euler equations; Method of undetermined coefficients; Method of variation of parameters; Laplace transforms, Shifting theorems, Convolution theorem.