Classes

Kinematics: configuration, deformation and movement. Fundamental principles of mechanics: principle of conservation of mass, principle of virtual powers (conservation of linear and angular momentum), principle of conservation of energy (first law of thermodynamics), second law of thermodynamics. Constitutive equations for solids: elastic solid, elasto-plastic solid, viscoelastic solid. Fourier’s law. Heat conduction. Wave propagation.

Part I. Ordinary differential equations: First order equations; Equations of order two and higher; Solutions of equations using power series; Systems of linear equations, Part II. Partial differential equations: Fourier series and expansion in eigenfunction series; Diffusion equation; Wave equation; Laplace equation.

Sets; Linear spaces; Linear varieties; Standardized spaces; Spaces; Domestic product; Banach spaces; Hilbert spaces; Bases; Linear transformations, tensors; Tensor analysis – tensor product, components of a tensor, sum and product of tensors, invariants of a tensor, tensor functions, change of base, eigenvectors and eigenvalues; Applications: (1) stress tensor and strain tensor, (2) abstract formulation of equilibrium problems – Galerkin method.