This unit starts with an investigation of linearity: linear functions, general principles relating to the solution sets of homogeneous and inhomogeneous linear equations (including differential equations), linear independence and the dimension of a linear space. The study of eigenvalues and eigenvectors, begun in junior level linear algebra, is extended and developed. Terms in this set (25) adulescens, adulescentis m. The unit then moves on to topics from vector calculus, including vector-valued functions (parametrised curves and surfaces vector fields div, grad and curl gradient fields and potential functions), line integrals (arc length work path-independent integrals and conservative fields flux across a curve), iterated integrals (double and triple integrals polar, cylindrical and spherical coordinates areas, volumes and mass Green's Theorem), flux integrals (flow through a surface flux integrals through a surface defined by a function of two variables, though cylinders, spheres and parametrised surfaces), Gauss' Divergence Theorem and Stokes' Theorem. Created by MMHSLatin Teacher Latin vocabulary flashcards based on Scene 2 of Auricula Meretricula. ![]() ![]() Test sets of vectors for linear independence and dependence calculate the span of a given set of vectors in various vector spaces apply the subspace test in several different vector spaces Auricula meretricula translation evaluate certain line integrals, double integrals, surface integrals and triple integrals extended (from first year). ![]() Evaluate certain line integrals, double integrals, surface integrals and triple integrals extended (from first year) their knowledge of vectors in two and three dimensions, and of functions of several variables apply diagonalisation to solve recurrence relations and systems of DEs test whether an n × n matrix is diagonalisable, and if it is find its diagonal form find bases of the fundamental subspaces of a matrix find a polynomial of minimum degree that fits a set of points exactly find bases of vector spaces and subspaces
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