线性代数与微分方程的研究与应用 Developments and Applications in Linear Algebra with Differential Equations
Matrix algebra and inverses, Gaussian elimination and solving systems of linear equations, determinants, vector spaces, linear dependence, bases, dimension, eigenvalue problems. First order differential equations including separable equations and linear equations. Linear nth order differential equations with constant coefficients, undetermined coefficients, first order linear homogenous systems of differential equations.
The concepts of a vector space, linearity and so forth found in linear algebra are what comes of stripping away the unnecessary information involved in solving simultaneous equations, studying systems of differential equations, higher order differential equations, multivariable calculus, as well as the physics of three (or four) dimensional space and advanced econometrics models. Just as a function is a higher level of abstraction than the quantity the function represents, vector spaces are more abstract than the functions, equations, or physical or economic situations which they represent.
Applications of differential equations to physical, engineering, and life sciences. Finite-dimensional vector spaces over R (real numbers) and C (complex numbers) presented from two view points: axiomatically and with coordinate calculations. Forms, linear transformations, matrices, eigenspaces.
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