【科研論文】線性代數(shù)與微分方程的研究與應(yīng)用

Category: 培訓(xùn)課程, 科研項目培訓(xùn)
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Date: 2023年2月22日下午2:58

旨在探討線性代數(shù)和微分方程在科學(xué)和工程領(lǐng)域中的基礎(chǔ)和應(yīng)用。項目包含：科研能力提升課程、課題研究、學(xué)術(shù)論文寫作指導(dǎo)等，研究方向：數(shù)學(xué)/理論數(shù)學(xué)/應(yīng)用數(shù)學(xué)/線性代數(shù)/微分方程/微分幾何。

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線性代數(shù)與微分方程的研究與應(yīng)用

Developments and Applications in Linear Algebra with Differential Equations

Research introduction:

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.

Topics covered:

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.