This chapter describes functions, limits, and continuity in the case of vector-valued functions through examples. f is vector valued and f 1 …, f m are called the coordinate functions or components of f . The range or image of f is the set of m -vectors obtained as X varies over D...
definite integral of a vector-valued function the vector obtained by calculating the definite integral of each of the component functions of a given vector-valued function, then using the results as the components of the resulting function
Our first step in studying the calculus of vector-valued functions is to define what exactly a vector-valued function is. We can then look at graphs of vector-valued functions and see how they define curves in both two and three dimensions....
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备注: 这种雅可比矩阵的定义是一般雅可比矩阵的特例,一般雅可比矩阵是对向量值函数(vector-valued function)定义的。我们将在第5.3节涉及到。 例5.6 偏导数的链式法则 对于f(x, y)=\left(x+2 y^{3}\right)^{2} ,我们使用链式法则求其偏微分:\frac{\partial f(x, y)}{\partial x}=2\left(x+2 y^...
Calculus of fuzzy vector-valued functions on time scales In this part, we will establish some basic results of calculus of fuzzy vector-valued functions on time scales. For convenience, we introduce the following notations. Let f,g:T→[RFn], where f=(f1,f2,…,fn), g=(g1,g2,…,gn)...
calculus of vector-valued functions wikidata 显示算法生成的翻译 将“ vector calculus "自动翻译成 希伯来文 חישוב וקטורי Glosbe Translate 添加示例 在上下文、翻译记忆库中将“vector calculus"翻译成 希伯来文 变形 干 匹配词 所有 精确 任何 We now have on the ord...
Jacobian matrix and determinant are mathematical concepts used to calculate the rate of change of a vector-valued function. The Jacobina matrix is matrix of all first-order partial derivatives of a vector-valued function, and the determinant is the numerical value obtained from the Jacobian matrix...
'Vector Calculus: This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial ...
Vector Calculusis concerned withvector-valued functionssuch asv(t) = − sin(t). By comparison: Single variable calculuscoverslimits,derivativesandintegralsfor one-variable functions like f(x) = x3. Multivariable calculusis the study ofmultivariate functionslike f(x, y) = x3+ e3y. ...