quartic

简明释义

英[ˈkwɔːtɪk]美[ˈkwɔrtɪk]

adj. 四次的

n. 四次方程；四次函数；四次曲线；四次曲面

英英释义

单词用法

同义词

反义词

例句

1.The qualitative theory of ordinary differential equations and numerical simulation method are employed to investigate the kink waves of a nonlinear quartic equation.

用微分方程定性理论结合数值模拟方法研究了一类非线性四阶波动方程的纽结波。

2.A complete quartic polynomial consists of 15 terms.

一个完整四次的多项式由15项组成。

3.This paper is concerned with the problem of quartic lacunary polynomial spline interpolation.

本文讨论四次缺插值多项式样条。

4.And what was the point of a quartic steering wheel?

而且四次式的方向盘又是怎么一回事啊？

5.In chapter two, using piecewise quartic polynomial as kernel function, we give analytical convolution solutions for points, line segments, arcs, quadratic Bezier curves and triangle segments.

在第二章中，我们采用截断多项式函数为核函数，解析的给出点、直线段、圆弧、二次曲线和三角面片等骨架的势函数。

6.The method of qualitative analysis of differential equation and bifurcation is employed to study two classes of quartic systems.

用微分方程定性分析方法和分支方法研究两类四次系统。

7.The applied interpolation method adopts quintic spline and derivatives generation approach for discrete points by using quartic polynomial, which can better meet the needs of high-accuracy machining.

所提出的插补方法采用五次样条和四次曲线多项式微分法近似求取导数，能够更好的满足精确加工的需要。

8.The intersection of two right circular cylinders is usually quartic curve.

正交两圆柱的相贯线，一般是四次曲线。

9.The distance from 3-direction quartic box spline surface to the central triangular planar patch of its control net is investigated as well as its bound.

研究了三向四次箱样条曲面与控制网格中心三角平面片间的距离和该距离的界。

10.Graphing a quartic function can reveal its complex behavior.

绘制一个四次函数的图形可以揭示其复杂的行为。

11.The quartic formula is more complicated than the quadratic formula.

四次公式比二次公式更复杂。

12.The solution to the equation involves finding the roots of a quartic equation.

这个方程的解涉及到寻找一个四次方程的根。

13.Understanding quartic equations is essential for advanced mathematics.

理解四次方程对于高级数学至关重要。

14.In algebra, a quartic polynomial can have up to four real roots.

在代数中，一个四次多项式最多可以有四个实根。

作文

In the realm of mathematics, the study of polynomials is fundamental, and among these, the quartic polynomial holds a special place. A quartic polynomial is defined as a polynomial of degree four, which means that the highest exponent of the variable in the expression is four. The general form of a quartic polynomial can be expressed as ax^4 + bx^3 + cx^2 + dx + e, where a, b, c, d, and e are constants, and a is not equal to zero. Understanding quartic equations is crucial for many advanced mathematical concepts and applications.One of the most interesting aspects of quartic polynomials is their ability to model various real-world phenomena. For instance, in physics, quartic equations can describe the motion of objects under certain conditions, such as the trajectory of a projectile influenced by air resistance. In economics, quartic functions can be used to analyze cost and revenue curves, helping businesses to determine optimal pricing strategies. Thus, mastering quartic equations is not only an academic exercise but also a practical skill that can be applied in various fields.Solving quartic equations can be more complex than solving linear or quadratic equations due to the increased degree. There are several methods to find the roots of a quartic polynomial, including factoring, using the Rational Root Theorem, and applying synthetic division. Additionally, there are formulas specifically designed for quartic equations, similar to the quadratic formula, although they are significantly more complicated. The Ferrari's method is one such technique that allows mathematicians to solve quartic equations by first reducing them to a simpler form.Graphically, quartic polynomials can exhibit a variety of shapes. Depending on the coefficients and the nature of the roots, a quartic function can have up to four real roots, and its graph can display different behaviors, such as turning points and inflection points. This variability makes quartic functions particularly interesting to study in calculus, where the concepts of derivatives and integrals come into play. Understanding the graphical representation of quartic polynomials can provide insight into their behavior and properties, which is essential for both theoretical and applied mathematics.In conclusion, the quartic polynomial is a vital component of higher mathematics, bridging the gap between simple algebraic expressions and more complex functions. Its applications span across various disciplines, making it a valuable topic for students and professionals alike. By delving into the intricacies of quartic equations, one can gain a deeper appreciation for the elegance and utility of mathematics. Whether in the classroom or in real-world applications, understanding quartic polynomials will undoubtedly enhance one's mathematical prowess and problem-solving skills.

在数学领域，多项式的研究是基础，其中quartic多项式占据了特殊的位置。quartic多项式被定义为四次多项式，这意味着表达式中变量的最高指数为四。quartic多项式的一般形式可以表示为ax^4 + bx^3 + cx^2 + dx + e，其中a、b、c、d和e是常数，且a不等于零。理解quartic方程对许多高级数学概念和应用至关重要。quartic多项式最有趣的方面之一是它们能够建模各种现实世界现象。例如，在物理学中，quartic方程可以描述在某些条件下物体的运动，比如受到空气阻力影响的抛射物的轨迹。在经济学中，quartic函数可以用于分析成本和收益曲线，帮助企业确定最佳定价策略。因此，掌握quartic方程不仅是学术练习，也是可以在各个领域应用的实用技能。解决quartic方程可能比解决线性或二次方程更复杂，因为其次数增加。有几种方法可以找到quartic多项式的根，包括因式分解、使用有理根定理和应用合成除法。此外，还有专门为quartic方程设计的公式，类似于二次公式，尽管它们要复杂得多。费拉里方法就是一种允许数学家通过首先将其简化为更简单形式来解决quartic方程的技术。在图形上，quartic多项式可以表现出各种形状。根据系数和根的性质，quartic函数最多可以有四个实根，其图形可以显示不同的行为，如转折点和拐点。这种可变性使得quartic函数在微积分中尤其有趣，在这里导数和积分的概念发挥作用。理解quartic多项式的图形表示可以提供对其行为和性质的深入了解，这对于理论和应用数学都是必不可少的。总之，quartic多项式是高等数学的重要组成部分，架起了简单代数表达式与更复杂函数之间的桥梁。它的应用跨越多个学科，使其成为学生和专业人士都值得学习的主题。通过深入探讨quartic方程的复杂性，人们可以更深刻地欣赏数学的优雅和实用性。无论是在课堂上还是在实际应用中，理解quartic多项式无疑会增强一个人的数学能力和解决问题的技能。