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所在平台: Udemy |
课程主页: https://www.udemy.com/course/scalar-and-vectors/
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## Coursera 课程《标量与矢量（数学）》内容摘要 本课程旨在为初学者提供一个全面、深入的标量与矢量学习体验。课程从基础定义出发，逐步引导学员掌握标量与矢量的基本属性、运算及其在实际问题中的应用。 **核心学习内容包括：** * **基础概念：** 深入理解标量和矢量的定义、性质及基本运算。 * **矢量运算：** 学习矢量的加法、减法、相等矢量、零矢量，以及如何计算矢量的模和单位矢量。 * **位置与方向：** 掌握位置向量的概念，并学习如何确定矢量的方向。 * **矢量判别：** 学会判断矢量是否平行、正交（垂直）或相等。 * **矢量运算法则：** 理解并应用三角形法则、平行四边形法则，以及矢量加法的交换律和结合律。 * **点积与叉积：** 学习点积（数量积）和叉积（向量积）的概念、计算方法及其区别。 * **高维矢量：** 探索二维和三维空间中的矢量，以及如何在不同维度间转换。 * **方向余弦与方向角：** 理解方向余弦和方向角的意义，并能计算两矢量之间的夹角。 * **应用与案例：** 学习点积和叉积在解决问题中的应用，包括判断矢量共面性。 * **标量三重积：** 掌握标量三重积的应用，并能计算平行六面体、四面体等的面积和体积。 课程通过大量的 **实例讲解、解题技巧** 和 **步骤化方法**，帮助学员掌握解决典型考试题型的能力。完成本课程后，学员将对矢量及其运算有清晰、实用的理解，能够自信地将所学知识应用于数学、物理和工程领域的各类问题。
Course Introduction: Scalars & Vectors Made SimpleWelcome to this comprehensive course on Scalars and Vectors, designed for students starting from the basics and progressing to more advanced concepts.In this course, you will:Learn the definitions of scalars and vectorsUnderstand their properties and basic operationsMaster how to find the magnitude and unit vectorExplore operations like vector addition, subtraction, equal and zero vectorsWork with position vectors and learn to find the direction of vectorsLearn how to check if vectors are parallel, orthogonal (perpendicular), or equalUnderstand laws like the Triangle Law, Parallelogram Law, Commutative and Associative Laws of AdditionYou'll also study:Dot and Cross Products and their differencesTheir applications in daily life and physicsVectors in 2D and 3D, including how to transition from two to three dimensionsThe meaning of direction cosines and direction anglesHow to find the angle between two vectorsUse dot and cross products to solve problemsLearn to check whether vectors are coplanarApply scalar triple products and find areas and volumes like those of parallelograms, parallelepipeds, and tetrahedronsThroughout the course, you'll practice with plenty of worked examples, problem-solving techniques, and step-by-step methods for tackling typical exam-style questions.By the end, you'll have a clear, practical understanding of vectors, their operations, and applications - ready to use in maths, physics, and engineering problems.
